Diagram 1 may still be a very tricky problem even after
you've read this book, but if you're clever you may be
able to solve it right now!
I'll give the solution in Chapter 2, but as a hint,
here's the solution with details erased:
Although it's been almost twentyfive years, I still remember
saying "Aha!" to myself when I guessed Red's
winning move in Diagram 1.
That was the moment I started to become a good player.
I wanted to prove that my move in Diagram 1
was the only winning move, so I wrote
a computer program to verify the solution.
One thing led to another and the computer solved another billion
positions as well: enough to prove that First Player can always win.
In 1988, Connect Four was the most difficult game
which had ever been solved by computer up until that time.
It would have taken a million dollars worth of computer time
to solve the game in 1970, but by 1988 speeds had improved so
that 1000 hours were enough on an ordinary workstation.
(Computers are even faster now, of course, and
your home PC, properly programmed, could solve the game
in a matter of minutes.)
I want to thank Alan Pruce for much helpful criticism
and input, especially the Pruce Defense.
Frank Stalone was also very helpful, and introduced me
to the ThirdRow Gambit.
(Neither Alan nor Frank claims invention of these opening styles.)
John Tromp, a master programmer who has made important
discoveries in Go and other games, also reviewed the early
draft but deserves special acknowledgment for a different reason:
While the Connect Four software I wrote 22 years ago to solve the game may have
historic or sentimental interest, for several years I've preferred
to use John Tromp's excellent Fhourstones implementation.
(Most of the analyses in this book have been verified by computer,
but if there are any errors, they were probably introduced
during my editing and shouldn't be blamed on Fhourstones.)
Finally, I should thank the anonymous bartender in Banglamung
who used Diagram 1 25 years ago to make me aware that
Connect Four is not an easy game!
We will present the Rules of Connect Four
by watching a game unfold.
This will also give us a chance to agree on some basic terminology.
The game of Connect Four is played by two players
on a vertical board of six rows and seven columns.
One player has twentyone disks of one color, say Red.
The other player has twentyone disks of another color, say Black.
It doesn't matter what the two colors are, as long as they can be
easily distinguished.
In Connect Four, the name of the game is the same as the object of the game.
You want to align (or "connect")
four disks of your own color in a straight row.
(Call that fourinrow.)
The four disks must be adjacent but may line up horizontally, vertically
or diagonally.
As soon as you've achieved this, the game is over  you've won!
Unlike Chess (where White always goes first),
in Connect Four each player retains the same
color throughout a session but usually he and his opponent
alternate going first.
However, it simplifies things in this book to have
the Red player play first in every game; Black
will always play second.
We label the columns A through G as shown in Diagram 2.
Red can start in any column, but it's by far best for Red that he
start in the central column (D) and you will rarely
see any deviation from this.
Gravity makes his disk drop down to the 1st (bottommost) row;
the cell it lands on is called D1.
Hence we say this game starts 1 D1.
Instead of "D1" we could have written just
"D"  once a player chooses which column to drop
his disk into, there's only one row it can end up on.
Diagram 2
Black to play (will lose)
At the top of every diagram we indicate what the outcome
of the game will be, assuming perfect future play.
Since Black has no chance against a perfect Red player,
we indicate that Black "will lose."
(Don't despair if you're Black and Red starts with the winning move D1!
Very few humans play perfectly.)
In chess notation, particularly good moves are shown with
an exclamation mark ("!").
We adopt that idea, but change the meaning somewhat.
When a move is the only move that leads to victory
(assuming perfect play), we mark that move, in a Diagram's move list,
with an exclamation mark.
We've done that here, because D1 is Red's only winning first move.
(We also use the exclamation mark when a move draws and all other
moves lose.)
The game continues with players alternating turns.
At the bottom of Diagram 3, we show a record of all the
plays leading up to the diagrammed position.
Since it was already shown in a previous
diagram, we may reduce clutter by omitting the "1" label on Red's 1st disk.
(Actually, all the labels could be omitted in this case:
since a disk will always settle above previous
disks in the played column, it's clear in Diagram 3
in what order the disks must have been played.)
Diagram 3
Red to play, with only one move to win
Moves:  (1) D1! (2) d2 D3! d4 (5) __

We will always show Red's moves in uppercase,
and Black's moves in lowercase.
This will add clarity when we discuss moves or move sequences.
Black's 4 d4 is probably his best move but we do not
show it with an exclamation mark: that mark is reserved for
a move that gives a better result than any other move
against perfect computer play, but here a "perfect"
Red player will win whether Black plays well or poorly.
As shown, we give each disk a different number.
This means we won't speak of Red's 1st, 2nd, 3rd moves, etc.
but rather his 1disk, 3disk, 5disk, etc.
Black plays the evennumbered disks.
It works out nicely that Red plays the oddnumbered disks because,
in Chapter 5 when we give strategic principles, we will advise
you to memorize the mantra Red likes odd numbers.
We will write a question mark ("?") after a move
if the move leads to a draw (against a perfectplaying opponent)
where another move would win.
We also use the question mark after a move which loses when
another move would draw.
A move which loses when a win was available is, in a sense,
twice as bad as the types of blunder just mentioned
(it has the effect of converting a win to a draw but also then
converting the draw to a loss); we show such moves
with a double question mark ("??").
In Diagram 4 Red's move at 5 C1 loses (with perfect play)
even though a winning move was available so
we mark it in the move list with a double question mark ("??")
as just explained.
Diagram 4
Black to play, with only one move to win
Moves:  (1) D1! d2 D3! d4 (5) C1?? e1 A1 (8) __

As the game continues in Diagram 4, Red
threatens to achieve fourinrow and win the game.
By analogy with chess, Red might say check
as a courtesy when he plays 7 A1
(warning the Black player, since it isn't much fun to win
through the opponent's simple oversight).
Most players don't say check,
but we will use the term check to describe
an immediate fourinrow threat, like B1 in Diagram 4.
We've marked the threatened check with
a Red "C" (C for check).
(By the same analogy with chess, completion of a gamewinning
fourinrow can be called mate.)
The game continues as shown in Diagram 5.
Black plays 8 b1 of course; despite being obvious,
by our convention the move is shown with an exclamation mark.
Black 10 c3 is also shown with an exclamation mark:
That it is a mandatory play for Black will be clear
to you after reading this book.
b4 is a threat cell for Black, but won't become a check
(immediate threat) until cells B2 and B3 have been occupied.
An important threat that is not check (usually because the cell under
it is empty) is called a Strategic Threat.
Black's threat at b4 is shown with an uppercase "T" and
called a Major Threat because he's already got three of
the four disks needed for fourinrow.
Black of course hopes Red is eventually forced to play at B3:
if Black is the one who plays at b3, Red will simply answer at B4.
Diagram 5
Black to play and win
Moves:  (1) D1! d2 D3! d4 C1?? e1 A1 (8) b1! C2 c3! G1 g2 A2 (14) __

Red hasn't achieved a major threat of his own yet, but we use
lowercase Red "t"'s to show a
Minor Threat Pair for him at A4B3 and another one at E4F5.
A minor threat is one of two cells needed to convert
two aligned disks to fourinrow.
We also show a minor threat pair for Black at e2f2 since
capturing both those cells would give Black a win.
While a cell that is available for immediate play is
never called a "major threat" (it would be called a "check"),
it may be termed a "minor threat" as e2 is here.
A threat will be called an OddRow Threat
or an EvenRow Threat if it is on, respectively,
an oddrow (3rd or 5th row) or evenrow (2nd, 4th or 6th row);
this attribute is called the threat's RowParity.
Remember that it is the empty cell threatening
to complete a fourinrow that is critical and defines
the threat's rowparity.
The two threat cells of a minor threat pair may be both evenrow or
both oddrow, or they may comprise one oddrow and one evenrow
threat; the latter case is called a Mixed Threat Pair.
A game position might have many cells that meet the
definition of major or minor threat, but
in the diagrams we will label the threats with "T" or "t"
only when they are decisive or relevant to the discussion;
even relevant threats may be left unlabeled to
avoid cluttering the diagrams.
This first example game, however, is just to introduce terminology,
and threats are labeled just for that purpose.
After more moves, the position in Diagram 6 is reached.
Red establishes his own major threat at B3.
This undercuts (renders worthless) Black's major threat at b4.
(A Black threat like b4 may not be completely worthless.
Eventually Red will be forced to spend a turn blocking
it with a disk at B4  a turn Red might have preferred to spend elsewhere.)
Diagram 6
Black to play and win
Moves:  (1) D1! d2 D3! d4 C1?? e1 A1 b1! C2 c3! G1 g2 
 (13) A2 (14) e2 C4 d5 E3 e4 C5 a3 A4 (22) __

On the rightside of the board, Black has established major threats
at f2 and f3.
This combination is called an Adjacent Threat Pair
and it means that Black can win the game very quickly,
just by playing in the Fcolumn.
(In this book the word adjacent will always refer to
neighboring rows, not neighboring columns.)
Black will lose if he ever plays a disk at b2, so we've
marked that cell with a black "no."
Similarly Red won't play F1 so it's marked with a red "no."
The game continues in Diagram 7.
Black could have won by playing 24 f3,
but he chose a different way to win just
so we could complete our review of basic terminology.
In the final position, Black has double check
at f4 and g5.
Red will play at one of these cells;
Black will play the other and win.
Diagram 7
Red to play (will lose)
Moves:  (1) D1! d2 D3! d4 C1?? e1 A1 b1! C2 c3! G1 g2 A2 e2 
 (15) C4 d5 E3 e4 C5 a3 A4 (22) f1 F2 g3 F3 g4 (27) __

I've been careful to mark all the moves in all the diagrams in this
book with exclamation and question marks as just explained.
This makes it possible to count question marks
in the move list and determine the perfectplay result
of any position reached during the moves in that game.
For example, any move list with an odd total number
of question marks will lead to a drawn position
(assuming perfect further play).
In Diagram 4 the move list tells us that
the game should properly be won for Red at any point before
his 5 C1 blunder, and is properly won by Black at any point thereafter.
It also means that you can use any move sequence in the book
as a basis for studying good play, as long as you verify
that the moves aren't listed with question marks).
(I use the same meanings even in the solutions to
quick victories: exclamation marks are not awarded for moves
that are the only way to quick victory if there are other winning moves.)
The above game ended in doublecheck, but we will soon look at a real
expertlyplayed game that ends in triple check!
Terminology
During this first example game, we introduced some special
terminology like oddrow threat and major threat.
We will define these more carefully later, but we need such words
in order to explain Connect Four strategic principles.
A useful term we will never use in this book is
double threat.
We avoid it because different people might intend double threat
in any of several different ways:
 double check,
 adjacent threat pair,
 other cases with two samecolored threats in same column,
 threats by both Red and Black at same cell,
 two major threats,
 minor threat pair.
Terms like triple threat, quadruple threat
and sextuple threat seem less likely to cause confusion
than double threat, and we will use these
terms, giving them very specific meanings.
Drawn Games
It will sometimes happen that the game will play
out until the board is completely full, with
no one establishing fourinrow.
This is a draw.
There's surprising variation in Connect Four
depending on player's style.
Some players may find 20% of their games ending in draw.
Others will find drawn games to be rare.
How to Become a Master Player
This book will show you some of the tactical and strategic
ideas you will need to become a master at Connect Four,
but there is no "secret formula" for success.
Connect Four is an easier game than chess or even checkers,
but you'll still need to think for yourself and plan ahead.
Look back at Diagram 1; did you guess the right move?
Let's deduce it step by step.
 Red does have threats in the upper leftside of the
board, but they are not quite enough to win,
so Red must be prepared to force victory on the right
side depending on how Black defends.
 To have any chance of building a threat on the right side,
Red must somehow get past the Black major threat at F2.
 If you've just started this book, you may not yet realize
that a major threat at F2 (or at any point on the 2nd, 4th or 6th
row) is not going to disappear by itself!
Black will never play f1 unless there is very strong compulsion.
 You can compel Black to play f1.
All you have to do is play at C4.
It may not be obvious that Red will get C4, but he does
get help from his own threat at C5.
Anyway, Red can reason "Getting C4 is my only chance,
so I may as well assume I will get it."
 Now, when Black puts himself in Red's shoes he'll realize
C4 is Red's paramount goal.
Can he prevent that?
 Yes; if Black plays b6, Red C4 loses immediately.
Black wants to play b6, but it's Red's turn.
 The opponent's best move is our best move.
Red must play B6 so Black doesn't get it.
Later Red will play C4, followed by F2.
It may not be clear yet exactly how Red will win in the upper rightside,
but if he doesn't play B6 right now, Black will play there
and Red will have no chance whatsoever on the rightside.
This book contains many example games with many expert
moves; too many expert moves to explain each in as much detail as
we just did for Red's disk 17 in Diagram 1.
If you don't understand the moves in a game, set them up on your
own board and try to figure them out.
(Or, for more more rapid experimentation, use one of the
fine Connect Four software packages, e.g. John Tromp's Fhourstones.)
Most of the example games will be played expertly,
perhaps with one or two mistakes to help make a point.
(The game just reviewed in Diagrams 2  7
had many simple mistakes just to introduce terminology easily.).
Before continuing, I'll try to whet your appetite
with another expert game, shown in Diagram 8.
By the exclamation marks, we can infer that Black found
a sequence of moves that caused each of Red's
first thirteen disks to be forced.
This unique mostforced game then
ends in Red victory via a rare triple check!
Diagram 8
Black to play (will lose)
Moves:  (1) D1! d2 D3! d4 D5! d6 C1! b1 F1! e1 E2! e3 E4! b2 
 (15) C2! e5 C3! c4 C5! g1 F2! b3 B4! b5 F3! (26) __

After studying this book, come back and look at this
opening again.
Set it up on your own board and try variations;
see if you can figure out why the players made
some of the moves they did.
(Black's 24 b5 allowing the triple check may seem peculiar,
but experienced Black would simply resign rather than allow
Red B5.)
It may seem amazing but, as shown by the exclamation marks
in the move list, all thirteen moves played here by Red
were each absolutely essential to his guaranteed victory.
(E1 could be substituted for C1, but we treat C1 as a
uniquely winning move anyway, since E1 leads to the position's
mirror image and thus obviously yields the same result.)
After you've studied this book from cover to cover, you should
find that most of the moves in this game are evidently best.
We will develop the key concepts of Connect Four
play with example games.
When a problem is posed, be sure and try to guess the winning move
before reading ahead.
The book will emphasize strategic principles
but first we need to look at tactical sequences.
Before leaving the Introduction, we must mention that the
triple check in Diagram 8 hardly holds the record for
most simultaneous checks.
That record is indubitably held by
John Tromp's Septuple Check, shown in Diagram 9.
Diagram 9
John Tromp's Septuple Check
Moves:  (1) C1? d1 D2 d3! E1? d4 C2 c3 E2 e3 
 (11) B1 b2! F1 f2 C4 d5 E4 (18) __

While strategy refers to the evaluation and
selection of longterm threats, tactics refers to the
"parryandthrust" that occurs move by move.
Obviously strategy and tactics work together:
it is through your tactical skill that you will be able
to establish winning strategic threats.
Value of Opponent's Reply
An important tactic is to make your disk more valuable than
the opponent's reply.
In Diagram 10, any of the central cells C5, D4 or E3
might seem like a useful location for Red's disk13, but
C5 is the winning move.
Black can answer 13 D4 or E3 by taking a valuable central cell
(d5 or e4), but Red needn't worry about Black taking the remote cell c6.
(But judge all cases on their own merits:
with a slight change,
D4 or E3 might be the winning move.)
Diagram 10
Red to play, with only one move to win
Moves:  (1) D1! d2 D3! c1 C2 c3 C4 g1 G2! g3 E1! e2 (13) __

Even better than a move which gives up no strong cell for the
opponent, is one which forces the opponent to waste a move.
This idea is seen in several of the Problems, for example Problem 155
where Black, already occupying f3 and f4, is delighted to play 12 f5
since Red then has to waste a tempo with the otherwisealmost
useless blocking move at F6.
Tactical Sequences for Quick Win
A long sequence of forcing moves is called a tactical sequence,
or forcing combination.
Where should Red play in Diagram 11 to win quickly?
Diagram 11
Red to play, and mate in 4
Moves:  (1) C1? d1 D2 d3! D4! b1? C2? f1? (9) __

Red plays a sequence of forcing moves and wins quickly,
as shown in Diagram 12.
Since Red completes his fourinrow by playing just three
Red disks after Diagram 11, we can say that from
that Diagram, Red has a guaranteed fourinrow in three moves,
or, as we will say for brevity, Mate in Three.
Diagram 12
Red has won
Moves:  (1) C1? d1 D2 d3! D4! b1? C2? f1? (9) C3 c4 B2! a1 A2 (14) __

It turns out that Red (the player who moves first)
can win every game if he or she plays perfectly,
but that doesn't mean Black (player who moves second)
has no chance.
There are many many difficult variations, and even the
very best human player in the world isn't fully
confident of victory when he moves first.
When two experts play each other Red almost always wins,
but nonexpert play varies.
(In casual play against opponents of medium skill,
the author usually wins almost effortlessly moving second,
but has to concentrate when playing as first player.)
Unlike Diagram 11 (a nonstandard opening with
several bad moves), Diagram 13 comes from an expert
opening, with Red 13 D5 being a notsoobvious blunder.
It is Black who can now win with a tactical sequence,
specifically fourinrow in five.
Remember to find it yourself before reading ahead!
Diagram 13
Black to play and win
Moves:  (1) D1! c1 F1 b1 G1 e1 F2 d2 F3 f4 D3! d4 D5?? (14) __

Solution is shown in Diagram 14.
Take full credit if you started with 14 b2
instead of e2  that play also leads to Mate in Five.
(The other five possibilities for Black's play 14 each lead
to Red victory.)
Diagram 14
Black has won
Moves:  (1) D1! c1 F1 b1 G1 e1 F2 d2 F3 f4 D3! d4 
 (13) D5?? (14) e2 E3 b2! C2 c3! A1 c4 E4 e5! (23) __

Diagram 15 (related to the opening in Diagram 157)
shows a winning combination.
(The exclamation marks here indicate that not only were the
Red moves the only plays to achieve Mate in Four,
they were the only plays to win at all.)
Diagram 15
Black to play (will lose)
Moves:  (1) D1! e1 A1 c1 E2? e3! C2 c3 C4 f1? 
 (11) (11) D2! f2 B1! b2 D3! (16) __

In Diagram 16,
the maneuver by which Black has "pushed" in one column with b1b2b3,
forcing a B4 reply, and then seized b5, is called the pushup play.
Diagram 16
Black has won
Moves:  (1) D1! b1 D2? d3! C1? c2 C3 c4 D4 a1? 
 (11) A2? c5 F1 e1! F2 d5?? G1 g2 D6 a3 
 (21) A4? b2? C6? a5! G3? (26) b3! B4 b5! (29) __

In the examples above, the forcing moves were clearcut forces,
threatening a quick win.
More often, a forcing move will force the opponent to prevent
a strategic longterm threat.
There are many examples of this in this book,
for example in Diagram 95.
Preventing a Tactical Ploy
If your opponent has a winning tactical ploy, it may be
that you should have seen it coming and prevented it.
Often the ordinary stronglooking move will serve this
purpose, but sometimes you will have to make an unusual
move to stop a ploy.
Diagram 17 shows an interesting example.
Where should Red play to win in Diagram 17 ?
(These opening moves may look quite peculiar,
but this is actually an expertly played opening.)
Diagram 17
Red to play, with only one move to win
Moves:  (1) D1! e1 B1 a1 B2! b3 B4 a2 (9) __

Red's plan will be to play D2 when appropriate and build
minor oddrow threats at A5 and C3, but he must watch out lest
Black foil this with a pushup play.
An expert Black will play 10 a3 A4 a5 in response to 9 B5,
or play as shown in Diagram 18 in response to 9 E2.
Thus Red's winning play is 9 A3 to prevent this pushup play.
With the center still largely unplayed, A3 will
strike most players as an unlikely "best move".
(Some Red players might try 9 D2 d3 first and then play 11 A3,
but this allows Black 10 d3, 12 e2, followed by 14 d4 or e4.)
Diagram 18
Black to play and draw
Moves:  (1) D1! e1 B1 a1 B2! b3 B4 a2 (9) E2? a3! A4! e3! D2 a5! 
 (15) B5! d3! G1 g2! G3 g4! E4! e5 E6! b6 A6! (26) __

In Diagram 18 after Red's mistaken 9 E2,
most of the moves are shown with exclamation marks:
Black must play very precisely to get his draw,
and Red must defend very precisely to ensure Black
gets no better than a draw.
If Red plays instead correctly with 9 A3, the game is
likely to continue as shown in Diagram 19.
One way to understand why A3 is a better play than E2
is to look at the cells above where opponent now
has opportunity to play.
A4 is almost worthless, while E3 is a prime central cell.
Diagram 19
Black to play (will lose)
Moves:  (1) D1! e1 B1 a1 B2! b3 B4 a2 (9) A3! e2 
 (11) E3! e4 A4 a5 E5! b5 D2! d3 D4! (20) __

Races
If your tactical plan depends on playing up one column,
while the opponent has a tactical play in a different column,
the phrase The Race is to the Swift may apply.
Diagram 207 below discusses a very interesting
(and difficult) example of such a race;
the position is repeated here as Diagram 20.
Give yourself a big pat on the back if
you can guess Red's next move!
Diagram 20
Red to play, with only one move to win
Moves:  (1) D1! d2 D3! d4 D5! e1 E2 e3 E4! b1 B2 e5 
 (13) B3 b4 G1! g2 B5 c1 G3 g4 (21) __

More Examples of Quick Victory
It's always more fun to win quickly than slowly,
and sometimes a tactical sequence will lead directly
to fourinrow after just a few moves.
Often the player first forces an adjacent threat pair,
and then converts this to quick victory.
This applies in Diagram 21.
Do you see Red's quick win?
Diagram 21
Red to play, with only one move to win
Moves:  (1) D1! c1 G1 f1 F2! (6) d2 D3! d4 F3! d5 F4! f5 
 (13) D6! b1 B2! b3 E1! b4 B5! b6 G2 g3 (23) __

Solution: In Diagram 22, Red gets an adjacent threat pair
and wins quickly.
Not only is 23 E2 the move that wins quickly, it's the only
move that wins at all!
If instead Red plays as in Diagram 23, Black
builds his own major oddrow threat and gets a draw.
Diagram 22
Black to play (will lose)
Moves:  (1) D1! c1 G1 f1 F2! d2 D3! d4 F3! d5 F4! f5 D6! b1 
 (15) B2! b3 E1! b4 B5! b6 G2 g3 (23) E2! g4 E3! (26) __

Diagram 23
Red to play and draw
Moves:  (1) D1! c1 G1 f1 F2! d2 D3! d4 F3! d5 F4! f5 D6! b1 
 (15) B2! b3 E1! b4 B5! b6 G2 g3 (23) G4? e2! E3! g5! (27) __

Often the purpose of a tactical sequence won't be to
get a fourinrow quickly but just to establish
a winning strategic threat.
Diagram 24 shows an example of this;
where should Red play next?
Diagram 24
Red to play, with only one move to win
Moves:  (1) D1! d2 C1?? e1 D3 c2?? C3 e2 (9) __

Diagram 24 is of historic interest.
It appears in the thesis of Victor Allis where he presents
a solution to the game of Connect Four.
Diagram 25 shows how a precise tactical sequence
yields a winning strategic threat for Red.
Diagram 25
Black to play (will lose)
Moves:  (1) D1! d2 C1?? e1 D3 c2?? C3 e2 (9) A1! b1 
 (11) B2! d4 B3! e3 E4! (16) __

In Diagram 26, Red can achieve a winning
adjacent threat pair in three moves.
As shown in Diagram 27, he may need four additional
moves to complete a fourinrow.
Diagram 26
Red to play, and mate in 7
Moves:  (1) D1! c1 C2? c3! C4 c5? F1? a1? A2? c6? A3 d2 (13) __

Diagram 27
Black to play (will lose)
Moves:  (1) D1! c1 C2? c3! C4 c5? F1? a1? A2? c6? A3 d2 
 (13) (13) A4 a5 D3 g1 D4 g2 B1 g3 G4! d5 B2 (24) __

Here's a final example of Quick Victory.
(There are more in the Problem Sets.)
In Diagram 28 Red will win no matter where he plays,
but only one move assures him of fourinrow in three.
Diagram 29 shows the solution.
Diagram 28
Red to play, and mate in 3
Moves:  (1) D1! d2 D3! c1 C2 c3 D4 d5 G1! e1 G2! g3 E2! d6 (15) __

Diagram 29
Black to play (will lose)
Moves:  (1) D1! d2 D3! c1 C2 c3 D4 d5 G1! e1 
 (11) G2! g3 E2! d6 (15) E3 e4 F1 (18) __

Most games between good players are won in the ending,
rather than with a quickly forced fourinrow early in the game.
When a player does make a key sequence of forcing moves early
in the game, often he will do so to establish a longterm
strategic threat, rather than an immediate fourinrow.
Therefore a player must understand what strategic threats
will lead to a successful endgame, and which threats are worthless.
Let us begin our study of strategic principles.
Not only will these principles tell you what threats of your own to seek,
but they will tell which of your opponent's potential threats to block.
We first consider the simplest cases, and
then gradually study the effects of complications.
Black Wins on 2nd (or 4th or 6th) Row
If Red lets Black occupy two center cells in the second row
(along with a third cell underneath one of them), the game
may be essentially over already, although Black won't complete fourinrow
until the ending.
Diagram 30 shows an example of this.
Diagram 30
Black to play and win
Moves:  (1) D1! d2 D3! e1 D4 a1 A2?? e2! D5 d6! E3 (12) __

In Diagram 30, the game seems to have just begun,
and it is Red who may appear to be building strength
in the upper center of the board.
Yet Black is just as certain of victory here as he was with
the "fireworks" in games like Diagram 13.
Black has the entire 2nd row locked up with his minor threats,
and will win easily as long he avoids playing in the 1st row.
Red will eventually be forced to play in each remaining 1strow cell,
and Black will get to play disks in all the 2ndrow cells.
If Black plays b1, c1, f1, or g1 he loses, but otherwise it
hardly matters where he plays; simplest
is for Black to take e4 now and then just "play
wherever the opponent plays".
This will lead eventually to the position in Diagram 31.
Diagram 31
Red to play (will lose)
Moves:  (1) D1! d2 D3! e1 D4 a1 A2?? e2! D5 d6! E3 
 (12) (12) e4 E5 e6 A3 a4! A5 a6! G1 g2! G3 g4! G5 g6! 
 (25) C1 c2! C3 c4! C5 c6! (31) __

In Diagram 31 B2 and F2 have become major threats
for Red as well as Black  in fact Red has adjacent threat pairs
at B2C3 and F2F3  but it's his turn to play.
Whatever Red does now, Black will win at his next turn.
Black wins easily in Diagram 30
because of his two disks in the second row;
Red must watch out and not let Black achieve this.
Notice that Red threats above the second row
will be useless  the game will end before they're reached.
Instead of the second row, Black can win with
disks in another evennumbered row (4th or 6th row), though then he would
have to worry about Red threats below
the Black threats.
It's essential to have a Black disk under the two disks
on the evennumbered row.
In Diagram 30 e1 is essential as well as d2e2;
Otherwise Red's 1strow threats would undercut Black's 2nd row.
Similarly a 4throw winning combination for Black might involve d4e4e3
and a 6throw winning combination might involve d6e6d5.
In Diagram 30, Black has only two disks aligned instead of three,
so hasn't yet achieved a major threat.
In fact, even the second Black disk often isn't even essential!
Consider Diagram 32.
In the Diagram, two major 2ndrow threats are shown for
Red, while the entire 6th row is shown as minor threats for Black
even though, so far, he has only one disk out of the four
he'll need to complete a fourinrow.
Diagram 32
Black to play and win
Moves:  (1) D1! e1 E2? e3! D2 d3! D4! d5 E4? d6! A1 c1! C2 (14) __

Black has an inevitable and easy win on the 6th row
in Diagram 32.
In fact, he doesn't just get fourinrow, he can get seveninrow!
Play this game out a few times and you'll see what I mean.
The easiest way to prove that Black wins in Diagram 32
is, as in Diagram 31 above, for Black to start by playing
14 a2. This leaves every column with an even number of empty cells;
and Black can then adopt the simple rule "Black plays where Red just played."
Red ends up with every remaining cell on the 1st, 3rd and 5th rows
(and gets no fourinrow); Black ends up with every remaining cell
on the 2nd, 4th and 6th rows and completes not just fourinrow,
but seveninarow on the 6th row.
There are many Connect Four players
who haven't learned the strategic rules
and will play exactly as Red did in Diagram 32.
They may look at their major threats at B2 and F2
and even think they're winning!
But it is Black (Second Player) who wants and needs
threats on the 2nd row (or 4th or 6th row), not Red.
Just knowing this one "trick" may improve your Connect Four
reputation quite a bit.
In fact, the ease with which Black won in these games may deceive
you into thinking Connect Four is an easy game!
But if this is your only "trick" you won't stand a chance against
a good player.
Read on, and become a master!
As implied by an exclamation mark, Black's 12 c1 in Diagram 32
was essential.
If instead he starts "playing where Red just played"
prematurely, he'll lose quickly as shown in Diagram 33.
Diagram 33
Black to play (will lose)
Moves:  (1) D1! e1 E2? e3! D2 d3! D4! d5 E4? d6! 
 (11) A1 (12) a2?? B1 c1 B2! (16) __

First and SecondPlayer Strategies are Not the Same
The strategies for Red
and Black are quite different in Connect Four.
Black (Second Player) will usually be quite happy
if Red (First Player) makes the mistake of
trying for two disks of his own on an evennumbered row.
Red should try to build threats on the 3rd or 5th row.
(In the middle of a game, to know whether to strive
for odd or evenrow threats, you will often need to remind
yourself whether you were First Player or Second.
Of course it is usually very simple to figure out which player went
first: First Player "always" plays his first disk at D1.)
Zugzwang: It is Not always an advantage to move
We must introduce the concept of Zugzwang, which is essential
to the strategic analysis of endgames in Connect Four.
This German word means "compulsion to move."
Diagram 34
Whoever plays next will lose
Moves:  (1) D1! d2 D3! e1 D4 e2 G1?? a1?? D5! d6 E3?? g2! 
 (13) G3 g4 G5 g6 A2 a3 A4 a5 A6 e4! E5 e6! 
 (25) B1 b2! B3 b4! B5 b6! (31) __

In Diagram 34 you will see that C2 is a major threat
for both Red and Black;
likewise F2 is a major threat for each player.
Whoever moves next will lose: the opponent will get fourinarow
immediately afterwords.
There are the same number of disks (15) of each color, so it may not
be obvious whose move it is.
(We've agreed that Red always moves first in this book, but in
real games players usually keep the same color and move first in
alternate games.)
Zugzwang is a chess term referring to a position
where any move loses  your only chance would be to pass
your move, but that's not allowed.
Diagram 35 gives another, less obvious, example of Zugzwang:
Diagram 35
Whoever plays next will lose
Moves:  (1) B1?? d1? B2 f1? E1 e2 A1?? e3?? D2 d3 
 (11) D4 d5 F2?? b3?? F3 a2 E4 (18) __

Again, if it is Red's move then Black wins;
if it is Black's move then Red wins!
(Never mind that Red has played 9 disks to Black's 8,
so we would know whose move it really is.)
That the position in Diagram 35 is Zugzwang is far from obvious:
there's still a lot of play left in the game, and care will be
needed.
Diagram 36 shows this game after another 14 disks
have been (well) played; again, whoever plays next loses.
Suppose it's Black's turn and he temporizes by putting his disk at e6.
Where must Red then play to win?
Diagram 36
Whoever plays next will lose
Moves:  (1) B1?? d1? B2 f1? E1 e2 A1?? e3?? D2 d3 D4 d5 
 (13) F2?? b3?? F3 a2 E4 (18) e5 D6 f4 F5! b4 B5 b6 
 (25) G1 g2 G3 g4 G5 g6 F6 (32) __

I hope you saw that Red must make the temporizing move at C1:
if instead A3, then Black plays a4 and wins with his
adjacent threat pair at C2C3.
If it were Black's turn to play in Diagram 36, Red will be the one
forced to play A3; Black will play a4 and win with the adjacent threat pair.
If you've played much Connect Four you already realize that
Zugzwang is a very common occurrence
(although you may never have heard this unusual German word).
EvenRow Threats are not influential
In Diagram 37 Red wins with his major oddrow threat
even though Black has two columns with major evenrow threats.
Diagram 37
Black to play (will lose)
Moves:  (1) D1! e1 D2? d3! C1? c2? C3? c4? E2? d4 
 (11) G1 g2 D5 b1 G3 a1 C5 a2?? G4! d6 
 (21) A3 a4 B2 a5 A6 g5 C6 g6 F1! (30) __

Black can play f2 and lose at once, or play b3 (or e3) and
sacrifice one of his evenrow threats.
Sacrificing an evenrow threat will do Black no good: after b3 B4 b5 B6
it will be Black's turn to play again and he'll be in the same dilemma.
In other words, evenrow threats have no effect on Zugzwang Control
because such columns will have an even number of unfilled cells
(after any safe cells are taken)
and those cells will be divided evenly between Red and Black.
Relative Values of Threat Types
A strategic threat can be called a horizontal
threat or a diagonal threat, depending on which
kind of fourinrow is threatened.
(Vertical threats can be key to tactical sequences,
but only rarely fit the definition of strategic threat.)
All other things being equal,
in order of preference Red will seek oddrow
horizontal threats as most valuable, followed by diagonal threats,
with evenrow horizontal threats the least valuable.
For Black the different threat types have roughly equal value.
Both players must seek also to block
their opponent's useful threats.
All other things being equal, threats are better low on the board.
A major threat on the 2nd or 3rd row often leaves any threats
in the same column and above it as having little or no value,
while a threat on the 6th row undercuts nothing.
(But be aware that the low threat usually does not
neutralize any threats of the same rowparity.)
All other things being equal, it is better to occupy
cells in a central column.
For example, in terms of diagonal threats, B3 participates
only along A2B3C4D5E6, so relates diagonally to only four other cells.
C3 participates along A1B2C3D4E5F6 and E1D2C3B4A5.
so relates diagonally to nine other cells.
Cells on diagonals that point up toward
the center of the board are better points to occupy
than cells on diagonals that point up toward an edge.
For example, A1B2C3D4 is much more likely to develop into
an important diagonal threat than D1C2B3A4;
and A3B4C5D6 is usually better than D3E4F5G6.
(Similarly, B2C3D4E5 may be slightly more likely, a priori,
to develop into a good threat
than C2D3E4F5, and so on.)
The reason for this is that, as the game develops, it is often
easy to play (or threaten to play) near the bottom
or center of the board.
If building your threat requires instead that you capture a cell
near an upper corner (e.g. A5 or B6),
the opponent will often be able to direct early play elsewhere.
This general rule about "good" versus "bad" diagonals
explains why corner cells like A1, B1, B2
are often good plays in the early game.
Of course you hope to follow up A1 or B2 with a disk at D4, but if the
opponent gets D4 instead, your disk at A1 or B2 isn't wasted: at
least the opponent can't use it for his own diagonal threat.
The remarks in this section are just tendencies
and shouldn't be overemphasized.
Many games are won because of
a horizontal threat on the 6th row, a diagonal threat
involving A5, or some other threat of "poorish" a priori quality.
Each case needs to be judged on its own merits.
In this chapter we show you how to calculate victory
in the very simplest case: when game outcome depends only on major threats.
The rules in this chapter do not cover
undercutting threats, interacting threats (and associated races),
minor threat cases (equivalent to an odd, adjacent, or undercutting
major threat), overcutting threats, or adjacent threat races.
Black even minor threats used to break an oddrow threat draw
can be promoted to "gimme's", so these are considered.
The reader may ask: why bother learning whether
I or the opponent has a certain victory?
By the time the position is stable enough to apply the rules,
it will be too late!
Yes, you do need to look ahead in Connect Four,
but you'll need the strategic rules to know what to
look ahead for!
As a Connect Four game develops, and emerging threats come
into focus, you will need to know which threats will lead to victory
and which are useless.
You will need to understand the effects of two threats in the
same column:
Does your threat neutralize the enemy's threat above it?
Do two samecolored threats in the same column enhance each other?
In this chapter we outline the answers to these questions,
and show how a game's major threats predicts its outcome.
Summary
When there are two major threats in the same column, whether
of the same color or different colors, four
cases can be distinguished:
 Adjacent rows. Wins if same color;
upper threat neutralized if different color.
 2nd and 5th rows Very strong if same color;
upper threat neutralized if different color.
 Same Rowparity. (Both threats on even rows,
or both threats on odd rows.) Threats have no effect on each other.
 3rd and 6th rows. Threats have no effect on each other.
After resolving columns with multiple threats, the game outcome
depends on the major oddrow threats.
The result can often be inferred from the mantra
Red (First Player) likes odd numbers.
Only if the oddrow threats imply a draw, does Black's evenrow
threat become relevant.
Red's (isolated) evenrow threat is never relevant.
In the remainder of this chapter, we explain these general principles,
and present some transformation and victory rules.
The transformation rules teach us which threats can be ignored and
which can be simplified; after we've simplified the threats using
these transformations, the victory rules inform us who will win the game.
The rules in this chapter are not complete, because
they do not cover
 minor threats,
 columns with three or more major threats, or
 tactical interactions between columns.
Nevertheless, the principles will guide you to
understand which potential threats have value and which don't;
and if you understand these "simple" cases,
you should be able to figure out more complicated cases as well.
General Principles
G1: In the final column, Black gets the evenrow cells,
Red gets the oddrow cells.
If the board ends up completely filled in, Black will place the final
disk (disk42) on a 6throw cell.
Working backward from there, Principle G1 becomes obvious.
This principle implies that Red seeks specifically oddrow threats,
while Black may win with an evenrow threat.
G2: Red's oddrow threat has priority over a Black evenrow
threat in a separate column.
Black to move loses; Red to move draws
In the diagram, if Black moves in the first column, Red wins at once.
It does no good for Black to play in the second column, because that
column has an even number of vacant cells, and Black will be
in Zugzwang anyway after those vacant cells are taken.
On the other hand, if it is Red's move in the diagram he can play in
the first column, forfeiting his own threat, but there are an odd
number of vacant cells in that column and
Zugzwang control will reverse;
it will be Black's turn to move (and forfeit his own threat)
when the second column is finally played.
In other words, evenrow threats have no effect on Zugzwang control,
but oddrow threats lead to a reversal of Zugzwang control.
We will refer to columns with an oddrow threat as OddThreated Columns.
G3: Red (First Player) likes odd numbers.
With no oddthreated columns, Black wins (if he has an evenrow threat),
so we say Black has Zugzwang control.
With one oddthreated column, Red wins (if the oddrow threat is his);
Red has Zugzwang control.
With a second oddthreated column (belonging to Black), Zugzwang control
reverses back to Black; and so on.
So Red (who can only win in an odd row) wants there to be an
odd number of oddthreated columns.
Recall this principle by memorizing the mantra:
Red (First Player) likes odd numbers.
The simplest application of this principle is that if Red
has one oddrow threat, he wants to stop Black from getting
an oddrow threat in a separate column.
Diagram 38 shows a fairly routine opening
which has been played "perfectly"  no mistakes have been made yet.
Where must Red play next to keep the game "perfect"?
Diagram 38
Red to play, with only one move to win
Moves:  (1) D1! e1 B1 e2 B2 b3 D2 e3 E4! a1 D3 d4 B4 a2 
 (15) D5 a3 A4! a5 E5 b5 C1 c2 G1! g2 D6 g3 (27) __

Answer: Red must play 27 B6 so that Black does not get
an oddrow counterthreat at c5.
G4: Adjacent major threats win.
If Black has major threats at both b4 and b5, he can simply
play up the Bcolumn and win, without waiting for the endgame.
Sometimes one player will have adjacent threats on one side of
the board while the other player has adjacent threats on the other side.
This leads to a race: whoever plays up to his threats first, wins.
G5: 2ndrow and 5throw threats work together.
When the two threats at these two points are oppositecolored
the 2ndrow threat has maximum value: the 5throw threat is
undercut so worthless.
When the two threats are both yours
you can force opponent into Zugzwang, later
forfeit the 2ndrow threat and use the 5throw threat to Zugzwang your
opponent a second time.
Perhaps a simple way to think of this is to memorize that
A samecolored 2nd/5throw threat pair is equivalent to two
oddthreated columns.
G6: When a column has major threats of both players,
with same rowparity, the game will not end in draw.
Obviously, there cannot be a draw if each player has
a major threat at, say, F3.
If one player has a threat at F3 and the other a threat at F5,
a draw is theoretically possible, but only if one player
makes an illogical blunder.
Transformation Rules
To determine the outcome of a game with only major threats,
first mentally replace any complicated column with an
equivalent but simpler column (or column pair).
This is done with the following transformation rules.
T1: Adjacent major threats win.
Adjacent Red major threats win.
Adjacent Black major threats win.
T2: Threats may neutralize (undercut) opponent's threats with opposite rowparity.
A Red evenrow threat neutralizes any Black oddrow threat above it.
A Black evenrow threat neutralizes any Red oddrow threat above it.
A Red oddrow threat neutralizes a Black evenrow threat immediately above it.
T3: 2ndrow and 5throw threats of the same player in the same column will exert Zugzwang control twice.
The 2nd and 5throw samecolumn threats are equivalent to two oddrow threats in separate columns.
The 2nd and 5throw samecolumn threats are equivalent to two oddrow threats in separate columns.
(Most of the other transformation rules are simple or obvious,
but this peculiar rule, where a 2ndrow threat can be visualized as
equivalent to an oddrow threat, may come as a surprise.)
T4: Threats with same rowparity have no influence on each other.
A Red evenrow threat has no effect on Black evenrow threats.
There's no bonus for two oddrow threats in same column.
When both players have oddrow threats in the same column, the rows of the threats don't matter.
T5: 3rdrow and 6throw threats do not influence each other.
A Red 3rdrow threat has no effect on Black 6throw threat.
Red's 6throw threat is always worthless (unless part of adjacent pair).
There's no bonus for two oddrow threats in same column.
Black's 6throw threat is independent of 3rdrow threat in same column.
T6: Red's isolated evenrow threat has no value.
Except as noted in other rules, Red evenrow threats are worthless.
T7: Red and Black oddrow threats in separate columns cancel each other.
Red and Black oddrow threats in separate columns cancel each other.
Victory Rules
After applying the Transformation Rules to all the major threats
in a position, you will have a simplified system with only five
types of column:
The five types of fundamental column:
Oddrow threat of Red, Black or both; Black evenrow threat; No threat.
Next scan the following Victory Rules in order.
The first Rule that applies will tell you the game's outcome.
V1: Red wins with three major oddrow threats in separate columns.
"Red likes odd numbers."
(With major oddrow threats in four separate columns,
Black wins, but this situation will be rarer than a fourleaf clover.)
V2: Black wins with two oddrow threats in separate columns.
Black needs two (uncanceled) oddrow threats to win.
Black's two oddrow threats win despite Red's threats in the same column
("Black likes even numbers.")
V3: Red wins with an oddrow threat.
Red's (uncanceled) oddrow threat wins.
V4: Black wins with an evenrow threat.
Black's evenrow threat wins only if neither player has an oddrow win.
V5: Otherwise the game is drawn.
Without a winning threat, no one wins.
Columns with Two Threats
The transformation rules allow you to mentally
convert any column with two major threats to a simpler form.
The rules for adjacent threats (like 3rd & 4throw)
and sameparity threats (like 3rd & 5throw) are pretty simple.
The special cases (2nd & 5throw, or 3rd & 6throw)
are more interesting.
We will use some threat combinations involving
these special cases to illustrate how to apply the above rules.
In the following example of an endgame with four major
threats in three columns, our rules correctly predict that
the game will be drawn.
(Zugzwang will occur four times as the ending is played out,
and all four threats will be relinquished.)
Apply T3, T7, T7, V5
The next two examples illustrate that a 2nd/5throw
threat pair is always better for Red than a 3rd/6throw
threat pair.
Apply T3, T7, V3: Red wins.


 
Apply T5, T7, V5: Drawn.

The next two examples illustrate that a 3rd/6throw
threat pair is often better for Black than a 2nd/5throw
threat pair.
Apply T3, T7, V5: Drawn.


 
Apply T5, T7, V4: Black wins.

Minor Threats
Using the same style of diagram as above, here are some of the
simplest facts about minor threats (shown with lowercase "t").
Chapter 8 discusses minor threats in more detail.
Major threats "overcut" minor threats
Black's isolated minor evenrow threats are fulfilled
Mixed (diagonal) threat pair undercuts
Three minor oddrow threats in separate columns are equivalent to one major oddrow threat
Another type of triple threat
Sometimes a "triple threat" is comprised of four threats
If Red prepares a major oddrow threat on the rightside,
say at F5, Black has two ways to respond.
(1) He can form his own oddrow threat on the left side, perhaps at a3 or a5,
getting a draw  this is called Counterthreat;
or (2) Black can undercut Red's F5 threat with his
own major threat at f2 or f4.
If Black is sure Red won't get a second major oddrow threat,
he'll naturally prefer a winning undercutting threat to
a counterthreat good enough only to draw.
If Red does get two major oddrow threats,
Black will usually seek a counterthreat and
an undercutting threat.
If your opponent has a threat at C5 you
can Undercut that threat by constructing a threat
of your own at c4.
More generally, any threat is an Undercutting Threat
if it lies in the same column and immediately underneath
a threat of the other player.
Unlike an ordinary threat at c4, where the holder is reluctant
to play c3, an adjacentrow undercutting threat can be played up to:
Black is happy to play c3 if c3 C4 c5 wins.
For this reason a 1strow check that destroys a 2ndrow threat
is also termed undercut.
As a special case, a 2ndrow threat undercuts
opponent's 5throw threat, though it isn't on an adjacent row.
The undercutting threat usually renders the threat above it
almost worthless.
The undercutting threat need not be a major threat;
indeed interesting examples usually comprise two disks
(and two minor threats) along a diagonal.
Sometimes one disk (three "minor threat" fulfillments
needed for fourinrow) is enough for a successful undercut.
Diagram 39
will lead to some undercutting in the very early game.
Where should Black play?
(This can be phrased as a quick victory problem 
Black to play and achieve fourinrow in eight  with the
moves for the quick victory also the only moves that win at all!)
Diagram 39
Black to play, with only one move to win
Moves:  (1) D1! e1 B1 b2 B3?? d2! D3 (8) __

Black 8 e2 may appeal since a major 2ndrow threat at c2 would
undercut any future Red threat at C3 or C5.
But Diagram 40 shows that this doesn't work: Red can undercut
the c2 threat with a check at C1.
(Diagram 41 shows a possible victorious continuation for
Red; obviously Red couldn't achieve this without getting Black
to open up the Ccolumn.)
Diagram 40
Black to play (will lose)
Moves:  (1) D1! e1 B1 b2 B3?? d2! D3 (8) e2?? A1! c1 C2! (12) __

Diagram 41
Black to play (will lose)
Moves:  (1) D1! e1 B1 b2 B3?? d2! D3 e2?? A1! c1 C2! 
 (12) (12) c3 B4! b5 C4 a2 E3 e4 E5 e6 A3 a4 C5! (24) __

The winning play in Diagram 39 is shown in Diagram 42.
Black's 8 a1 prevents Red's 1strow check, and leaves
Black with two ways to build a major threat at c2.
Red cannot prevent both ways so Black gets his 2ndrow
undercutting threat and, as it turns out, victory
in the early game.
Black's victory is very straightforward but is a
"fourinrow in eight" instead of "fourinrow in five"
because Black had to spend three disks (12 e4, 14 a4, 18 b6)
foiling Red's simple counterplays.
(Red can't be allowed to build a major threat of his own at C2;
it would undercut Black's win at c3.)
Diagram 42
Red to play (will lose)
Moves:  (1) D1! e1 B1 b2 B3?? d2! D3 (8) a1! E2 a2! E3 e4! 
 (13) A3 a4! B4 d4! B5 b6! D5 c1 (21) __

Instead of a major threat, undercutting threats will often
comprise a pair of minor threats along a diagonal.
Moreover, Black may have such a diagonal (involving say f4)
that undercuts a Red threat at F5,
but with Red developing a diagonal threat (including F3)
that in turn undercuts Black's diagonal.
Such a Diagonal Undercutting Diagonal Undercut
is a very common theme in Connect Four games.
Diagram 43 shows a game which has been very well
played on both sides.
(Note Black's pushup play b3B4b5 which eliminates any possible
leftside win for Red.)
It's Red's turn, but Red has already established a winning
major oddrow threat at F5.
Can you figure out what counterplay Black intends and
how to defend against it?
We've not discussed this kind of situation yet, but try anyway.
Diagram 43
Red to play, with only one move to win
Moves:  (1) D1! d2 D3! d4 D5! d6 C1! b1 F1! e1 
 (11) E2! e3 E4! b2 C2! b3 B4! b5 (19) __

Red isn't worried about Black playing b6 to build a major
threat at c5: Red has that undercut already with his own threat at C4.
Red's key move is 19 G1.
In Diagram 44 we see that Red has a winning major oddrow threat
at F5.
Black undercuts it with his diagonal threat f4g5 but to no avail
since Red has the lower undercut at F3G4.
Diagram 44
Red to play and win
Moves:  (1) D1! d2 D3! d4 D5! d6 C1! b1 F1! e1 E2! e3 
 (13) E4! b2 C2! b3 B4! b5 (19) G1! g2 (21) __

19 G1 is Red's only winning move in Diagram 43.
If he plays elsewhere, Black gets to capture f3 as in
Diagram 45;
Black's undercut at f4g5 now works and Red will have to remember
to block at B6 just to salvage a draw.
(He can delay the B6 play somewhat;
in fact he should next try 23 G2
to see if Black is foolish enough to fall for
the pushup play 23 G2 b6? G3! g4 G5!
with the F5 threat now a winner.)
Diagram 45
Red to play and draw
Moves:  (1) D1! d2 D3! d4 D5! d6 C1! b1 F1! e1 E2! e3 
 (13) E4! b2 C2! b3 B4! b5 (19) E5? f2 G1! f3 (23) __

Diagram 46 shows a very common situation
involving an undercut.
One way or another, Red is destined to get a major oddrow threat
at B5 or A5.
Where should Black play to circumvent this?
Diagram 46
Black to play, with only one move to draw
Moves:  (1) D1! d2 D3! d4 D5! c1 C2 c3 C4! f1 F2 f3 
 (13) F4 f5 A1 d6 B1! a2 E1! b2 C5? (22) __

Answer: Black has the undercutting diagonal threats
a5b4 to neutralize Red's 5throw threat.
But Red in turn undercuts that with his diagonal threats A4B3.
Black neutralizes that by grabbing b3 himself, right now.
Play might continue as in Diagram 47 which leads
to the classic undercut endgame and therefore a draw.
(Two columns have oddrow threats; "Red likes odd numbers to win"
but two isn't an odd number.)
Red could have played 23 B4 b5 F6 instead of just 23 F6, but
F6 is essential for Red just to salvage a draw:
if Black gets an evenrow threat anywhere he wins.
Diagram 47
Red to play and draw
Moves:  (1) D1! d2 D3! d4 D5! c1 C2 c3 C4! f1 F2 f3 F4 f5 
 (15) A1 d6 B1! a2 E1! b2 C5? (22) b3! F6 g1 E2 g2 G3 g4 
 (29) G5 g6 C6 a3! E3 e4! E5! e6! (37) __

A Black major 3rdrow threat normally doesn't neutralize
a Red major 5throw threat in the same column,
but will still be effective in some cases
(see Diagram 210 below.)
Where must Black play in Diagram 48 ?
Diagram 48
Black to play, with only one move to draw
Moves:  (1) D1! e1 E2? e3! E4 a1! A2 a3 E5 d2 G1 d3! 
 (13) C1! f1 A4 c2 C3! f2! F3 f4! G2 e6 A5 (24) __

Black is almost in Zugzwang and a6 is the only safe cell.
Play continues and in Diagram 49 we see clearly that Red's
major oddrow threat is undercut.
Diagram 49
Red to play and draw
Moves:  (1) D1! e1 E2? e3! E4 a1! A2 a3 E5 d2 G1 d3! C1! f1 
 (15) A4 c2 C3! f2! F3 f4! G2 e6 A5 (24) a6! F5 f6! G3 g4! 
 (29) G5! g6! B1 b2! B3 b4 B5 b6! (37) __

In most of these undercutting examples, Black has 2 disks along
a diagonal, yielding two minor threats (one oddrow, one evenrow)
that undercut a Red major oddrow threat.
We will give a final example of undercutting, in which Black has only
1 disk along his undercutting diagonal,
so there are three minor threats
that have to be fulfilled for the fourinrow, yet Black's
undercut does work.
The author is indebted to Alan Pruce who provided this interesting
and instructive game.
Diagram 50 is a wellplayed (if perhaps slightly unusual) opening
in which Red may play 11 A2 or E2 next and form the indicated triple threat.
Diagram 50
Black to play (will lose)
Moves:  (1) D1! e1 B1 a1 B2! b3 D2 d3 D4 (10) __

If Black plays 10 a2 Red is likely to answer at E2, and vice versa.
If Black plays 10 d5 Red can win
with either 11 A2 or E2 (or with 11 B4).
But if Black moves at 10 b4,
even an expert Red may answer incorrectly, as shown
in Diagram 51.
Diagram 51
Black to play, with only one move to win
Moves:  (1) D1! e1 B1 a1 B2! b3 D2 d3 D4 
 (10) (10) b4 E2?? b5! B6 e3! G1 g2! D5 (18) __

Red still has his triple threat, which we've indicated at E5
(Red can march up the Ccolumn, capture C3, and promote E5
to a major threat whenever he wishes); however, we've focused attention
on Black's minor threats.
Black's threats along the diagonal c2f5 successfully undercut
Red's E5 threat, even though Black as yet has only one of the 4 stones
needed for the fourinrow!
(Black's evenrow threats along the a6d3 diagonal are relevant because
they give Black a win instead of just a draw.)
Although Black's major threat at c3 is irrelevant in this game,
Black's possession of the cell e3 is essential:
If Red had this cell, his diagonal C1F4 would undercut
Black's c2f5 diagonal.
Since Black's oddrow threat at f5 is key to his undercut,
he must be alert for any Red attempt to undercut it with an evenrow threat
in the Fcolumn. This is why he played 16 g2.
Do you see the more subtle Red threat possibility?
Where should Black play next in Diagram 51 ?
Black will win in this Diagram if he's careful,
but the reader may still wonder what was special about Black's 10 b4.
The answer is that when Black plays well
(and this Black is playing very well),
Red will often need to develop chances on both sides of the board,
but with b3b4b5 all in Black's hands (and Red wasting a turn
to answer b5 at B6), Red has no chance for any winning threat on
the leftside.
The correct move for Black in Diagram 51 is 18 d6
because if Red captures that cell, he'll have threats along
the D6G3 diagonal, as shown in Diagram 52.
Red's minor threat pair E5F4 cannot win by itself of course
(F4 is an evenrow cell) but it does serve to undercut
Black's minor threat at f5.
Red now wins easily, e.g. by playing up the Fcolumn
and capturing F5 if Black takes f4.
Black should have played 18 d6.
Diagram 52
Black to play (will lose)
Moves:  (1) D1! e1 B1 a1 B2! b3 D2 d3 D4 b4 E2?? b5! 
 (13) B6 e3! G1 g2! D5 (18) a2?? G3 g4 D6! (22) __

By the way, in Diagram 50 Red need not actually form his
triple threat immediately.
If play goes as in Diagram 53, Red gets a winning plethora of
minor threats on the rightside similar to
the sextuple threat defined in Chapter 8.
Diagram 53
Black to play (will lose)
Moves:  (1) D1! e1 B1 a1 B2! b3 D2 d3 D4 a2 
 (11) A3 e2 E3! b4 D5! b5 B6! (18) __

Diagram 54 shows a possible continuation from Diagram 53.
Black is now in Zugzwang and about to let Red form a major oddrow threat.
Diagram 54
Black to play (will lose)
Moves:  (1) D1! e1 B1 a1 B2! b3 D2 d3 D4 a2 
 (11) A3 e2 E3! b4 D5! b5 B6! c1 C2 d6 
 (21) F1 f2 F3 f4 F5! f6 A4! a5 A6! (30) __

So far we have dealt mostly with major threats (cells
whose capture would complete a fourinrow)
but minor threats (cells whose capture creates a major threat)
are also important.
And of course, every major threat starts life as a minor threat.
We can't provide detailed transformation rules for minor threats as we did
for major threats: there are too many cases and sometimes
six or more minor threats will interact together to create a win.
Instead we will explore minor threats by looking at examples.
There are a few basic patterns you will see over and over.
One can always hope that a minor threat will become
a major threat, perhaps due to opponent's error, but we will
usually not speak of minor threats unless they already
have strategic significance.
We will divide such strategic threats into six categories:
 Simple Black evenrow threat.
 Mixed diagonal undercutting threat.
A mixed threat pair (evenrow and oddrow) which has no "offensive"
value may nonetheless undercut an oddrow threat above it.
 Triple threat.
Three (or four) threats will sometimes work together to have the
same strategic value as one major oddrow threat.
Such configurations are so common and important
we give them the name "triple threat."
 Winning quadruple threat.
This is a specific but common configuration of four threats which win.
 Sextuple threat.
This is a common configuration of six threats which are equivalent to
a triple threat.
 Plethora of threats.
Sometimes five or more threats work together to create
or counter a winning threat.
Some such situations may arise when one player has a preponderance
of disks in the upper center of the board.
We've already discussed Black minor evenrow threats above
and mention them here just for completeness.
These threats are easy to understand, but important since
they lead directly to Black victory whenever Red cannot form
a winning oddrow threat.
We now clarify the other five categories of strategic minor threat
with examples.
Mixed Diagonal Undercutting Threat
In Diagram 60 Black gets a draw despite the Red
major threat at F5 because Red's threat is undercut with Black's mixed
diagonal threats f4g5.
Black was happy to play up the Fcolumn and let Red play F4 whenever
he wants  Black isn't trying to win with this diagonal,
just kill Red's threat at F5  so it is Black who has Zugzwang
control (the F and Gcolumns comprise two oddthreated diagonals).
This game arises from one in Diagram 43, but with Red making
a mistake:
Red should have maintained his own mixed diagonal threats at F3G4
to undercut Black's diagonal.
Diagram 60
Red to play and draw
Moves:  (1) D1! d2 D3! d4 D5! d6 C1! b1 F1! e1 E2! e3 
 (13) E4! b2 C2! b3 B4! b5 (19) E5? f2 G1! f3 (23) __

On the opposite side of the board in Diagram 60, it happens that
Red is undercutting Black's c5 threat with major threat C4, but the
topic here is undercutting with minor threats.
In Diagram 60, by the way, Red should next try 23 G2
(hoping Black overlooks the winning pushup G3 g4 G5)
and remember to play B6 so that Black can't form a horizontal 6throw
threat.
(No need to worry about Black playing E6: Red's 5throw threat
isn't good enough to win, but is good enough to undercut
any Black threat at f6.)
Triple Threat
In Diagram 61, Red has formed minor oddrow threats
in three separate columns.
Although he has only minor threats, Red has Zugzwang control
(an odd number of oddthreated columns) and will win:
Black will eventually be in Zugzwang, but instead of then being forced
to give Red an immediate fourinrow, Black will be forced
to give Red a winning major threat.
(Later Black will be in Zugzwang again.)
The threat configuration in the Diagram is called
a Triple Minor OddRow Threat.
Diagram 61
Black to play (will lose)
Moves:  (1) D1! d2 D3! d4 D5! b1 B2! b3 B4! f1 
 (11) F2! f3 F4! b5 (15) F5! (16) __

In Diagram 62 Red has three threats on the leftside,
and again the three threats will lead to Red victory.
This time only two of Red's threats are oddrow threats,
so this threethreat configuration is called
a Triple Mixed Threat.
Diagram 62
Black to play (will lose)
Moves:  (1) D1! d2 D3! d4 D5! e1 B1 a1 E2 
 (10) (10) e3 E4! e5 G1 g2 B2 b3 B4 b5 D6 (20) __

In Diagram 62, there are only two oddthreated
columns, but it is still Red who has Zugzwang control.
This is because of Red's evenrow threat: Black can't
play c1 so will have to play at a2 eventually.
The simplest way to remember this is to recall Rule T3 above:
the Ccolumn, with threats on both 2nd and 5throw,
should be counted as two oddthreated columns.
Instead of the 2nd/5th combination, the evenrow threat in a
triple mixed threat can simply be in a row adjacent to one of the
oddrow threats.
Diagram 63 shows a variation of the triple mixed threat.
Here the evenrow threat (G4) is just a minor threat,
but it is an effective triple threat because the minor threat (F3)
which would convert the minor evenrow threat to a major threat
is itself one of the very cells which form an oddrow horizontal threat.
The configuration shown in Diagram 63 is called the JShape because
the four Red disks form a shape like the letter "J."
Diagram 63
Black to play (will lose)
Moves:  (1) D1! d2 D3! e1 E2 d4 E3 (8) __

When play goes up a column, the players take alternating cells
(if there are no other tactical issues) so sooner or later
Red must get either G3 or G4 in Diagram 63.
In either case F3 becomes a major threat, so it is easy to see that
this triple threat is equivalent to a major oddrow threat.
Black played poorly in this Diagram.
As a general rule (though with exceptions)
Black shouldn't let Red build horizontal 3rdrow threats so easily.
Either the triple minor oddrow threat
or the triple mixed threat becomes equivalent to a single
major oddrow threat.
We will use the term Triple Threat as a shorthand
to refer to either of these situations.
Diagram 64 shows a triple threat comprised by
four minor oddrow threats.
It's still called just a "triple" threat because there are three
oddthreated columns, and it functions exactly as an ordinary
triple minor oddrow threat.
(When Red has two oddrow threats in the same column
as C3 and C5 here, the threats are linked and usually behave
like a single threat: if Red occupies C3 he'll usually
end up with C5 as well.
I'm grateful to Johan 'Eliten' Nordlund,
Connect Four champion of Sweden, who provided Diagram 64.)
Diagram 64
Black to play (will lose)
Moves:  (1) D1! c1 G1 g2 F1 e1 E2 e3 E4 a1 G3 g4 
 (13) E5 g5 A2 b1 E6 b2 D2 b3 B4! b5 G6 d3 
 (25) B6 d4 D5 f2 A3 d6 F3! (32) __

In Diagram 65 Red has two minor evenrow threats,
each in one of his oddthreated columns,
and has a winning endgame.
In the eventual Zugzwang, Red will get to play either
D5 (forming a major oddrow threat) or F2 (forming an ordinary
triple threat).
Thus, this Diagram works just the same as a triple threat
and we call it a triple threat even though there are
actually four threat cells.
(We do not call it quadruple threat  that term is reserved
for the very special configuration we'll examine in a moment.)
Diagram 65
Black to play (will lose)
Moves:  (1) D1! e1 B1 b2 A1! c1 C2 c3 C4 e2 
 (11) E3?? e4 E5 e6?? C5 (16) __

Winning Quadruple Threats
Diagram 66 (which is repeated below as Diagram 110)
shows a winning position for Red.
Either F3G3G4 or F4F3G3 would constitute a triple threat,
but a triple threat isn't good enough: Black has built
a counterthreat at c3.
The four threats working together give victory however;
when Red eventually captures F3 or G3 due to Zugzwang he
doesn't just get a major oddrow threat:
he gets an adjacent major threat pair.
Diagram 66
Black to play (will lose)
Moves:  (1) D1! d2 D3! d4 D5! e1 B1 a1 E2 b2 
 (11) E3 e4 A2! b3 B4! b5 (17) D6! a3 E5! (20) __

In this Diagram, if Red gets F3 he also establishes a C3 threat.
For this reason Red wins even if G4
(but not both G4 and C3) is a "blue cell."
(To handicap Red, sometimes a specific cell is designated as a
Blue cell which Red cannot use to win.
See Chapter 12.)
Black could get a draw against this threat configuration
if he had two
major oddrow threats of his own in columns separate from
the quadruple threat.
But that would be exceedingly rare, so I just call
the configuration a Winning Quadruple Threat.
Sextuple Threat
In Diagram 67 (which is based on Diagram 74 below)
Red has six threats on the rightside which are equivalent to
a triple threat.
When the Fcolumn is played Red will get F3 or F4;
in the former case E4E3G3 will form a triple threat,
in the latter case E4E3G5 will form a triple threat.
Thus Red always gets a triple threat, so the six threats
are equivalent to a triple threat.
This configuration is common enough to deserve its
own name: Sextuple Threat.
Diagram 67
Red to play and win
Moves:  (1) D1! e1 B1 b2 A1! c1 C2 c3 C4 e2 
 (11) B3? c5 D2 (14) a2? D3 d4 G1 d5 (19) __

Although Red's win depends on eventually playing
up the Fcolumn, he must be patient and let Black play
f1 (as he will eventually, in Zugzwang, when e3 or g2 would
be more disastrous).
(If Black gets f2 he'll have a double check after his
next move: do you see it?)
Red mustn't play E3 in the diagram either: Black then gets
his own key minor threat at f3.
Finally Red mustn't play G2: he needs to maintain both
his oddrow threats in the Gcolumn.
In addition to the six rightside threats that form
the sextuple threat,
Red's A4 threat is also essential in this Diagram:
it undercuts a possible Black counterthreat at a5.
(Without this threat Red would still have Zugzwang Control and be
able to block at B5, but Black would then take b6
which upsets Red's plans on the rightside).
Thus Red needs two major threats and five minor threats to guarantee
victory here!
In addition to the Black leftside minor threats (needed only
to explain why Red's A4 threat is essential), we've also marked
Black major threat e5, even though it is undercut,
because if Red is forced to block there,
the wasted turn could spell defeat.
Black has several other relevant threats in Diagram 67
(though we didn't clutter it up by trying to show them all)
that could come into play if Red isn't careful.
In Diagram 68, we show how these Black threats come
alive if Red errs in the continuation with 21 B5.
Red must settle for a draw in Diagram 68
since 29 F2? f3 G2 f4 would win for Black.
Diagram 68
Red to play and draw
Moves:  (1) D1! e1 B1 b2 A1! c1 C2 c3 C4 e2 
 (11) B3? c5 D2 a2? D3 d4 G1 d5 (19) D6 b4 
 (21) B5? b6 E3! e4! E5! e6 C6 f1! (29) __

We mentioned that Red shouldn't play 19 E3 in Diagram 67.
Diagram 69 shows the result if Black answers Red correctly.
Red has finished in Zugzwang; if he plays 33 F2, Black f3 is check
so Black gets f4.
The "trick" in the problem is the temptation to start with
22 c6 and make an immediate Black major threat at f3.
That's a logical way to defeat Red's rightside threats but
Black would get only a draw, since Red answers 23 D6.
Black needs to "go for broke" with 22 d6, the only way to guarantee
a horizontal 6throw win.
Diagram 69
Red to play (will lose)
Moves:  (1) D1! e1 B1 b2 A1! c1 C2 c3 C4 e2 B3? c5 
 (13) D2 a2? D3 d4 G1 d5 E3?? e4! E5 (22) d6! C6 e6! 
 (25) F1 b4! A3 a4! B5 b6! A5 a6! (33) __

In the moves of Diagram 69, after 19 E3(?),
Black makes seven consecutive moves that are uniquely forced
for his guaranteed win.
This actually becomes twelve consecutive
uniquely forced moves if the game then continues
33 G2 g3! G4 f2! G5 g6! F3 f4! F5 f6!.
It isn't only Red who must play with utter precision in Connect Four!
There were blunders in the moves up to the sextuple threat
in Diagram 67, but Diagram 284 below shows a sextuple
threat that arises in a wellplayed opening.
Plethora of Threats
The winning quadruple threat and sextuple threat are very
specific threat combinations that each has a very clear meaning
(though the play continuation can get complicated).
But there are several other ways that five or more threats
can work together in a complicated fashion, and we can't cover them all.
You'll just have to "feel your way" along in such positions.
Diagram 70 (which is an early position reached
in the game shown below in Diagram 177) shows a position
where Red's win requires no less than seven threats
(six of them minor) in the D and Fcolumns.
In a handicap game, Red wouldn't win if any of these
cells were nominated as the "blue cell."
(Blue cell is defined below in Chapter 12.)
Red threat D5 is undercut by Black's major threat,
but still has good value: Black may not be able to answer D4 at d5 because
of the check at F2.
Diagram 70
Black to play (will lose)
Moves:  (1) D1! c1 C2? c3! C4 c5? F1? a1? G1 e1 G2 a2 B1? e2! 
 (15) G3 g4! E3 e4! E5 b2 B3! c6 G5 e6? D2 (26) __

Later, Diagram 393 shows a position where Black's
five minor threats win despite a Red major oddrow threat.
In Diagram 379 the position in
Diagram 71 is reached, with
Black victory depending on seven distinct minor threats.
Diagram 71
Red to play (will lose)
Moves:  (1) D1! b1 F1 e1 F2! f3 D2! d3 C1 d4 
 (11) F4! c2 (13) C3?? d5! D6 c4! (17) __

Diagram 260 (repeated here as Diagram 72)
shows a position where Red needs no less than ten minor
threats (or potential minor threats) to win!
Diagram 72
Black to play (will lose)
Moves:  (1) D1! e1 E2? e3! E4 a1! A2 a3 E5 d2 G1 d3! 
 (13) (13) C1! g2? A4! c2 C3! f1 B1 b2 B3 (22) __

Another example is Diagram 390 where Red uses nine minor threats to win.
Earlier chapters have covered the basic ideas of winning play.
In this chapter we give further examples.
Red must force an OddRow Threat
Many openings feature an unrelenting quest by Red to
establish an oddrow threat.
Diagram 73 is an example of this; although some of Red's moves may
seem weakish he never blunders and does finally achieve
his oddrow threat.
Diagram 73
Red to play and win
Moves:  (1) D1! e1 B1 a1 B2! b3 D2 d3 D4 e2 E3 a2 A3! b4 
 (15) D5! e4 B5 e5 F1! b6 A4 a5 F2! g1 (25) __

Red plays 5 B2 hoping to get B3 and pursue a 3rdrow horizontal threat.
7 D2 aims at a future B4 with oddrow threats along the A5D2 diagonal;
similarly 9 D4 aims at the B2E5 diagonal and also threatens to play D5.
11 A2 might have led to an easier Red victory, since it would
give him a triple threat (C2C3E5) immediately.
13 A3 is needed to prevent a quick Black win (13 F1?? a3 A4 d5 with
a Black adjacent threat pair c3c4).
15 D5 and 17 B5 aim at a horizontal 5throw threat;
19 F1 prevents an undercutting Black threat at c4;
21 A4 aims at A5 but just delays the key F2
which finally Red establishes his C5 threat.
We've stated a purpose for each Red move in this opening;
and with Red's intentions clarified, most of Black's moves
have a clear purpose as well.
Space won't permit us to give the same detail on other example games;
the reader should work to understand them by himself.
(The question and exclamation marks should be of much help,
since all blunders in the example games are identified,
along with special winning moves.)
Diagram 74 shows a game that illustrates the great importance of
the 5th row.
Where should Black play?
Diagram 74
Black to play, with only one move to draw
Moves:  (1) D1! e1 B1 b2 A1! c1 C2 c3 C4 e2 B3? c5 D2 (14) __

I'm afraid many people will try the forcing move 14 e3,
but it is Black who ends up being forced in Diagram 75.
Here Red's disk at D5 gives him an easy win.
He can play C6 next with an obvious major oddrow threat at F3,
or may prefer to tease Black and just make weakishlooking
moves, since there is no way for Black to escape.
(If Red does let Black get c6, Red must not ever play G1.
Red has a plethora of rightside threats that are equivalent
to a winning triple threat but, without C6, the threats F3G2 are essential.)
Diagram 75
Red to play and win
Moves:  (1) D1! e1 B1 b2 A1! c1 C2 c3 C4 e2 B3? c5 
 (13) D2 (14) e3? E4! d3 D4! b4 D5! a2 (21) __

Black should have played 14 d3 in Diagram 74.
Diagram 76 then shows a correct continuation.
Where should Red play next?
Diagram 76
Red to play, with only one move to draw
Moves:  (1) D1! e1 B1 b2 A1! c1 C2 c3 C4 e2 B3? c5 
 (13) D2 (14) d3! A2 b4 E3 b5 A3 a4! A5! c6 B6 g1 
 (25) G2 g3 G4 g5 G6 f1 A6 f2! (33) __

Red cannot play E4 (Black e5 creates
an adjacent threat pair at d4d5) but he needs to avoid
D4 as well, since Black wins on the 6th row
after 34 d5! F3 d6!.
Black also avoids d4 and e4 for now, so the game
will continue 33 F3 f4 and result in a draw.
Returning to Diagram 74, 14 a2 may be a tempting
play since it stops Red from getting an easy D5 threat.
But Red will still win easily with a sextuple threat
(see Diagram 67).
Black EvenRow Wins
We'll give a few examples showing how easy it is for
Black to win if Red neglects to block Black's horizontal
evenrow threats.
Playing Black, I think you will be able to achieve the position
in Diagram 77
quite often if your opponent hasn't read this book!
Red dominates the 2nd row, but evenrow threats are useless for Red.
As shown with threat symbols ("t"), Black will eventually win on the (even)
4th row, even though he has only one disk there so far.
Diagram 77
Red to play (will lose)
Moves:  (1) D1! e1 D2? d3! E2? d4 (7) __

In Diagram 78, Black will win on the 2ndrow
if he plays correctly.
Red has established an oddrow (3rdrow) threat, but it's
almost useless because it's undercut by
Black's 2ndrow threat.
Of Black's seven possible plays in the Diagram, one wins, and the
the other six lose.
Where should Black play next in Diagram 78 ?
Diagram 78
Black to play, with only one move to win
Moves:  (1) D1! d2 D3! e1 D4 e2 E3?? (8) __

If you're puzzled, examine the continuation
in Diagram 79 and then return to the problem.
Diagram 79
Black to play (will lose)
Moves:  (1) D1! d2 D3! e1 D4 e2 E3?? (8) d5?? B1 b2 
 (11) A1! c1 C2! e4 C3! b3 B4 (18) __

After Red 9 B1, Black 10 b2 preserves
his 2ndrow threat but only temporarily:
11 A1 is check so Red gets C2 and kills Black's threat.
C2 is also check so Red gets C3 and forms his own oddrow threat at F3.
I've shown a Black minor threat at f2 but it does not
undercut Red's winning threat at F3 because Red will not
be so foolish as to play G1.
Study this; then return to Diagram 78
and find Black's only winning move.
The solution is shown in Diagram 80.
Did you guess right?
8 a1 kills Red's 1strow threat, so preserves Black's 2ndrow threat.
(Red can take A2 if he wants, but Black's E2 means he doesn't
need A2: the Acolumn will be irrelevant in this game.)
Diagram 80
Red to play (will lose)
Moves:  (1) D1! d2 D3! e1 D4 e2 E3?? (8) a1! (9) __

In Diagram 81 Red overlooks an impending 2ndrow
threat by Black. Black's 2ndrow threat is blocked of course, but
Black is able to capture d3 and win.
Diagram 81
Red to play (will lose)
Moves:  (1) D1! e1 B1 b2 A1! c1 B3?? d2! C2 d3! (11) __

Diagram 82 shows a game where Black
blunders back with 8 b4 and Red plays with utmost precision
to get a draw.
Red must play 9 C2 (9 E2 in the Problem).
Other moves lose, for example as in Diagram 83.
A key difference between the moves 9 C2 and 9 D2 in
these Diagrams is that C2 loses value if delayed.
Diagram 82
Black to play and draw
Moves:  (1) D1! e1 B1 b2 A1! c1 B3?? b4? C2! c3! 
 (11) D2! c4 B5! c5 C6! d3 D4! (18) __

Diagram 83
Black to play and win
Moves:  (1) D1! e1 B1 b2 A1! c1 B3?? b4? D2? d3! D4 d5 
 (13) B5 e2 F1 e3! E4 f2 F3 d6! B6 (22) __

Pushup Play
In Diagram 84, Red will win the ending with his major oddrow threat
at A3. (Black's evenrow threat on the opposite side of the board is
irrelevant.)
Red obtained his threat by playing C1C2C3, which let him take
C5 in a socalled pushup play.
Black's play 20 e5 was a mistake.
He would have won if he had played 20 c3 instead and prevented the pushup.
Diagram 84
Black to play (will lose)
Moves:  (1) D1! d2 D3! d4 D5! e1 E2 e3 E4! b1 B2 b3 
 (13) B4 b5 D6 g1 C1?? b6! C2 (20) e5?? C3! c4 C5! (24) __

In Diagram 85 Red has just blundered and
Black can destroy Red's winning threat
with a simple pushup beginning 14 e3.
(Black could have played the pushup 12 e3 E4 e5 instead of
12 b4, but then Red would play 13 B4 and get a different triple threat.)
Diagram 85
Black to play, with only one move to draw
Moves:  (1) D1! e1 B1 a1 B2! b3 D2 d3 D4 e2 A2 b4 B5? (14) __

In Diagram 86 Red doesn't yet have an evenrow threat
and has just erred with the weak move 13 F1.
Where should Black play?
(Don't jump to conclusions!)
Diagram 86
Black to play and win
Moves:  (1) D1! e1 B1 a1 B2! b3 D2 d3 D4 a2 A3 e2 F1?? (14) __

In Diagram 87, Black does the pushup e3E4e5
to kill Red's oddrow threat in the Ccolumn.
Black isn't worried about Red threats in other columns
because he has his own major oddrow threat.
However, Black has no place to build an evenrow threat
and will have to settle for a draw.
Diagram 87
Black to play and draw
Moves:  (1) D1! e1 B1 a1 B2! b3 D2 d3 D4 a2 
 (11) A3 e2 F1?? (14) e3? E4! e5 D5! d6 E6! (20) __

Black does better to play 14 d5 as in Diagram 88,
and secure an evenrow threat.
Red answers 15 E3 to stop the pushup of course.
Where should Black play next?
Diagram 88
Black to play, with only one move to win
Moves:  (1) D1! e1 B1 a1 B2! b3 D2 d3 D4 a2 
 (11) A3 e2 F1?? (14) d5 E3 (16) __

Solution: Black must play 16 b4 at once in Diagram 88
because if Red gets to play there he'll threaten to make
C4 his major evenrow threat (and Black defenses against that
at a4 or e4 lead to Red A5 or E5 and a major oddrow threat).
After Black's correct 16 b4, the game may develop to
Diagram 89 where Black has just played g6 and
eventually wins the endgame on the 6th row.
Some players might be tempted to play c2 (followed by c3) instead of g6,
but this serves no purpose.
We've marked two Red threats in the Diagram just to emphasize
that the Red's threat at C3 is not part of a triple threat.
Diagram 89
Red to play (will lose)
Moves:  (1) D1! e1 B1 a1 B2! b3 D2 d3 D4 a2 A3 e2 
 (13) F1?? d5 E3 b4! B5 d6 G1 f2! B6 c1 G2 a4 
 (25) A5 a6 G3 g4! G5 (30) g6! (31) __

Triple Threats
If Black prevents Red from building a major oddrow threat in
the opening, Red will need a triple threat to win,
so the establishment of such a threat configuration is a very common theme.
Diagram 90 is an example; 13 D6 may seem weakish
but this strong point ends up key to Red's winning threats.
(13 A1 or F3 would also win, but the followup moves are
not so easy to see.)
Diagram 90
Black to play (will lose)
Moves:  (1) D1! d2 D3! d4 D5! c1 C2 c3 C4! f1 
 (11) F2 c5 D6 a1 C6! f3 F4! f5 F6! (20) __

Diagram 91 (derived from Diagram 75 earlier)
illustrates a rather complicated configuration of threats.
Red will win: try to understand why.
A few poor moves were made in this game:
Red's 11 B3 leads to a draw with perfect play
(Red should have played 11 C5);
Black's 14 e3 loses (d3 was needed);
Red's plays 212527 were weakish
but he's just taunting Black, since Red still has a won game.
Diagram 91
Red to play, with only one move to win
Moves:  (1) D1! e1 B1 b2 A1! c1 C2 c3 C4 e2 
 (11) B3? c5 D2 e3? E4! d3 D4! b4 D5! a2 
 (21) B5 d6 A3! a4 A5 c6 A6 b6 (29) __

Red's threats G2F3F4 are not by themselves enough
to win: for a winning triple threat, at least 2 of the
threats must be oddrow threats.
Red's threats F5G5F4 would be a winning triple threat
since two of the threats are odd, but Black's f3 threat undercuts this.
But working together,
the five threats F5G5F4F3G2 do give Red victory here.
The Fcolumn will be played first, and Red will get F3.
A way to understand that Red's configuration wins is to
treat F3G2G5 as an ordinary triple threat,
noticing that whenever Red gets F3, he gets F5 as well.
Since three minor oddrow threats in three separate
columns constitute a win for Red, it's also a win
if one of the threats is a major threat!
Thus Diagram 92 is not analyzed properly as
a draw because players have one major oddrow threat each in
separate columns.
Rather it is a very easy win for Red because of his triple threat.
Diagram 92
Red to play and win
Moves:  (1) D1! d2 D3! d4 D5! e1 E2 e3 E4! b1 B2 b3 
 (13) B4 b5 D6 f1 G1 c1 G2! e5 E6 b6 (23) __

In Diagram 93 Black plays 10 b5 to avoid the
triple oddrow threat shown in Diagram 61.
Red responds by building a triple mixed threat as shown.
Diagram 93
Black to play (will lose)
Moves:  (1) D1! d2 D3! d4 D5! b1 B2! b3 B4! 
 (10) (10) b5 F1! e1 E2! e3 D6 (16) __

Because the threat at C4 is a major threat adjacent to a minor threat,
the endgame win in Diagram 93 is rather trivial:
Red can play up the Ccolumn, capture C5 and establish a major threat
at A3.
There is no way for Black to build a significant
counterthreat.
Red's play has been quite precise
(though he can substitute 15 G1 for D6).
If Black plays to prevent the Red triple threat in Diagram 93 by
playing 14 d6 instead of e3, Red plays 15 E3 and gets
a different triple threat.
In the preceding example, Red's evenrow threat C4 was adjacent to
his oddrow threat C5.
Instead, as shown in Diagram 94, a threat at C2
can be combined with a threat at C5.
In other words, the tactical value of adjacent threat pair
is not essential in these threat configurations:
the Ccolumn evenrow threat leads to Zugzwang control
and Black will eventually be forced to play up the Acolumn
and surrender his minor oddrow threat.
Once Red achieves that, he cheerfully relinquishes his Ccolumn evenrow threat.
(The one evenodd threat combination of no value to Red is 3rdrow
and 6throw.)
Diagram 94
Black to play (will lose)
Moves:  (1) D1! d2 D3! d4 D5! e1 B1 a1 E2 
 (10) (10) e3 E4! e5 G1 g2 B2 b3 B4 b5 D6 (20) __

Diagram 95 is essentially the same as Diagram 94
except that Red interposes two moves (15 G3, 17 G5)
which accomplish little but do moreorless force Black's
replies (16 g4, 18 g6).
Once these temporizing moves are played out, the
key moves at B2, B4, D6 are onlywaytowin moves,
as shown with exclamation marks.
Diagram 95
Black to play (will lose)
Moves:  (1) D1! d2 D3! d4 D5! e1 B1 a1 E2 (10) e3 E4! e5 
 (13) G1 g2 G3 g4 G5 g6 B2! b3 B4! b5 D6! (24) __

Where should Red play in Diagram 96?
(This position is also discussed at Diagram 110.)
Diagram 96
Red to play, with only one move to win
Moves:  (1) D1! d2 D3! d4 D5! e1 B1 a1 E2 b2 
 (11) E3 e4 A2! b3 B4! b5 D6! a3 (19) __

Both players played well in Diagram 96; the only deviations
permitted to Red would be 11 A2, 9 B2, or 7 E2.
Red already has a triple threat but Black has a counterthreat at c3.
Red's winning move now is 19 E5 which builds an invincible
quadruple threat!
After the key 19 E5, players will make temporizing moves
until Diagram 97 (or something similar) is reached.
Black is in Zugzwang and must either relinquish his
threat at c3, play g2 G3 with Red getting the winning
adjacent threat pair F3F4, or play f2 F3 with Red getting the winning
adjacent threat pair G3G4.
(The threat at G4 isn't strictly necessary, since Red
also gets a major threat at C3 after f2 F3.
In other words, Red needs to use either the threat at C2
or the one at G4; having both is unneeded luxury.)
Diagram 97
Black to play (will lose)
Moves:  (1) D1! d2 D3! d4 D5! e1 B1 a1 E2 b2 E3 e4 A2! b3 
 (15) B4! b5 D6! a3 (19) E5! a4 A5 b6 A6 g1 E6 c1 F1! (28) __

Diagram 98 shows another triple threat.
Black has little chance here for a relevant counterthreat.
(Diagram 38 above is derived from this position.)
He can play G1 and claim F2 as a threat, but a rightside
evenrow threat will have no effect on Red's leftside win.
(Black would like a major oddrow threat on the rightside to
reverse the endgame Zugzwang and negate Red's threat,
but there is no real chance for a Black oddrow threat in this Diagram.)
Diagram 98
Black to play (will lose)
Moves:  (1) D1! e1 B1 e2 B2 b3 D2 e3 E4! a1 D3 d4 B4 (14) __

Red's move 13 B4 seems clearcut: it establishes the
minor oddrow threats along a diagonal.
But it is interesting to note that Red had other winning moves.
One possibility would be to substitute 13 D5.
Black will then probably take b4 to prevent the easy
Red win in the preceding Diagram.
Where should Red then play his next two disks?
Solution: Red should play as in Diagram 99.
Now a Black threat at f2 would be relevant so Red kills
that with G1.
G1 is a forcing move: Black must play g2 to prevent an easy
Red major oddrow threat at F3.
Black ends up with b5, but Red gets the
winning triple threat C2C5F5.
Diagram 99
Black to play (will lose)
Moves:  (1) D1! e1 B1 e2 B2 b3 D2 e3 E4! a1 
 (11) D3 d4 D5 b4 (15) G1! g2 E5! b5 B6! (20) __

Red can change the order of his moves slightly in Diagram 99,
for example playing 13 G1 and delaying D5.
He can also play 13 B4 and win on the leftside with the
triple threat A5C3C2.)
Diagram 100 shows a position that can arise in one of the
standard openings if Red makes a subtle blunder.
I've marked A3C5C4 as though it were a (winning) triple threat
for Red, even though Red cannot play F1 to convert C4 to a true threat.
Be aware of these subtle threat configurations that can play a
role similar to a more ordinary triple threat.
Where must Black play next in this Diagram?
Diagram 100
Black to play, with only one move to draw
Moves:  (1) D1! d2 D3! d4 D5! e1 E2 e3 E4! b1 B2 b3 B4 b5 
 (15) D6 g1 B6! c1 E5 e6 G2? g3! C2 g4 G5 a1 G6 (28) __

Answer: Black is almost in Zugzwang but can salvage a draw by playing
F1 to kill Red's "threat" at C4.
Otherwise the play will be as in Diagram 101, with Red getting
full value for his C4F1 threat.
Diagram 101
Black to play (will lose)
Moves:  (1) D1! d2 D3! d4 D5! e1 E2 e3 E4! b1 B2 b3 
 (13) B4 b5 D6 g1 B6! c1 E5 e6 G2? g3! C2 g4 
 (25) G5 a1 G6 (28) c3? C4! f1 F2! f3 F4! f5 C5! (36) __

Next we look at a triple minor threat configuration so common
it warrants its own subchapter.
JShape
Diagram 102
Red to play and win
Moves:  (1) D1! d2 D3! d4 D5! d6 C1! e1 E2 c2 E3 c3 (13) __

In Diagram 102 Red has established three minor threats
on the rightside that will lead to his victory.
In this case, it is easy to see how Red can convert the triple
minor threat to a major oddrow threat: he marches up the Gcolumn
and is sure to capture either G3 or G4. In either case,
F3 will become a major oddrow threat.
Red wins from Diagram 102.
The four Red disks at D3, E3, E2, D1 (3,11,9,1 in Diagram 102)
look a bit like a capital letter "J", so I call this common
configuration the Jshape.
(Of course sometimes a mirror image of this shape will arise
and have the same effect.
And still other configurations of Red disks will give rise
to a similar group of Red minor threats.)
In Diagram 102 Red has established his Jshape and
should win the game easily.
When playing Red against an incautious opponent, you
will often be able to establish a Jshape early in the game
and win easily.
However a Jshape does not guarantee victory, and there are
ways Black can counterattack or foil your Jshape.
It's Red's turn to play in Diagram 102 and six of
his moves win, but one loses.
See if you can figure out what Red's losing
move is in Diagram 102.
Later in the Chapter we'll give the answer to this,
along with more discussion
of the Jshape.
JShape Races
Here's Diagram 102, but presented
in its mirrorimage form so you get used to seeing
the mirrorJ.
Have you figured out what Red's one losing move is?
Diagram 103
Red to play and win
Moves:  (1) D1! d2 D3! d4 D5! d6 E1! c1 C2 e2 C3 e3 (13) __

Answer: Red must not play 13 B1 in Diagram 103
(or 13 F1 in Diagram 102).
This would lead to the position shown in Diagram 104
Diagram 104
Red to play (will lose)
Moves:  (1) D1! d2 D3! d4 D5! d6 E1! c1 C2 e2 
 (11) C3 e3 (13) B1?? e4! E5 c4! A1 b2 (19) __

Black will soon play b3 to kill Red's leftside Jshape.
Black's major evenrow threat at f4 will then give him an eventual victory.
Red cannot play B3 of course because of Black's major threat at b4.
We've looked at undercutting threats where Red's
5throw threat is neutralized by a Black 4throw threat underneath it,
but here we have an overcutting threat
where Red's minor threat on the 3rd row is
neutralized by Black's major threat above it.
The reader may well ask why 13 B1 was Red's only
losing move.
It was a forcing move that provoked Black to play e4 ... c4,
but couldn't Black play that way anyway?
Let's see.
Examine Diagram 105, but now look for Red's only winning
move.
(Hint: remember the specific reason why
Red's triple minor threat can be converted to a major oddrow threat.)
Diagram 105
Red to play, with only one move to win
Moves:  (1) D1! d2 D3! d4 D5! d6 E1! c1 C2 e2 
 (11) C3 e3 (13) G1 f1 F2 e4 E5! c4 (19) __

I call Diagram 105 a Capped Jshape or Overcut Jshape.
Red has achieved his triple minor threat, but Black has
major 4throw threats in compensation.
Best for Red of course is to prevent Black from achieving
the disk trio c4d4e4, but often Black cannot be prevented.
In the Diagram, Red must start with A1 and continue to play up the
Acolumn.
Major threats cannot be overcut;
so Red needs to hurry and convert his B3 minor threat to a major threat.
Diagram 106
Red has won
Moves:  (1) D1! d2 D3! d4 D5! d6 E1! c1 C2 e2 C3 e3 G1 f1 
 (15) F2 e4 E5! c4 (19) A1! b1 A2! b2 A3! b3 A4! (26) __

Diagram 106 shows clearly that the players are engaged in a race.
Red wants to play up the Acolumn quickly and convert his B3 threat
to a major threat. Black wants to play up the Bcolumn
and capture b3 (or b4) before Red achieves his Acolumn goal.
Looking at Diagram 106 we see that Black has, in a sense, won
this race, but "lost the war": Red gets victory at A1A2A3A4.
Let's look at some more openings where Red achieves the Jshape.
Diagram 107
Black to play (will lose)
Moves:  (1) D1! d2 D3! d4 D5! d6 E1! c1 C2 c3 
 (11) E2 c4 E3 e4 G1! f1 G2! (18) __

In Diagram 107 Black plays 10 c3 to avoid giving Red an easy Jshape,
but then has to let Red build Jshape on the rightside (12 e3 loses
immediately to 13 F1).
Red gets his Jshape with 13 E3; Black gets his overcutting threat with 14 e4;
Red plays 15 G1 and 17 G2 and wins the Gcolumn versus Fcolumn race.
One lesson to take from Diagram 107 is that Black's 8 c1
was a weakish move: it led directly to Red's winning Jshape.
Black would do better to play 8 f1, in accordance with a general principle
that b1 and f1 are often better early plays than (the more central)
c1 and e1.
When Red achieves a Jshape, and Black is unable to get the
Overcutting c4d4e4, Black should strive to counter Red's threat with his
own major oddrow threat on the opposite side of the board.
For example, consider Diagram 108.
Diagram 108
Black to play (will lose)
Moves:  (1) D1! d2 D3! d4 D5! e1 B1 a1 E2 b2 E3 (12) __

As shown, Black has a leftside major oddrow threat, and Red has
a rightside triple threat equivalent to a major oddrow threat.
If Red cannot establish a second significant threat he will
draw or even lose.
Diagram 108 has immediate tactical possibilities, since
Black threatens a2, which would give him the adjacent threat pair c2c3;
while Red threatens E4, which would give
him an undercutting major threat at C2.
This makes the players' next moves pretty clearcut:
Diagram 109
Red to play, with only one move to win
Moves:  (1) D1! d2 D3! d4 D5! e1 B1 a1 E2 b2 
 (11) E3 (12) e4 A2! b3 B4! b5 (17) __

The moves shown in Diagram 109 were all absolutely essential:
12 e4, 13 A2 to prevent threats at C2;
14 b3 to prevent a Red major threat at C3;
15 B4 to prevent a Black adjacent threat pair c3c4;
16 b5 to dampen Red's hopes for threats at C4C5.
(Although "essential," Black's moves don't qualify for an exclamation
mark by definition: against perfect Red play,
Black will lose wherever he plays.)
In Diagram 109, Red's next move (disk 17) must
also be placed with precision.
Can you see where?
(After making this best play, assume Black's obvious reply and
find the proper disk 19 for Red as well.)
With each player having a major oddrow threat or the equivalent,
the game will be drawn if neither player establishes
another significant threat.
Red's play 17 D6 in Diagram 110 makes it impossible for Black to establish
a 6throw threat, but more importantly, he threatens A3 which would
establish C5 as a second major oddrow threat for Red.
Black's counter at 18 a3 is mandatory of course;
Red's followon at 19 E5 is also the only winning move.
Red ends up with a winning quadruple threat
essentially identical to the one in the earlier Diagram 97.
Diagram 110
Black to play (will lose)
Moves:  (1) D1! d2 D3! d4 D5! e1 B1 a1 E2 b2 
 (11) E3 e4 A2! b3 B4! b5 (17) D6! a3 E5! (20) __

Diagram 111 shows a possible continuation from
Diagram 110.
Diagram 111
Black to play (will lose)
Moves:  (1) D1! d2 D3! d4 D5! e1 B1 a1 E2 b2 E3 e4 A2! b3 
 (15) B4! b5 D6! a3 E5! (20) f1 G1 e6 C1 a4 B6 a5 A6! (28) __

Before looking at more variants of Jshape
openings, let's return to Diagram 108 and see
what might have happened if Black played 10 e3
to prevent Red from getting the Jshape.
Diagram 112
Red to play, with only one move to win
Moves:  (1) D1! d2 D3! d4 D5! e1 B1 a1 E2 (10) e3 (11) __

Red should play 11 E4 at once to establish a major threat at C2.
Although he may not get a major oddrow threat in the opening,
with the threat at C2 "already in the bag", it will be rather easy for
Red to achieve a winning triple threat combination.
A likely result after that was shown earlier in Diagram 94.
Diagram 113 (related to Diagram 218)
shows another opening where both players play well.
Black can't play e3 of course, so Red
can (moreorless) treat E3 as if he already occupied it himself.
Diagram 113
Red to play and win
Moves:  (1) D1! d2 D3! d4 D5! e1 B1 b2 A1 c1 C2 c3 E2 c4 (15) __

In Diagram 113 Red hasn't yet formed the actual
Jshape, so we call this configuration Future Jshape.
With this shape, Red can play E3 early on to complete the actual "J",
or he can delay  either way E3 belongs to Red.
It is most logical for Red to delay the play, so that he need
not worry about Black playing e4 and getting
an overcutting threat at f4.
However it may be slightly easier to understand the
position once you actually place a Red disk on E3,
so you'll be forgiven for making that play
right away provided it doesn't sacrifice your victory.
How about in Diagram 113?
Can Red play E3 at once and still win?
If you can figure this out without reading ahead or experimenting
with your Connect Four set, you demonstrate excellent
visualization.
As shown in Diagram 114, when Red plays 15 E3
he allows Black to construct the overcutting threat f4,
apparently loses the resultant
race in the F and Gcolumns, yet still wins the game,
with a different triple minor threat.
(If Black next plays g2, Red G3 gives Red an adjacent threat pair
at F3F4; if Black instead plays f3, Red F4 gives Red a
winning major oddrow threat at G3.)
Diagram 114
Black to play (will lose)
Moves:  (1) D1! d2 D3! d4 D5! e1 B1 b2 A1 c1 C2 c3 
 (13) E2 c4 (15) E3 e4 E5! f1 G1 c5 C6! f2 D6! (24) __

Instead of 23 D6 in Diagram 114, Red might be tempted to play
as in Diagram 115, where he has a winning major oddrow threat:
Diagram 115
Black to play (will lose)
Moves:  (1) D1! d2 D3! d4 D5! e1 B1 b2 A1 c1 C2 c3 E2 c4 
 (15) E3 e4 E5! f1 G1 c5 C6! f2 (23) G2?? f3?? F4! g3 F5! (28) __

However Black made an error in Diagram 115.
How should he have responded in Diagram 116 ?
Diagram 116
Black to play, with only one move to win
Moves:  (1) D1! d2 D3! d4 D5! e1 B1 b2 A1 c1 C2 c3 
 (13) E2 c4 E3 e4 E5! f1 G1 c5 C6! f2 (23) G2?? (24) __

Answer:
Black must play as in Diagram 117,
with an endgame win at b4.
Diagram 117
Black to play and win
Moves:  (1) D1! d2 D3! d4 D5! e1 B1 b2 A1 c1 C2 c3 E2 c4 
 (15) E3 e4 E5! f1 G1 c5 C6! f2 (23) G2?? g3! G4 f3! F4 (28) __

As implied above, Red could have avoided complications
like Diagram 117
by simply delaying the play 15 E3 in Diagram 113, playing
up the Gcolumn instead.
Diagram 118 presents some interesting problems.
As usual, try to solve these problems before reading on.
(1) Red played well except for one blunder.
What was the blunder? Where should Red have played instead?
(2) Red still has a strong tactical threat available. What is it?
(3) Where should Black play next? (There are several
possibilities.)
Diagram 118
Black to play and win
Moves:  (1) D1! d2 D3! d4 E1?? c1 C2 c3! E2 c4! 
 (11) E3 e4! G1 f1! G2 c5 C6 d5 E5 (20) __

Diagram 118 shows a position
where Red has achieved a Jshape, won the Gcolumn "race"
to establish F3 as a major threat, and yet still loses
to Black's powerful threats on the leftside.
Assuming Red's rightside configuration is equivalent to
a major oddrow threat, on the leftside Black will need
an oddrow threat (to cancel Red's oddrow threat) and an evenrow threat
(to get a win instead of just a draw).
Black has his evenrow threat (at b4) already (unless Red establishes
a B3 threat to undercut it); the question is: Will
Black get his oddrow threat on the leftside?
I've indicated several Black and Red threats in Diagram 118
to show how the analysis proceeds.
The triple threat at a5b5b4 would provide Black with the equivalent
of a major oddrow threat,
but Red's diagonal threats at A4B3 would
normally undercut Black's a5 threat and thus thwart Black.
(When the Adiagonal is played, Black will want a4 so Red
doesn't get the B3 major threat, but Red than takes A5 to kill
Black's oddrow threat.)
However Black can undercut Red's diagonal
by playing a1, and if Red plays A1 Black plays a2 to build
a major oddrow threat at b3.
(I've tried to depict this last possibility by showing b3
as Black's threat cell.)
In other words, Black might wish to play a1 and construct a threat at b2,
not to build an evenrow threat in the bcolumn (he's already got one
at b4), but to neutralize any possible Red threat at B3.
Did you guess where Red's blunder was in Diagram 118 ?
The cell D5 is one of the most powerful on the board;
here it leads to Black's 5throw counterthreat
and therefore victory.
It was essential for Red to take D5 the first chance he got,
answering 4 d4 with 5 D5.
(As the game played out, Black had to play almost exactly as
he did to win, and never got a chance to take d5 until disk 18.
However, once he passed up his first chance,
Red never got an effective opportunity to play D5 either.)
We asked you to guess Black's next move in Diagram 118.
He has several winning moves (though not 20 f2 G3 with
Red getting double check).
But did you guess 20 e6 to build an adjacent threat pair at b3b4 ?
Sorry, that doesn't work.
In Diagram 119 you will see
that Red would then get his own adjacent threat pair
and win the resultant race.
Diagram 119
Black to play (will lose)
Moves:  (1) D1! d2 D3! d4 E1?? c1 C2 c3! E2 c4! E3 e4! G1 f1! 
 (15) G2 c5 C6 d5 E5 (20) e6?? G3! g4 D6! b1 F2! (26) __

Diagram 119 shows the Red's tactical possibility alluded to above.
Black can prevent this with 20 g3 or 20 d6,
but 20 a1 or 20 b1 also work for Black since now he wins this race:
Diagram 120
Red to play (will lose)
Moves:  (1) D1! d2 D3! d4 E1?? c1 C2 c3! E2 c4! E3 e4! G1 f1! 
 (15) G2 c5 C6 d5 E5 (20) b1 G3 g4! D6 a1 B2 b3 (27) __

In fact Black has a forced Mate in Seven
in Diagram 118.
As seen in Diagram 121, the reason it's Mate in Seven instead of
in Three
is that Red has his own tactical threats that can delay Black's victory.
Diagram 121
Red to play (will lose)
Moves:  (1) D1! d2 D3! d4 E1?? c1 C2 c3! E2 c4! 
 (11) E3 e4! G1 f1! G2 c5 C6 d5 E5 
 (20) (20) b1 G3 g4! A1 a2 F2 f3! F4 d6! (29) __

Diagram 122 shows a different variation on this opening.
Where must Black now play to maintain his victory?
Diagram 122
Black to play, with only one move to win
Moves:  (1) D1! d2 D3! d4 E1?? c1 C2 c3! E2 c4! E3 e4! G1 f1! 
 (15) G2 c5 C6 d5 (19) G3 g4! E5 d6 E6 a1 A2 g5 A3 (28) __

Answer to Diagram 122.
If you played 28 a4 to block Red from playing there
and making a major oddrow threat at B3,
please give yourself a big ... thumb's down !
Red will take A5; Black ends up with no oddrow
counterthreat; Red wins with his F3 threat.
Playing 28 b1 B2 b3 B4 b5 doesn't work either: it leads quickly
to the establishment of a Black major oddrow threat, but
Black's evenrow threat evaporates, and Black needs both
the odd and the evenrow threat to win.
Black's only winning move is to play 28 g6 to temporize;
the game will continue as in Diagram 123;
Red's threat at B3 is neutralized by Black's threat at b2.
Black wins with the adjacent threat pair b4b5.
Diagram 123
Red to play (will lose)
Moves:  (1) D1! d2 D3! d4 E1?? c1 C2 c3! E2 c4! E3 e4! 
 (13) G1 f1! G2 c5 C6 d5 G3 g4! E5 d6 E6 a1 
 (25) A2 g5 A3 (28) g6! A4 a5! A6 b1! (33) __

The "Pushup" Tactic
Diagram 124
Black to play, with only one move to draw
Moves:  (1) D1! d2 D3! d4 D5! d6 C1! b1 F1! e1 E2! e3 
 (13) E4! b2 E5? f2 G1! a1 A2 a3 A4 (22) __

There is an important tactical maneuver that you need to
be alert for, both using it when you can, and blocking
it when your opponent is about to use it.
We'll introduce this topic with the problem in Diagram 124.
Red has built a triple threat in the upper left
and will win unless Black is careful.
Where should Black play in Diagram 124 ?
Answer: The successful play for Black is shown
in Diagram 125.
Black plays 22 b3 and, because this threatens an immediate
vertical win, can follow with 24 b5 to destroy
Red's leftside threat.
Starting with just disks at b1 and b2, Black is able to "push up" the
bcolumn all the way to b5  that's why I call this the pushup play.
Diagram 125
Red to play and draw
Moves:  (1) D1! d2 D3! d4 D5! d6 C1! b1 F1! e1 E2! e3 E4! b2 
 (15) E5? f2 G1! a1 A2 a3 A4 (22) b3! B4! b5! (25) __

In Diagram 125, it is now Red who must be careful just to get a draw.
If he plays as in Diagram 126
to construct a rightside major oddrow threat, Black
plays b6 and forms a winning 6throw threat.
Red should have played B6 before Black got a chance to play there.
The force at 29 F4 was needed, followed by 31 B6.
Diagram 126
Red to play (will lose)
Moves:  (1) D1! d2 D3! d4 D5! d6 C1! b1 F1! e1 E2! e3 
 (13) E4! b2 E5? f2 G1! a1 A2 a3 A4 b3! B4! b5! 
 (25) (25) G2 f3! G3 g4! G5? b6! (31) __

Diagram 127 is an interesting position.
Black has achieved major evenrow threats on the leftside
and an undercutting diagonal threat on the rightside.
Where should Red play next?
Diagram 127
Red to play, with only one move to win
Moves:  (1) D1! d2 D3! d4 D5! d6 C1! b1 F1! e1 E2! e3 E4! b2 
 (15) G1?? b3 B4 c2?? C3! c4 G2 c5 F2! f3 (25) __

Answer: Red makes the pushup play G3g4G5 as in
Diagram 128.
Red will take either E5 or G6 next and build a winning major oddrow threat.
Diagram 128
Black to play (will lose)
Moves:  (1) D1! d2 D3! d4 D5! d6 C1! b1 F1! e1 E2! e3 E4! b2 
 (15) G1?? b3 B4 c2?? C3! c4 G2 c5 F2! f3 (25) G3! g4 G5! (28) __

Overcutting Threats
A major threat can neutralize the opponent's minor threat underneath it.
Whereas an undercutting threat can neutralize either a major or minor
threat, an overcutting threat lies above the opponent's
threat and will have little value unless the opponent's threat is just
a minor threat.
(I write "little value" rather than "no value" because a blocking
disk must be spent when the column is played, and sometimes the
move wastage will be critical.)
Here's a rather difficult problem in which a key
theme is an overcutting threat.
Where should Black play in Diagram 129 ?
Diagram 129
Black to play, with only one move to win
Moves:  (1) D1! d2 D3! d4 D5! e1 E2 e3 E4! b1 
 (11) B2 b3 B4 b5 D6 g1 E5?? (18) __

Diagram 129, which is likely to arise in a very common opening,
is a complicated position, and it may seem far too early
to predict the outcome just by examining the strategic
threats.
Nevertheless, we can understand how Red intends to
win using the threats I've indicated in the Diagram.
Before discussing those Red threats, we note that Black
has two ways to build a major threat in Diagram 129:
18 c1 would build a threat at f4; 18 b6 would build a threat at c5.
But just one of those moves wins; the other loses.
If C4 were a Red threat, Red would have a routine
win with his triple threat A3C5C4.
But of course Red can't play F1 to establish C4 as a threat:
Red's minor threat at F1 is overcut by Black's major threat at f2.
But Red's C4 is still a valid threat.
Red will play up the Ccolumn eventually and take C4.
(Black can't take c4 because Red C5 turns A3
into a major oddrow threat.)
As soon as Red takes C4, Black must answer at f1 and Black's f2 threat
then disappears.
After this, Red's rightside triple threat F5G5G6
becomes active and gives Red victory.
But Black can foil this plan! Return to Diagram 129
and figure out Black's winning move.
If you give up, Diagram 130 shows the result
of Black's play 18 b6; Diagram 131 shows the result
of Black's play 18 c1.
Diagram 130 shows the solution to Diagram 129.
Black's 18 b6 constructs a threat at c5
and thus overcuts Red's threat to play c4.
As long has he never plays in any of the cells marked "no"
(and plays above Red when Red plays in such a cell)
Black will now win easily with his major evenrow threat at f2.
(The same key move also occurred in Diagram 84.)
Diagram 130
Red to play (will lose)
Moves:  (1) D1! d2 D3! d4 D5! e1 E3 e4 E5! b1 
 (11) B2 b3 B4 b5 D6 g1 E6?? (18) b6! (19) __

Diagram 131 shows why 18 c1 (or any play except 18 b6)
loses for Black.
Eventually Red will play C4, forced moves will follow in the Fcolumn,
but after Red 29 F4, Black has no further forcing moves.
He'll play f5, Red will reply C5 and win eventually at A3.
In the Diagram, Red took G2 to build an F3 threat, but he doesn't
really need it: if Black takes g2, Red gets G3, and wins another way
with an F4 threat.
If Black plays 20 e6 instead of 20 c2, Red 21 G2 would be
a subtle blunder (shown in Diagram 100);
instead Red would play as in Diagram 132.
Diagram 131
Black to play (will lose)
Moves:  (1) D1! d2 D3! d4 D5! e1 E2 e3 E4! b1 
 (11) B2 b3 B4 b5 D6 g1 (17) E5?? c1?? B6! c2 
 (21) G2 g3 C3 e6 C4! f1 F2! f3 F4! (30) __

Diagram 132
Red to play and win
Moves:  (1) D1! d2 D3! d4 D5! e1 E2 e3 E4! b1 B2 b3 
 (13) B4 b5 D6 g1 (17) E5?? c1?? B6! e6 C2 c3 C4 f1 
 (25) F2! c5 C6 f3 F4! f5 (31) __

(Diagrams 131 and 132 contain the move sequence
17 E5 c1 B6 where both E5 and c1 are blunders.
The blunders cancel, however, and lead to the same positions
achieved in "perfect" openings with the moves 17 B6 c1 E5.)
``I play where you play''
Surprisingly often, best play for a player will be to
play above the opponent's justplayed disk;
the Candlesticks Opening, in Diagram 236 below,
is one example.
When you can identify a situation where this imitative play is good enough,
it makes successful play very easy.
There are some proofs about openings based on imitative play.
For example, Black never loses against opening Red 1 B1.
In Diagram 133, the hatchedcolored disks may be either Red or Black,
but do alternate color up the columns.
That is, Black takes either c2 or c3, and so on.
(Similarly Black waits for Red to take F1 or G1, then takes the other.)
You will see that if Red gets fourinrow on, say, the 3rd row,
Black must have achieved fourinrow earlier on the 2nd row.
Victor Allis was first to prove, in this simple way, that Black
can assure himself of at least a draw after Red 1 B1 or Red 1 C1.
Diagram 133
Red to play, does not win
Similarly, Black can assure himself of victory if Red starts with 1 A1.
He does this by answering A1 at d1;
playing in the Dcolumn (and then "switching off the autopilot")
as soon as Red plays at any of A4, B5, C3, E3, F5 or G1;
making a winning move (in the F or Bcolumn) after D6;
and otherwise playing immediately above Red's last disk.
Red's only counter to this Black strategy is to play up the Dcolumn
to prevent Black from forming any horizontal evenrow threat.
To prove that Black always wins, therefore, we must show that
he always has a winning move in response to Red D6.
If Black follows the strategy just stated, when Red eventually plays
D6 there will be 0, 2 or 4 disks in the Fcolumn.
If Red can play F1 or F5, that play will win;
Diagram 134 shows an example: there's no
place left for Red to build a winning oddrow threat.
Look at Diagram 134 and you will see plainly that if
Red had omitted D2, D4 or D6, Black could take that
cell and get a horizontal evenrow win.
James D. Allen was first to prove (without computer assistance) that Black
can assure himself of a win after Red 1 A1.
Diagram 134
Red to play, loses
There is one complication to this proof.
If there are exactly two disks in the Fcolumn when Red plays D6,
and Red has already captured C1, then f3 may not win for Black,
since Red gets a major oddrow threat as in Diagram 135.
Instead, in such cases,
Black should answer D6 by playing in the bcolumn.
(As depicted by the threats b3c4e6, Black would
have won in the Diagram if he'd played 14 b3 instead of f3.)
Diagram 135
Black to play, with only one move to draw
Moves:  (1) A1?? d1 C1 c2 D2 d3 F1 f2 D4 d5 
 (11) B1 b2 D6 (14) f3? F4! (16) __

The continuation from Diagram 135 is interesting.
Red has a major oddrow threat so Black wants to build either
undercutting diagonal threats along the b5e2 diagonal or
an oddrow counterthreat.
Red won't be able to prevent this, as it turns out, so will want to
salvage a draw by preventing Black from getting an evenrow threat.
Diagram 136 shows the continuation; note that ten consecutive
plays (five by Red, five by Black) are uniquely forced to achieve the
drawn result.
Diagram 136
Red to play, with only one move to draw
Moves:  (1) A1?? d1 C1 c2 D2 d3 F1 f2 D4 d5 B1 b2 D6 
 (14) (14) f3? F4! b3! C3! c4! A2! e1! C5! a3! A4! a5! G1 g2 (27) __

In this Chapter we'll look at a few example
games in detail.
We may look at several variations of a given game, and the
game title might not apply to all of them.
Triple Threat versus Triple Threat
We next look at some games related to the triple threat in
Diagram 137 (which was shown as Diagram 65 above).
Diagram 137
Black to play (will lose)
Moves:  (1) D1! e1 B1 b2 A1! c1 C2 c3 C4 e2 
 (11) E3?? e4 E5 e6?? C5 (16) __

Instead of the blunder 14 e3,
in Diagram 138 Black plays 14 d2 and should win.
(What is his next correct move?
Solution is shown in Diagram 358.)
Diagram 138
Black to play, with only one move to win
Moves:  (1) D1! e1 B1 b2 A1! c1 C2 c3 C4 e2 (11) E3?? e4 
 (13) E5 d2! C5 g1 G2 d3! E6 g3 C6 g4! G5 (24) __

Red 11 D2 earlier in this opening would also be a blunder,
and would allow Black
to announce fourinrow in seven with a series of forcing moves!
Find it.
(Solution is shown in Diagram 354.)
I've shown Diagram 137 to help you understand
Diagram 139, where an expert might understand that
Red has the same winning endgame as in Diagram 137.
Diagram 139
Black to play (will lose)
Moves:  (1) D1! e1 B1 b2 A1! c1 C2 c3 C4 e2 C5! (12) __

In Diagram 139 I've indicated the same winning threats
as in Diagram 137, even though in each case Red
so far has only one of the four necessary disks.
These six Red threats become equivalent to a triple oddrow threat,
so the effect is similar to the sextuple threat we defined
earlier, but this is actually somewhat more intricate.
Red's diagonal threats at D3 and E4 are also essential (perhaps
we should call this an octuple threat!).
Because of D3, Black cannot allow Red to capture E4;
this means Black will have to let Red capture both E3 and E5.
The moves in Diagram 139 were played in topnotch expert fashion.
(Red can substitute 7 E2 for C2.)
It is quite common for a 5throw play to be best, as Red's 11 C5 here,
because it "gives up" only a comparatively valueless 6throw point.
(D2 would give up d3; E3 would give up e4; etc.)
By trying to show the winning threat configuration that
Red intends to achieve, I may have misled the reader
into thinking Diagram 139 is a cutanddried position
with no interesting play left.
This is far from the case.
Black may get a counterthreat on the leftside,
and there's another Black threat that might cause
Red to waste a key turn.
Suppose Black plays 12 g1 in Diagram 139;
Can you figure out where Red must then play?
Answer: Red must answer 12 g1 with 13 G2.
Otherwise Diagram 140 or 141 might result.
In Diagram 140
Red has a plethora of threats which, though not good enough
to win, salvage a draw in the face of Black's major threat at d4.
In Diagram 141 Red makes a second blunder (15 E5), after which
Black 16 d2 threatens to play d3 and a2 but
Red can only block one of those.
Diagram 140
Black to play and draw
Moves:  (1) D1! e1 B1 b2 A1! c1 C2 c3 C4 e2 C5! 
 (12) (12) g1 E3? e4! D2! e5! A2 b3 A3! a4! A5 (22) __

Diagram 141
Red to play (will lose)
Moves:  (1) D1! e1 B1 b2 A1! c1 C2 c3 C4 e2 
 (11) C5! (12) g1 E3? e4! E5? d2! G2 d3! (19) __

Red played 17 G2 in Diagram 141
because if Black got that point, his major threat
at f2 would negate Red's rightside threats.
But this gave Black the chance to play 18 d3
and establish his own winning threat configuration on the
leftside.
(Black's oddrow threat at a3 neutralizes Red's future
major oddrow threat at F5, so Black wins the endgame at b4.)
From Diagram 141 the game might continue
as in Diagram 142 or as in Diagram 143.
In each case, where must Black play next?
Diagram 142
Black to play, with only one move to win
Moves:  (1) D1! e1 B1 b2 A1! c1 C2 c3 C4 e2 C5! g1 E3? e4! 
 (15) E5? d2! G2 d3! (19) C6 d4 D5 e6 D6 g3 G4 g5 G6 (28) __

Diagram 143
Black to play, with only one move to win
Moves:  (1) D1! e1 B1 b2 A1! c1 C2 c3 C4 e2 C5! 
 (12) (12) g1 E3? e4! E5? d2! G2 d3! E6 g3 G4 g5 G6 (24) __

I'm sure the reader played 28 f1 correctly in
Diagram 142, since alternatives sacrifice his
own threats.
But since the Fcolumn has an even number (six) of
empty cells in the Diagram, it might seem that play there
just postpones the inevitable: Black will be forced to
play at a2 anyway, after the Fcolumn fills up.
But the play in the Fcolumn is essential because
it is Red who suffers Zugzwang and who must let Black
capture Red's threat cell F5.
Once Black accomplishes this, he no longer needs his own
oddrow threat and is happy to play a2.
In Diagram 143, Black 24 c6 is the winning move
which places Red in Zugzwang, forced to give up
part of his triple threat, or to let Black win quickly.
Perhaps one might analyze this position as having
no less than six oddthreated columns: Black's
leftside triple threat and Red's rightside triple threat each
counted as three oddthreated columns.
Diagram 144 shows another instructive variation,
where Red takes 9 E2 instead of C4.
The game can then develop in various ways; Diagram 144
is just one example.
Diagram 144
Red to play and win
Moves:  (1) D1! e1 B1 b2 A1! c1 C2 c3 E2 c4 
 (11) G1 c5 C6! a2 E3 e4 E5! e6 (19) __

Again Red's intended threats are shown with "t" symbols.
The threat at F3 isn't developed yet, but Black can't stop it.
Similarly, a Black major threat at d5 is shown: Black
can establish that whenever he chooses to play b3.
(Red doesn't want to take B3 and see B3b4D2d3.)
The Red configuration may not seem to fulfill
victory requirements, given Black's counterthreat,
but he'll end up getting a winning adjacent threat pair
in the endgame.
Red's 11 G1 (for which C5 could be substituted successfully)
may seem odd, but experts understand the special value of the
corner diagonals like G1F2C3D4.
The game might continue as shown in Diagram 145.
Black is now in Zugzwang.
If Black plays 34 d4 D5, Red wins with his major oddrow threat at F3.
If Black plays 34 f1 F2, Red wins immediately with double check.
(Red 19 A2 also succeeds in Diagram 144, with a possible
continuation shown in Diagram 297.)
Diagram 145
Black to play (will lose)
Moves:  (1) D1! e1 B1 b2 A1! c1 C2 c3 E2 c4 G1 c5 
 (13) C6! a2 E3 e4 E5! e6 (19) A3 a4 A5 b3 B4! a6 
 (25) B5 b6 G2! d2 G3 g4 D3! g5 G6 (34) __

Diagram 146 shows a continuation in which Red blunders with 27 F1,
and then blunders again with 31 F3.
Red gets his adjacent threat pair G3G4 but it's Black's
move and 32 d4 (or f4) wins quickly.
Diagram 146
Black to play and win
Moves:  (1) D1! e1 B1 b2 A1! c1 C2 c3 E2 c4 G1 c5 
 (13) C6! a2 E3 e4 E5! e6 A3 a4 A5 b3 B4! a6 
 (25) B5 b6 (27) F1? d2! D3 f2! F3? (32) __

Red's early play 5 A1 was essential in the games we've
just considered. If Red omits this, the game might go as
in Diagram 147.
There, Black will play a2 or e2 at his next turn (whichever Red doesn't take)
and get a major threat at C2; this will effectively lock up the game.
Black's moves at 6 d2 and 8 a1 were key:
6 b4 (and 8 b4) would draw; other Black plays would lose.
Diagram 147
Red to play (will lose)
Moves:  (1) D1! e1 B1 b2 B3?? d2! D3 a1! (9) __

Missed Opportunities
Diagram 148 shows an example of a triple oddrow threat
where a fourth threat is actually needed:
E2 where neither Red nor Black can afford to play.
Red needn't worry about Black getting a5 to undercut the
B5 threat with Black threat b4  if Black gets a5 that means Red
got A4 and a major threat at B3.
In other words, Red's partial diagonal C4D3 is undercut by Black's
partial diagonal c3d2 but that in turn is undercut by the Red partial
diagonal at C2D1.
Finding the bottommost such diagonal threat is an essential
part of most endgame analyses.
Diagram 148
Black to play (will lose)
Moves:  (1) D1! d2 D3! c1 C2 c3 C4 c5 G1? f1! 
 (11) F2 d4! F3? f4 D5 f5?? A1! a2 E1! (20) __

There were three errors in the game shown in Diagram 148.
Red should have played 9 E1 to win.
Black should often hesitate before playing d4, but of course 12 d4 was
mandatory here to prevent a Red major oddrow threat.
Red should have responded 13 D5 (his only way to draw).
Later, Black 16 a1 was the correct play to win; his actual play 16 f5
(and all other moves) loses.
The position still has interesting play.
If Black plays 20 c6 in Diagram 148, Red must respond at D6
and vice versa.
Otherwise the position in Diagram 149 may develop,
where Red's minor threat B5 is overcut by Black's winning major threat at b6.
Diagram 149
Red to play (will lose)
Moves:  (1) D1! d2 D3! c1 C2 c3 C4 c5 G1? f1! F2 d4! 
 (13) F3? f4 D5 f5?? A1! a2 E1! (20) d6 F6?? c6! B1 b2! 
 (25) A3 a4! A5 a6! B3 b4! (31) __

It would be inconsistent for Black to substitute
8 d4 as in Diagram 150.
Red can then play 9 D5 and reach the 54 Opening by transposition,
but will prefer to play 9 F1, building a threat at F2 and
winning easily, for example as in Diagram 150.
Diagram 150
Black to play (will lose)
Moves:  (1) D1! d2 D3! c1 C2 c3 C4 d4 F1 g1 
 (11) F2 f3 D5! c5 A1 a2 F4 f5 D6 (20) __

Diagram 151 shows another variation of the 34 Opening.
Diagram 151
Black to play (will lose)
Moves:  (1) D1! d2 D3! c1 C2 c3 C4 g1 G2! g3 E1! e2 C5! (14) __

As indicated in the move list with exclamation marks, several
of Red's moves are forced.
The play at 13 C5 may not be obvious  a way to understand this
move is that it gives up nothing (c6 is not an important cell,
while 13 D4 or E3 would give Black a prime location (d5 or e4)
for his 14disk).
Diagram 152 shows another variation where Red plays well.
Diagram 152
Black to play (will lose)
Moves:  (1) D1! d2 D3! c1 C2 c3 C4 g1 G2! g3 
 (11) E1! d4 E2! f1 E3! e4 G4 (18) __

11 E1 (threatening E2 with eventual win at B5) was a key move.
If Red omits it, Black will have a chance to show his skill as in
Diagram 153, where his evenrow threats will take him to victory.
Diagram 153
Red to play (will lose)
Moves:  (1) D1! d2 D3! c1 C2 c3 C4 g1 G2! g3 
 (11) C5?? d4! D5 a1! F1 g4! (17) __

D4 is Poison
Returning to Diagram 151, what should be Black's plan?
(Of course, he'll lose no matter what his plan if Red continues
to play perfectly, but if Red is sure to be perfect, Black would have
given up in response to 1 D1!
Black does have a plan likely to succeed against all but the cleverest Red.)
Black can't very well take a good cell like d4 or e3
since Red will get the even better cell above it (D5 or E4).
Since he's forced to play on the periphery, Black
should make the most of it.
If he can grab a1 and g4, followed by d4,
he'll have both sides of the board locked up with evenrow threats.
Of course Red will not permit this.
In fact Red must catch on to this plan at once (to avoid being
forced to take D4 later),
and play A1 (or B1) in response to g4 and specifically G4 in response to a1.
Diagram 154 shows a game where Red figures out Black's
plan in time and wins with clever play.
Black is in Zugzwang and will next see his forlorn threats at b2d4
disappear.
Diagram 154
Black to play (will lose)
Moves:  (1) D1! d2 D3! c1 C2 c3 C4 g1 G2! g3 E1! e2 C5! 
 (14) (14) a1 G4! c6 G5 g6 E3! e4 E5! a2 A3 a4 A5 a6 E6! (28) __

I call this instructive game D4 is Poison because Red cannot
afford to play there once Black gets g1, and (with an exception)
if Black ever plays there, Red answers D5 with an easy win.
(The exception was shown in Diagram 152; if Red
tries 13 D5 there, Diagram 155 might result, with
Black's major evenrow threats in control.)
Diagram 155
Black to play and win
Moves:  (1) D1! d2 D3! c1 C2 c3 C4 g1 G2! g3 E1! d4 
 (13) D5? f1! E2? e3 F2 e4! E5 a1! C5 (22) __

In Diagram 156, neither player has any threats.
Red has salvaged a draw, but that's all.
Diagram 156
Black to play and draw
Moves:  (1) D1! d2 D3! c1 C2 c3 C4 g1 G2! g3 
 (11) E1! e2 C5! (14) a1 E3? e4! D4! d5! D6 (20) __

The Computer's Game
Here's a game that seems to start much like Diagram 269 below.
Red substitutes 5 E2 for the 5 C2 move in that game,
but this turns out not to give him victory.
By the way, if Black substitutes 10 f1 in Diagram 157,
Red has a fourinrow in four; do you see it?
Diagram 157 is very difficult to analyze, but it strongly favors
Black, who has the upper part of the board
locked up with major evenrow threats at b4 and f4.
Either of these threats is enough for Black victory if Red
cannot counterattack.
Of Red's seven possible moves in Diagram 157, six lose
and only one leads to a draw with perfect play.
If you can guess Red's perfect (drawing) move in this
extremely difficult Diagram,
give yourself a big pat on the back.
(I call this The Computer's Game because I once
thought only a computer would be able to guess Red's best move!
But these days there are some very smart and practiced
players who may not find this so difficult!)
Diagram 157
Red to play, with only one move to draw
Moves:  (1) D1! e1 A1 c1 E2? e3! C2 c3 C4 (10) d2! D3! f1! E4! b1! (15) __

To achieve a draw in the face of Black's major evenrow threats,
it is essential that Red threaten a winning counterattack.
Red's major threats at B5 and F5 are worthless since they're undercut.
Some possible future minor oddrow diagonal threats for Red are marked
in Diagram 157,
but it will take a lot of work for Red to develop these.
In particular, D5 is essential but because of a variation
shown in Diagram 158,
Red may be unable to afford to take D5 even when Black plays d4.
Diagram 158
Red to play (will lose)
Moves:  (1) D1! e1 A1 c1 E2? e3! C2 c3 C4 d2! 
 (11) D3! f1! E4! b1! (15) A2? d4 D5 f2 (19) __

To prevent Black from getting D5 or the double check shown in
Diagram 158, Red must play on the C5F2G1
diagonal, but not at F2 which lets Black win easily.
The choices for Red in Diagram 157 are therefore
15 C5 or 15 G1.
Before considering either move, note that (if Black is a perfect
player) Red can't hope for better than a draw, since if Black
is worried about the counterattack, Black can force a
draw with ease, for example as in Diagram 159.
Diagram 159
Black to play and draw
Moves:  (1) D1! e1 A1 c1 E2? e3! C2 c3 C4 d2! 
 (11) D3! f1! E4! b1! (15) G1! c5 F2! d4 D5! e5 
 (21) B2! f3 F4! f5! F6! b3 B4! b5! B6! (30) __

Now let's suppose Red plays 15 C5 in Diagram 157.
Black, if he's clever, can now win with the plays shown
in Diagram 160.
18 a2 was especially smart and certainly far from obvious.
24 d4 was also essential, to avoid variations like 24 a3 A4 b3 B4 d4 B5.
Diagram 160
Red to play (will lose)
Moves:  (1) D1! e1 A1 c1 E2? e3! C2 c3 C4 d2! D3! f1! 
 (13) E4! b1! (15) C5? g1 F2 a2! E5 e6! C6 b2! G2 d4! 
 (25) D5 f3! F4 f5! G3 d6! (31) __

In Diagram 160, Red made some forcing moves
but his attack came to nothing.
If Red substitutes 15 G1 for C5, and the game continues
as in Diagram 160, Diagram 161 develops.
Diagram 161
Black to play (will lose)
Moves:  (1) D1! e1 A1 c1 E2? e3! C2 c3 C4 d2! 
 (11) D3! f1! E4! b1! (15) G1! c5 F2! a2? E5! e6 
 (21) C6 b2 G2 d4 D5 f3 F4! f5 G3! (30) __

In Diagram 161, Red wins with double check !
The disk at G1 turned out to have special significance,
namely the possible fourinrow G1G2G3G4.
Be on the lookout for such vertical pushes in the A and Gcolumns.
In Diagram 160, 18 a2 was a clever move, and the only
way for Black to win.
In Diagram 161, however, 18 a2 was a mistake 
Black should instead settle for a draw.
My Favorite Game
Diagram 162
Black to play (will lose)
Moves:  (1) D1! e1 A1 e2 B1 c1 B2! b3 C2! c3 
 (11) D2! a2 D3! d4 E3 e4 D5! c4 B4! (20) __

Diagram 162 is a lovely game worth memorizing.
With his plays 8 and 10, Black prevents Red from playing on
the 3rd row; Red would win easily if Black didn't defend this way.
Red gets two disks on the 3rd row, and because of
the adjacent minor threat pair F3F4, those two disks
are enough for a winning minor oddrow threat combination.
(The threat pair F3F4 means that one of G3 or G5 will become
a major threat.)
The play on the 3rdrow is both instructive and surprising;
that's why I call these moves My Favorite Game.
I consider Diagram 162 to be "lovely"
because, after 14 d4, Red has only two disks on the entire
board that can possibly contribute to a fourinrow,
while Black seems to have powerful possibilities in the upper left.
Yet Red has the strategic victory, with a sextuple threat.
Red's play 15 E3 was not essential, but was the simplest
way to settle the game.
If Red neglects to make this simplifying move now, it'll
be quite easy for him to go wrong later as in Diagram 163.
Diagram 163
Red to play (will lose)
Moves:  (1) D1! e1 A1 e2 B1 c1 B2! b3 C2! c3 D2! a2 D3! d4 
 (15) (15) C4 d5 E3?? e4! E5 b4 C5 d6! C6 e6 (25) __

Red's mistake in Diagram 163 was to play E3 and let Black get
both d5 and e4.
Another way for Red to err is shown in Diagram 164.
Diagram 164
Red to play (will lose)
Moves:  (1) D1! e1 A1 e2 B1! c1 B2! b3 C2! c3 D2! a2 D3! d4 
 (15) (15) C4 d5 B4?? c5! B5 b6! E3 e4! E5 d6! C6 e6! (27) __

In Diagram 164, 17 B4 was a mistake because it eventually
allowed Black to force Red to play E3 when he didn't want to.
All in all, Red should just play 15 E3 (or 15 D5) and avoid
these unnecessary complications.
Out of Nowhere
The game in Diagram 165 seems to contradict our basic principles.
Red has allowed Black to get two disks on the 3rd row,
while Red hasn't a single disk there.
Yet Red has played excellently and should win this game easily.
In addition to future prospects he threatens to play on
the C1F4 or G1D4 diagonals and establish E3 as a threat.
Diagram 165
Red to play and win
Moves:  (1) D1! b1 F1 e1 F2! f3 D2! d3 (9) __

In fact, if Black refuses to allow Red to establish the E3
threat, the game ends quickly as in Diagram 166.
Diagram 166
Black to play (will lose)
Moves:  (1) D1! b1 F1 e1 F2! f3 D2! d3 (9) D4 g1 F4 c1 E2 (14) __

... with Red winning easily with his two immediate threats.
Surely Red should take the easy win just demonstrated,
but it may be instructive to look at a slower way for him to win.
In Diagram 167 Red has built only evenrow threats
(and no matter how many of those Red gets, he can't win).
Can Red eventually build the oddrow threat he needs?
Where should Red play next in Diagram 167 ?
With proper imagination, you can visualize Red's winning threat
after he plays one more disk!
Diagram 167
Red to play, with only one move to win
Moves:  (1) D1! b1 F1 e1 F2! f3 D2! d3 (9) D4 g1 E2 g2 
 (13) G3! e3 E4! e5 B2 a1 F4 g4 (21) __

The solution is shown in Diagram 168.
Diagram 168
Black to play (will lose)
Moves:  (1) D1! b1 F1 e1 F2! f3 D2! d3 D4 g1 E2 g2 
 (13) G3! e3 E4! e5 B2 a1 F4 g4 (21) D5! (22) __

Did you get this one right?
Red will obviously get C3 and C5 when the Ccolumn is played,
and will certainly get one of B4 or B5.
Therefore A5 will become Red's major oddrow threat no matter what happens!
Almost all of Red's disks are on evenrow cells, yet he
obtains a 5throw horizontal win from Out of Nowhere.
Threats Everywhere
Starting from Diagram 169,
Red has two moves which lead to fourinrow in Seven,
four other winning moves, and one bad move which lets
Black salvage a draw.
See if you can guess the move(s) which lead to an early
fourinarow, and guess the weakest move.
Diagram 169
Red to play and win
Moves:  (1) D1! c1 C2? c3! C4 c5? F1? a1? G1 e1 G2 a2 (13) __

The quick win begins with F2 or G3.
One variation is shown in Diagram 170
Diagram 170
Black to play (will lose)
Moves:  (1) D1! c1 C2? c3! C4 c5? F1? a1? G1 e1 G2 a2 
 (13) (13) G3 g4 F2 e2 F3 f4 E3! a3 A4! e4 D2 (24) __

The bad move from Diagram 169 would be 13 B1,
after which Black will have to play very well
to claim his draw; and Red will have to play very well to take advantage of
any weakness by Black.
If you can guess most of the followup moves,
you are an expert!
Diagram 171 shows the continuation after 13 B1.
Black's 14 e2 and 18 e4 prevent Red from
getting a major threat at D3.
Red ends up with no major threats at all but,
as indicated in the Diagram he has a huge plethora of minor threats
that might turn into something.
Black has two moves that can salvage a draw.
Take full credit if you find either one.
Diagram 171
Black to play and draw
Moves:  (1) D1! c1 C2? c3! C4 c5? F1? a1? G1 e1 
 (11) G2 a2 B1? (14) e2! G3 g4! E3 e4! E5 (20) __

Before showing Black's successful moves, let's look
at his "third best" move.
This result is shown at Diagram 172.
Observe how Red uses his threats in the lower rightside as a springboard
to build a winning threat in the upper rightside.
(Do you see what happens if Red omits 23 A3 ?)
Diagram 172
Black to play (will lose)
Moves:  (1) D1! c1 C2? c3! C4 c5? F1? a1? G1 e1 
 (11) G2 a2 B1? e2! G3 g4! E3 e4! E5 
 (20) (20) e6? G5 b2 A3! a4 D2! d3 D4! f2 D5! (30) __

Returning to Diagram 171, Black must start with
20 g5 or 20 b2.
In Diagram 173, we look at 10 g5.
Diagram 173
Red to play and draw
Moves:  (1) D1! c1 C2? c3! C4 c5? F1? a1? G1 e1 G2 a2 B1? e2! 
 (15) G3 g4! E3 e4! E5 (20) g5 E6 c6 A3 a4! A5 a6 (27) __

This position will be drawn with perfect play, but I've marked
two Red minor oddrow threats that are relevant, although
undercut by Black's eventual threat at d4.
If Red grabs B2, thinking to prevent Black from playing there
and getting a threat at d4, Black ends up with an
easy win shown in Diagram 174.
Diagram 174
Red to play (will lose)
Moves:  (1) D1! c1 C2? c3! C4 c5? F1? a1? G1 e1 G2 a2 
 (13) B1? e2! G3 g4! E3 e4! E5 g5 E6 c6 A3 a4! 
 (25) A5 a6 (27) B2? b3! B4 g6! B5 b6! (33) __

Now Red has no useful threat; Black will win in the 6th row.
Why did this happen?
Answer: Red's diagonal threats B3D5, though too feeble to win,
are the undercutting threat Red needs to prevent Black from winning.
Red wants to force Black to block at d5 eventually,
then take D6 and kill Black's 6throw threat.
This is shown in Diagram 175.
Diagram 175
Red to play and draw
Moves:  (1) D1! c1 C2? c3! C4 c5? F1? a1? G1 e1 G2 a2 B1? e2! 
 (15) G3 g4! E3 e4! E5 g5 E6 c6 A3 a4! A5 a6 (27) G6 b2! 
 (29) B3! b4 D2! f2 F3! d3! D4! d5! D6 f4! (39) __

Returning to Diagram 171, Black may play 20 b2.
If the game then continues as in Diagram 176,
where should Black play next?
As in variations we've just seen, Red has plenty of minor
threats in the D and Fcolumns: you're not "out of the woods", yet.
Diagram 176
Black to play, with only one move to draw
Moves:  (1) D1! c1 C2? c3! C4 c5? F1? a1? G1 e1 G2 a2 
 (13) B1? e2! G3 g4! E3 e4! E5 (20) b2 B3! c6 G5 (24) __

First let's look at an unsuccessful effort.
In Diagram 177 Red drives up the Dcolumn and establishes a
winning threat at F5.
Diagram 177
Black to play (will lose)
Moves:  (1) D1! c1 C2? c3! C4 c5? F1? a1? G1 e1 
 (11) G2 a2 B1? e2! G3 g4! E3 e4! E5 b2 
 (21) B3! c6 G5 (24) e6? D2 d3 D4! f2 D5 (30) __

This win by Red, relied on a plethora of D and Fcolumn
threats, including the diagonal D2F4.
That's the key to Black's defense: it may seem like the least
of our worries, but it's the only threat we can kill.
Black must play 24 d2 in Diagram 176
to get a draw, for example as in Diagram 178.
Diagram 178
Black to play, with only one move to draw
Moves:  (1) D1! c1 C2? c3! C4 c5? F1? a1? G1 e1 G2 a2 B1? e2! 
 (15) G3 g4! E3 e4! E5 b2 B3! c6 G5 (24) d2! B4! g6 B5 b6! 
 (29) A3 a4! A5 a6 E6! f2! F3! d3! D4! d5! D6! f4 F5 (42) __

Threat in Reserve
The opening in Diagram 179
was rather wellplayed by both sides.
Red has a winning triple threat, but must be wary of Black's
adjacent threat pair, even though it is undercut.
For example, 19 B6 (building C5 threat)
would be the easy way for Red to win now, if not for Black's c4 threat.
Diagram 179
Red to play, with only one move to win
Moves:  (1) D1! e1 B1 a1 B2! b3 D2 d3 D4 b4 
 (11) B5 a2 E2 a3 A4! d5 E3 g1 (19) __

Red should play 19 G2 in the Diagram to prevent Black threats
on the d5g2 diagonal.
But we'll suppose Red overlooks this need and wastes his next turn
as in Diagram 180.
After this, Black g4 was mandatory to prevent Red major threat at F3,
but otherwise the players just fill in neutral cells waiting
for Zugzwang.
Neither Red nor Black can afford to play at E4:
If Black captures e5 he kills Red's triple threat,
while a Red disk at E5 gives quick victory with the adjacent threats C2C3.
I've marked several threats in Diagram 180 but, as we will see,
the winning Black threat is a different one altogether, still
almost invisible in this Diagram.
Diagram 180
Black to play, with only one move to win
Moves:  (1) D1! e1 B1 a1 B2! b3 D2 d3 D4 b4 B5 a2 E2 a3 
 (15) A4! d5 E3 g1 (19) D6?? g2! G3 g4! G5 a5 F1 b6 G6 (28) __

Black's winning move in Diagram 180 is of course to take the last
neutral cell with 28 a6, with the continuation shown in Diagram 181.
Diagram 181
Red to play (will lose)
Moves:  (1) D1! e1 B1 a1 B2! b3 D2 d3 D4 b4 B5 a2 
 (13) E2 a3 A4! d5 E3 g1 D6?? g2! G3 g4! G5 a5 
 (25) F1 b6 G6 (28) a6! F2 e4! F3 f4! F5 e5! (35) __

I call this game Threat in Reserve because two different
threats involving e4 are the keys to Black's victory, yet
Black loses quickly if he places a disk on e4 prematurely.
Don't Play in Dcolumn: Win There!
D3 and D5 are usually the best cells on the board.
Above we saw that "D4 is (often) Poison", but at least D4 occupies
an important long diagonal.
D2 is even more often a bad cell to play than D4.
Thus in Diagram 182, Red wants to eliminate Black's 2ndrow
horizontal threats immediately, but mustn't do so by playing D2.
Diagram 182
Red to play, with only one move to win
Moves:  (1) D1! e1 B1 b2 A1! c1 C2 c3 C4 e2 C5! g1 (13) __

As seen in Diagram 183, Black can win quickly
if Red plays 13 D2 in Diagram 182.
Diagram 183
Black to play and win
Moves:  (1) D1! e1 B1 b2 A1! c1 C2 c3 C4 e2 
 (11) C5! g1 D2?? e3! E4 d3! B3 d4! E5 (20) __

Red should have played 13 G2.
This might lead to Diagram 184,
although Red's 17 C6 was a weakish move.
I've depicted Red's key future threats: the 5th row
and two of the central diagonals.
It appears that Red can play E3, followed by either
E4 or E5, in either case getting a (sort of) triple threat,
but Red's job isn't quite that easy.
Diagram 184
Red to play, with only one move to win
Moves:  (1) D1! e1 B1 b2 A1! c1 C2 c3 C4 e2 
 (11) C5! g1 G2! b3 B4! b5 C6 g3 (19) __

If Red hurries to get a disk on the 5th row as in Diagram 185,
Black gets an undercutting threat on the 4th row.
Diagram 185
Red to play (will lose)
Moves:  (1) D1! e1 B1 b2 A1! c1 C2 c3 C4 e2 C5! g1 
 (13) G2! b3 B4! b5 C6 g3 (19) E3?? e4! E5 g4! (23) __

Instead Red must reply to 18 g3 with 19 G4
to block Black's 4throw threat.
Where should Red play next if Black answers 19 G4 with 20 a2 ?
Red must not allow Black to play a3 and establish a
major threat at d3, as in Diagram 186 where
Red's threats no longer work.
Instead Red must block with 21 A3 immediately.
Diagram 187 shows one possible continuation.
Diagram 186
Black to play, with only one move to draw
Moves:  (1) D1! e1 B1 b2 A1! c1 C2 c3 C4 e2 C5! g1 
 (13) G2! b3 B4! b5 C6 g3 G4! a2 (21) E3? e4! E5! a3! 
 (25) A4 a5 A6 b6 G5 g6 E6 f1! F2! f3! F4! (36) __

Diagram 187
Red to play and win
Moves:  (1) D1! e1 B1 b2 A1! c1 C2 c3 C4 e2 C5! g1 G2! b3 
 (15) B4! b5 C6 g3 G4! a2 (21) A3! f1 E3 e4 E5! a4 (27) __

In Diagram 187, for the first time in the entire game,
Red can play safely at D2.