Three Great Games
Barclay Cooke and Jon Bradshaw, 1974
From Backgammon, the Cruelest Game, Chapter 11, pp 167–178

The common denominator of war
is the duel.

— Karl von Clausewitz

The following game took place between two of the best players in the country, and illustrates much of what has been stressed throughout the book — for example, the vital importance of both 5 points. To obtain these, inordinate risks should sometimes be taken, and when both of them were secured, these two fine players held them tenaciously, no matter how tempting the inducements that were offered in an effort to break them.

 Tip:Click on any diagram to see a rollout

Note also these players’ ability to improvise, and to adjust their thinking to the constant flux in their respective positions. Risks are taken here, safe plays made there, and always the percentages are weighed.

In addition, the tremendous value of “owning” the cube is graphically displayed in this game. This all-important part of backgammon cannot be overemphasized. It has been stressed again and again in the chapter on doubling, and here, in the end game below, as a practical demonstration of what we have been trying to point out.

This specific game, played for high stakes, drew an audience, and though the two opponents happened to be friends, the ego factor began to emerge, as it usually does when a crowd gathers, so both players gave it their best. The result is backgammon of the highest caliber, full of imagination and expertise on both sides, and the reader cannot help but learn from it if he plays it out, move for move, on his own board.

Game 1

 Black White
1. 6-1:  13/7, 8/7 4-1:  13/9, 6/5
2. 5-1:  ?
Black to play 5-1.
Black moves the 5 from white’s 12 point to his own 8 point and drops the 1 from his 6 point to his 5 point. Both players are correctly trying to make their respective 5 points.

5-1:  13/8, 6/5 6-6:  ?
White to play 6-6.
White makes his own bar with two men from black’s 12 point and establishes his own 2 point with two men from his 8 point. This roll is too much too soon, but what else can he do? It would be wrong to break the 12 point here.

6-6:  13/7(2), 8/2(2)
3. 5-4:  ?
Black to play 5-4.
Black hits white on his 5 point with a man from his 1 point and keeps going out to white’s 10 point. He would prefer to make his own 5 point, but since he can’t, he is at least preventing his opponent from making his.

5-4:  24/20*/15 4-2:  bar/23, 24/20*
4. 5-4:  ?
Black to play 5-4.
Here black could enter on either the 4 or the 5 point and continue on to hit white on the 9 point, but instead chooses the correct tactic of entering on the 5 and then making this point with the man from the 1 point.

5-4:  bar/20, 24/20 4-2:  ?
White to play 4-2.
White in turn makes his opponent’s 5 point with a man from black’s 1 point and starts his own 4 point with a man from his 6 point. He is leaving two blots in his outer board because he is trying to lure black off his own 5 point. Once again, an example of correct expert tactics which are seldom, if ever, followed in average competition.

4-2:  24/20, 6/4
5. 2-1:  ?
Black to play 2-1.
Black starts his own 4 point with a man from his 6 point and moves a man from white’s 10 point to white’s 11 point, leaving 2’s everywhere. At this moment black doesn’t mind being hit, and this play gives him diversification.

2-1:  15/14, 6/4 4-3:  ?
White to play 4-3.
White moves the blot from his 8 point and covers his own 4 point, and starts his 3 point by moving off his 6 point. He is still leaving the blot on his 9 point to try to tempt black to break the vital 5 point.

4-3:  8/4, 6/3
6. 4-3:  ?
Black to play 4-3.
Black correctly refuses the bait. With a man from his 8 point he covers the blot on his 4 point, and plays the blot on white’s 11 point to his own 11 point. With this he is vulnerable to a 6, but to his opponent’s cost of breaking the 5 point. (Alternatively, this roll could have been played from white’s 11 and 12 points to black’s 10 point, thus blocking white’s 5’s. This move also has merit, and some experts might prefer it.)

4-3:  14/11, 8/4 5-3:  ?
White to play 5-3.
With the 3 white moves from black’s 2 point to the 5 point, and finally saves the man on his 9 point by moving it in to the 4 point. To come out all the way with the back man would leave black with too many options.

5-3:  23/20, 9/4
7. 5-3:  11/3 5-4:  ?
White to play 5-4.
White moves one man from black’s 5 point all the way to his own 11 point, making him vulnerable to a 6. But at what cost to black!

5-4:  20/11
8. 5-2:  ?
Black to play 5-2.
Black moves both men in from his 8 point, covering his 3 point and improving his board. Since white is clinging tenaciously to his 5 point, black’s 8 point has little value at this stage.

5-2:  8/6, 8/3 2-1:  ?
White to play 2-1.
There are some interesting choices here. White’s is to cover the 3 point in his board with the 1 and to play the 2 from black’s 12 point to his own 11 point to block black’s 6’s. By doing so he gives three extra shots (4-4, 5-3, 3-5) at the blots on black’s 12 point, but considers that blocking black’s 6’s is worth it. He could also have moved all the way from the 11 point to the 8 point, leaving only a 3, but in our opinion his move was much superior.

2-1:  13/11, 4/3
9. 2-1:  ?
Black to play 2-1.
Black hits white’s blot on the 12 point with a man from white’s 12 point and continues on to his own 10 point. A questionable play. It might have been better if black had split off his own 6 point; there’s no need to take any risks at this particular stage of the game. This is perhaps the only error by either player in the game, and it is a minor one. Still, unless white gets the “miracle roll” of double 5’s, it is doubtful that he would break his anchor to hit black were his next roll, say, 5-1 or 5-2.

2-1:  13/12*/10 2-1:  ?
White to play 2-1.
White enters on the 2 and plays the 1 from his own 2 point to his 1 point. Playing the 1 in this way is virtually forced, but these two open blots in white’s home board will strongly affect the strategy of both players henceforth.

2-1:  bar/23, 2/1
10. DOUBLE
Black doubles to 2.
Should White take?
Indeed, black promptly doubles because of these two open men in white’s board, and because white’s timing is bad.

TAKE      2
11. 4-2:  ?
Black to play 4-2.
Black brings the blot in from his own 10 point all the way. He doesn’t hit white on his 2 point because if white does not roll a 6 or a 3, he may have to play a man elsewhere in the board he does not want to move.

4-2:  10/4 4-4:  ?
White to play 4-4.
White moves two men out to black’s 9 point, at last breaking the 5 point, and two men from his 11 point to his bar. An awkward shot, but at least he has men to play now.

4-4:  20/16(2), 11/7(2)
12. 4-3:  ?
Black to play 4-3.
Black hits white’s blot on his 2 point with a man from his 6 point, and moves out to white’s 8 point with the 3, leaving 2’s everywhere. A roll of 2-2 by white now would be a disaster, but the risk is worthwhile. To move 3 from his own 6 point to his 3 point would of course be safer, but it is awkward and craven.

4-3:  20/17, 6/2* 5-3:  ?
White to play 5-3.
White enters on the 5 point and continues out to the 8 point. A good shot for white; if he had been forced to hit black’s blot on the 2 point and not been able to cover those in his board, it could have been the beginning of the end.

5-3:  bar/17
13. 4-1:  ?
Black to play 4-1.
Black hits white’s blot on the 8 point with a man from white’s 12 point. Black is going all out offensively now because of white’s two blots, and is correct in his decision not to make his own 2 point.

4-1:  13/8* 6-5:  ?
White to play 6-5.
White enters on the 5 point, and with the 6 is at last able to cover one of the blots in his board.

6-5:  bar/20, 7/1
14. 5-3:  ?
Black to play 5-3.
There are several choices here. For instance, black could cover his 2 point from his bar point and hit white’s blot on the 5 point, but this would leave five blots open around the board, and if he were hit and could not come in, even for a single roll, he might lose a gammon. Instead he rightly chooses to play conservatively, covering his 8 point with the 5 and making white’s 8 point with the 3.

5-3:  20/17, 13/8 5-4:  ?
White to play 5-4.
White moves out to black’s 9 point with the 4, and covers his own 2 point with the 5, establishing a five-point board.

5-4:  20/16, 7/2
15. 4-1:  7/2 3-2:  ?
White to play 3-2.
White brings one man in all the way from the bar, leaving one man out so that he won’t be forced to play a possibly awkward 6 from black’s 9 point.

3-2:  7/2
16. 6-5:  ?
Black to play 6-5.
Black makes his own 1 point with men from his 6 and 7 points. He could run with one of his back men, but this is risky — particularly because there is no assurance that he will be able to get by next time, and may have to leave an 8 again.

6-5:  7/1, 6/1 5-4:  16/7
17. 5-2:  ?
Black to play 5-2.
Black moves one of the men on his 8 point all the way in to the 1 point. He too is leaving a man out, just as white did earlier, in case he has an awkward 6 to play.

5-2:  8/1 5-2:  ?
White to play 5-2.
This time white plays both men in off his bar, figuring that black on his next move will have to either break his board or move off white’s 8 point. White wants to keep his board intact in case he gets this indirect shot.

5-2:  7/5, 7/2
18. 4-4:  17/13(2), 6/2(2) 6-3:  ?
White to play 6-3.
A very interesting decision for white: should he leave a 1 shot or a 4 shot? If he leaves a 4 and is not hit, black is slowed up drastically unless he gets both men on white’s 12 point past white with a very good roll. Yet to leave a 4 shot instead of a 1 is giving black 4 extra chances (15 instead of 11).

After much reflection, white decides that black’s position in a potential race is too strong, so he leaves the 4 shot and plays one man all the way to his bar.

6-3:  16/7
19. 5-2:  ?
Black to play 5-2.
White’s play pays off. Black has to play a man from his 8 point down to his 1 point.

5-2:  8/1 3-2:  16/11
20. 5-1:  13/12, 13/8 5-1:  11/6, 7/6
21. 5-2:  12/5 4-1:  4/off, 1/off
22. 4-2:  8/4, 2/off 4-3:  4/off, 3/off
23. 6-1:  5/off, 1/off 3-2:  3/off, 2/off
24. 6-2:  4/off, 2/off 6-2:  6/off, 2/off
25. 4-1:  4/off, 1/off 5-2:  5/off, 2/off
26. 6-5:  4/off(2) 2-1:  2/off, 1/off
Up till now, both players have rolled fairly well in bearing off, considering that there have been no doubles, but though black has been slightly in the lead all the way, his advantage hasn’t been really clear-cut until now. But white owns the doubler and black can do nothing but roll and hope. The advantage of having the cube on your side is graphically illustrated here. If it was black’s turn to double and he did so now, white would be hard put to accept, but since white has the doubler, he is in this game till the very end and cannot be forced out.

Look at the diagram and note that there is yet one more fascinating paradox here. With three men on the 6 point, 3-3 would be a better roll for white than 4-4, even though the latter roll has 4 more total pips! This is one more example of the distortions of the pip count.

27. 5-4:  3/off(2) 5-1:  6/off
28. 3-1:  2/off, 1/off 4-4:  6/off(2)
WIN SINGLE
 2 points
White wins the game on his last shot with his only double. Only 6-6, 5-5, 4-4, or 3-3 win for white in this position, making him an 8 to 1 underdog, but as is so often the case, because he had the cube he was able to hang in to the end and pull the game out at the last possible instant.

A few years ago during a pause in a major tournament in the Caribbean, two of the top entrants challenged each other to a few head-to-head money games. After all, what else could they do for relaxation? One of their games was the following, and it is worth close study.

Game 2

 Black White
1. 5-2:  13/11, 13/8 3-3:  ?
White to play 3-3.
White makes his own 5 point and moves two men up to his opponent’s 4 point to thwart black’s builder on the 11 point.

3-3:  24/21(2), 8/5(2)
2. 3-3:  ?
Black to play 3-3.
Black also makes his 5 point and moves up in his opponent’s board to the 4 point. An alternative would be to block white’s 6’s by moving two men to black’s 10 point, but his play is better.

3-3:  24/21(2), 8/5(2) 4-3:  ?
White to play 4-3.
White hits black’s blot on the 11 point with a man from black’s 4 point. A good play, because black can now only hit white with 4’s and 2’s anywhere in the board.

4-3:  21/14*
3. 4-3:  ?
Black to play 4-3.
Black enters on the 3 point and hits white’s blot on his own 4 point with a man from his 8 point. He should not even consider for an instant breaking his anchor on white’s 4 point and hitting white’s blot on the 8 point.

4-3:  bar/22, 8/4* 2-1:  ?
White to play 2-1.
White enters on the 1 point and saves his blot on the 8 point by moving it in to his 6 point. White must retrench at this moment because he has no defense.

2-1:  bar/24, 8/6
4. 3-3:  ?
Black to play 3-3.
There are lots of choices here. Black chooses to make the 3 point in his own board with two men from his 6 point, to hit white’s blot with his own blot on the 1 point, and to bring a man down from white’s 12 point to his own 10 point. This is a great shot, for if white fails to enter, it will be extremely hard for him to accept a double in light of his open man on black’s 11 point.

3-3:  13/10, 6/3(2), 4/1* 4-3:  ?
White to play 4-3.
White enters on the 4 point and hits black’s blot on white’s 3 point with a man from his 6 point. It is mandatory for white to hit here in order to try to keep black busy, thereby protecting his open man on black’s 4 point.

4-3:  bar/21, 6/3*
5. 6-2:  ?
Black to play 6-2.
Black enters on white’s 2 point and hits white’s blot on his own 4 point with the 6. Note that had white not hit black in his previous roll, the 6-2 would have pointed on white here.

6-2:  bar/23, 10/4* 6-3:  ∅
6. DOUBLE
Black doubles to 2.
Should White take?
At this point black gives a good gambling double. He has gammon possibilities, and white’s position is perilous. But white daringly takes in this position; he is perhaps showing off a bit because of the audience.

TAKE      2
7. 6-5:  ?
Black to play 6-5.
Black covers his 1 point with a man from his 6 point and starts his bar with a man from white’s 12 point. He is going all out to blitz white if he doesn’t enter on his next roll.

6-5:  13/7, 6/1 6-4:  ?
White to play 6-4.
A saving shot for white. He enters on the 4 point, hitting black’s blot, and continues on out to the 10 point.

6-4:  bar/21*/15
8. 6-2:  ?
Black to play 6-2.
Black enters on white’s 2 point and starts his own 2 point with a man from his 8 point. He does not save the open man on white’s 12 point because suddenly he needs badly to delay; having made his own 1 point, he is far too advanced at this stage of the game.

6-2:  bar/23, 8/2 3-2:  ?
White to play 3-2.
White covers the 3 point in his own board with a man from his 6 point and hits black on the 12 point with the 2. This is a close decision, but black’s board is now just good enough so that white feels he should avoid giving a direct shot.

3-2:  14/12*, 6/3
9. 5-2:  ?
Black to play 5-2.
Black enters on the 2 point and continues on out to the bar. Again, he does not make his own 2 point because he is ahead of himself.

5-2:  bar/18 5-5:  ?
White to play 5-5.
White hits black on the bar with a man from his 12 point and makes his 8 point with three men from black’s 12 point. He does not make his 1 point because he wants black to come in and be forced to play.

5-5:  13/8(3), 12/7*
10. 6-2:  ?
Black to play 6-2.
Black has to enter on the 2, and to avoid breaking his forward anchor must play the 6 from his 7 point to his 1 point. Black is now in a very bad position.

6-2:  bar/23, 7/1 DOUBLE
White doubles to 4.
Should Black take?
White now correctly redoubles. It is a bad emotional take by black — but he takes nonetheless, as happens with even the best of players from time to time.

11. TAKE      4  4-4:  ?
White to play 4-4.
A great roll. White makes his bar with the man on black’s 10 point, and makes the 9 point with the two men on black’s 12 point, establishing a five-point prime.

4-4:  15/7, 13/9(2)
12. 4-1:  ?
Black to play 4-1.
Black moves two men off his 6 point, making the 2 point. This could have been worse; he still has a four-point board.

4-1:  6/5, 6/2 6-4:  9/5, 9/3
13. 5-2:  ?
Black to play 5-2.
A tremendous saving shot for black, giving him a chance. Needless to say, he moves the back man off the 2 point all the way out.

5-2:  23/16 6-4:  7/3, 7/1
14. 3-2:  16/11 5-4:  ?
White to play 5-4.
White moves his forced 4 from his 5 point in to his 1 point, and the 5 from his 6 point also to the 1 point. By moving the 5 this way rather than bringing it in from outside, white still has two builders to bear if black decides to break his forward anchor.

5-4:  6/1, 5/1
15. 6-1:  11/4 5-1:  8/3, 6/5
16. 4-3:  ?
Black to play 4-3.
Black moves a man from the 4 point out to white’s 11 point. Black feels that he can’t afford to spoil his board any further and must break his forward anchor.

4-3:  21/14 6-2:  3/1
17. 4-1:  14/10, 5/4 5-1:  ?
White to play 5-1.
There are a wealth of fascinating critical decisions to be made with this roll. White could hit on the 4 point and move a man in from the 8 point. But this would leave two men open, which is dangerous, considering black’s five-point board. Secondly, he could play both outside men, saving one and leaving only one man open to a 3 or a 5. But white chooses to play conservatively and safely, taking both men off his 6 point.

5-1:  6/5, 6/1
18. 4-2:  21/19, 10/6 6-6:  ∅
19. 2-1:  ?
Black to play 2-1.
Again a tough choice. Black finally decides to come out all the way to white’s 9 point, relying on his back anchor to get a shot later.

2-1:  19/16 2-1:  ?
White to play 2-1.
Another intriguing decision. The best immediate percentage for white is to give black a 2 shot by starting the 4 point, but on his next roll he might not be able to cover, and might even have to leave two men open. In these circumstances white decides to move one outside man to his 5 point and gamble against a 6 — a 20 to 16 shot in his favor because 3-3 doesn’t hit.

2-1:  8/5
20. 1-1:  16/12 4-2:  ?
White to play 4-2.
White moves the outside man in to the 4 point with the 4, and moves a man from his 5 point to his 3 point, leaving four men on his 5 point. If he left five men there, a 6-6 or 5-5 on the next roll would leave two blots.

4-2:  8/4, 5/3
21. 6-4:  23/19, 12/6 6-3:  5/off, 4/1
22. 5-3:  19/11 5-1:  5/off, 1/off
23. 1-1:  11/7 3-1:  3/off, 1/off
24. 5-1:  ?
Black to play 5-1.
Black moves from the bar to the 1 point, pinning all his hopes on getting a shot on the next roll, for with his next 6 he will be forced to leave.

5-1:  7/1 4-1:  ?
White to play 4-1.
White has options, but must leave a blot. Taking another man off is desirable, but not at the cost of giving black two extra shots (2-1, 1-2) if he leaves the blot on his 5 point; therefore he moves both men down, the 4 to the 1 point and the 1 to the 4 point.

4-1:  5/4, 5/1
25. 3-2:  23/21*/18 4-4:  ∅
26. DOUBLE
Black doubles to 8.
Should White take?
Black now redoubles in this position. He is a favorite here because white has only five men off. But because of the men on black’s 1 point, white accepts the double, for the chances are that black is going to have to break his board immediately without getting any of the extra men off before he has to break. White’s take is correct in all money games.

TAKE      8
27. 3-1:  18/14 3-1:  ∅
28. 2-1:  14/11 6-5:  ∅
29. 6-4:  ?
Black to play 6-4.
Black moves his outside man all the way to the 1 point, justifying white’s take even more.

6-4:  11/1 6-1:  ∅
30. 4-1:  ?
Black to play 4-1.
Black bears one man off the 4 point and moves the other man down to the 3 point. Black doesn’t leave a blot because he has a chance to win even if white rolls the 4 immediately — though of course 4-4 would probably be disastrous.

4-1:  4/3, 4/off 2-2:  ∅
31. 2-2:  6/4(2), 2/off(2) 4-1:  ∅
32. 5-4:  5/1, 5/off 5-5:  ?
White to play 5-5.
White enters on the 5 point and goes all the way to his own 5 point. This “miracle” roll puts white right back in the game.

5-5:  bar/5
33. 6-1:  4/off, 1/off ?
Should White
double to 16?
Should white redouble now? Though he has only five men off to black’s six, it is his roll, and if he can continue to take two men off on each subsequent roll, he will win the game, barring doubles. But under no circumstances should he redouble at this stage. Any 2 ruins him; besides, with a minimum of five rolls remaining (if neither player throws a double), it is much too early.

6-5:  5/off, 3/off
34. 6-4:  4/off, 3/off ?
Should White
double to 16?
Once again white waits and doesn’t redouble, for then any 2 would lose him the game.

5-1:  3/off, 1/off
35. 6-3:  3/off(2) DOUBLE
White doubles to 16.
Should Black take?
Now white redoubles, at exactly the right time; he has not waited too long. On the other hand, black must take; any 2 except double 2’s will win outright for him because white certainly could not accept a redouble should he now roll any of the ten losing shots (2-1, 2-3, 2-4, 2-5, 2-6, or their reciprocals).

By redoubling here, white is admittedly forfeiting two probable further rolls for a chance to win with a double, should he now be unfortunate enough to roll a single 2. (That is, if white did not double here and then proceeded to roll a 2, black could not redouble him, since he would not own the cube, and white would have two turns to win by rolling a double.) But this chance should be taken, and his double here is technically and tactically sound — as is black’s acceptance of it.

Many players would drop if they were black in this position, but they are absolutely wrong. In this case, however, black correctly accepts white’s double.

36. TAKE      16  3-1:  ?
White to play 3-1.
White takes two men off. Now (assuming no doubles) only a 2-1 will lose for white.

3-1:  3/off, 1/off
37. 6-5:  1/off(2) 5-4:  3/off, 1/off
Black now needs any double to win, and is a 5 to 1 underdog. The doubler is at 16, and the stake is \$5 a point. How much should black offer, and how much should white accept, to settle their game here? You have all the equipment to work this out, so why not see if you can come up with the answer before reading further? (If necessary, refer to the chapter on settlements.)

In this particular situation, black offers to give \$50, and white counters by stating that he will take \$60. These offers show that both men know what they are doing, because \$50 is too low and \$60 is too high. They haggle for a while, and finally settle on \$55, which is about right. The nearest figure is between \$53 and \$54, so white receives a little bit the best of the settlement.

Even though both opponents in this game were fine players, it shows how the emotions can sometimes take over and affect anyone’s reason. In particular we feel that black was wrong in accepting white’s redouble on the tenth move — despite the fact that in this book we advocate the philosophy of taking a double whenever there is a doubt. But black’s position at this stage was almost untenable, and he should have dropped, as most good players would have. Hence, in this particular game justice was done, because after this foolhardy take, black did not deserve to win.

What follows is a game recently played by two of the world’s best in a tournament match in London that was televised and followed with great interest by players around the world.

Game 3

 Black White
1. 6-1:  13/7, 8/7
2. 6-4:  24/14 5-2:  13/11*, 6/1*
3. 5-1:  bar/20, bar/24*
A hitting contest then ensued, with each player attempting to establish a position, being hit, and forced in turn to hit again.

6-5:  bar/20, 11/5*
4. 2-1:  bar/23, 6/5* 4-3:  bar/22, 24/20*
5. 6-5:  bar/20*/14 3-2:  bar/22, 13/11*
6. 2-1:  bar/23, 6/5* 4-2:  bar/23, 24/20*
7. 3-1:  ?
Black to play 3-1.
Black enters on white’s 3 point and hits on his own 5 point with a man from his 6 point.

This was the first really major decision in the game. Black’s option was to come in on the 1 point, establishing two blocks, and to hit with the 3 from his 8 point. But the move as played is imaginative and daring. If black had come in on the 1 point, he would have been committing himself to a back game. Black can afford the play he made because white has made only his bar and has not yet made any points in his inner board. Hence, black is not necessarily in a back game as yet.

The drawback to this play, however, is that black has lost a builder by hitting white’s blot from his 6 point instead of from the 8 point. Nonetheless, this is an interesting example of early tactics. Black has decided against a back game this early in the game — going along with the theory that back games should if possible be avoided.

3-1:  bar/22, 6/5* 3-1:  bar/24, 23/20*
8. 6-1:  bar/24, 13/7 6-1:  ?
White to play 6-1.
White makes his own 5 point with men from the 6 point and 11 point.

By far his best choice. He, of course, could have hit black’s blot on the bar point, but this would serve no purpose, since white has too many of black’s men in his inner board already.

6-1:  11/5, 6/5
9. 3-1:  ?
Black to play 3-1.
Black moves from white’s 1 point to white’s 4 point and makes his own bar point with a man from his 8 point.

Another interesting play. Black might have left the blot on his bar point and made white’s 4 point instead. Another alternative would have been to hit white’s blot on black’s 5 point with the 3 and to make the 3 point in white’s board with the 1. But both of these moves would commit him to a back game, which he is still reluctant to get involved in.

But because white now has his 5 point and a four-point block, we believe that black should have made the move. However, we imagine that black, seeing that white had four men in his inner board, was still attempting to avoid a back game. In this case, we feel he was wrong. White’s four back men do give him good timing to defend a back game, however, and black decided against it.

3-1:  24/21, 8/7 DOUBLE
White doubles to 2.
Should Black take?
At this point, white doubles black to 2. It is interesting to speculate on whether or not white would have doubled if black had used the 1 to make white’s 4 point. Despite the fact that white has a good position, it is still a bold double. Black has no serious flaws in his game. He has a defensive anchor and opportunities for delay, and white is short on builders in his outer board. Black must have felt the same, since he accepted white’s double.

10. TAKE      2  5-3:  8/3*, 6/3
11. 6-5:  ∅ 3-3:  ?
White to play 3-3.
White makes his own 4 point with two men from his bar point and moves one from black’s 12 point to white’s 10 point and one from black’s 1 point to black’s 4 point.

There are many ways of playing these double 3’s. With two of black’s men on the bar already and a four-point board, white could have made the 1 point, thereby sabotaging black’s back game entirely. Admittedly it is an awkward and unnatural move to make, but well worth considering in this instance. But having rejected it, white surely should have started his bar with the fourth 3, rather than the weak and aimless move up to the 4 point in black’s board.

3-3:  24/21, 13/10, 7/4*(2)
12. 3-1:  ?
Black to play 3-1.
Black enters on the 1 point. A great roll for black; he still has one man on the bar, but he has secured that vital second point in his opponent’s board.

3-1:  bar/24 2-2:  22/20(2), 13/11, 10/8
13. 4-1:  bar/24, 13/9 5-2:  ?
White to play 5-2.
White moves from black’s 5 point to black’s 12 point, not hitting black’s blot with the man from black’s 4 point. This is the correct play. White does not want to delay black further and so declines to hit. At this juncture, he has a distinct edge in every area. He even holds his enemy’s 5 point.

5-2:  20/13
14. 3-1:  ?
Black to play 3-1.
Black hits white’s blot on black’s 12 point with a man from white’s 12 point and moves the 3 from white’s 12 point to his own 10 point.

This is one of the most fascinating decisions of the game. If white’s two men on the 5 point had been on the 4 point, we are sure that black would have blocked his 9 point with the 3-1, thereby containing white’s three men in his inner board unless white rolled a 6. In this position white has very little in reserve and might easily be forced into breaking his blockade. But since the men were on the 5 point, black elected to go into a massive back game. An ingenious and daring play.

3-1:  13/10, 13/12* 4-3:  ?
White to play 4-3.
White enters on the 3 point and moves from black’s 5 point to black’s 9 point, hitting black’s blot. White still does not relish hitting, but in order to break up black’s countering blockade, he decides to attack. If he had entered on the 4 point and played the 3 to his own 8 point, he could be blocked with low numbers. Double 3’s would be especially disastrous. A good example of going against the usually sound premise of not hitting in a back game. The situation is unique, and white correctly improvised.

4-3:  bar/22, 20/16*
15. 5-5:  ∅ 2-1:  ?
White to play 2-1.
White moves men on black’s 3 and 4 points up to his 5 point. White might have hit two more of black’s men, but rightly decided to bring two men up. An expert play.

2-1:  22/20, 21/20
16. 6-1:  bar/18 5-2:  ?
White to play 5-2.
White moves from black’s 5 point to black’s 10 point, hitting, and from black’s 9 point to black’s 11 point. Here again, white makes a crucial error, in our opinion.

The 2 is vital. Following the practice of not hitting when you are defending against a back game, white does not hit twice — but he should have. It is a time to ensure that black does not make white’s bar point by rolling a 6-1, 6-2, or 5-2, a total of six shots. (He should not use 5-1 to hit, because the 2 point is too faluable.) It is a calculated risk, but we think white was in error here. If white secures his bar and establishes a prime, he has an excellent chance to contain his opponent’s men long enough so that black’s remaining forces will be well out of play. In other words, black’s other men will have been forced to move to the forward points in his inner board before white’s blockade breaks.

5-2:  20/15*, 16/14
17. 5-2:  ?
Black to play 5-2.
Black enters on the 2 point and makes white’s bar point. Because white did not hit twice and black did roll the 5-2, he has come from far behind and is about even money now.

5-2:  bar/18 5-5:  ?
White to play 5-5.
White moves two men from black’s 5 point to black’s 10 point, one from black’s 11 point to white’s 9 point, and one from white’s 11 point to white’s 6 point. A very cautious play. What is white afraid of? He wants to be hit, and by playing safely he has made himself too fast.

5-5:  20/15(2), 14/9, 11/6
18. 5-3:  ?
Black to play 5-3.
Black moves his two men from his 8 point to his 5 point and 3 point, deliberately leaving two blots. It is entirely to his advantage to be hit, and if white rolls 3’s and/or 2’s, he will have to hit or strip his board. Curiously, since white does not want to hit under any circumstances, black is partially “blocking” white with his two separated blots.

5-3:  8/5, 8/3 6-2:  ?
White to play 6-2.
White moves from black’s 10 point to white’s 9 point, and from white’s 6 point to white’s 4 point. Again white is dogging it by playing safe. Black has perfect timing now.

6-2:  15/9, 6/4
19. 6-3:  24/15 6-4:  15/11, 15/9
20. 4-1:  ?
Black to play 4-1.
Black moves from black’s 12 point to black’s 8 point, and from black’s 7 point to black’s 6 point. There is no point in hitting; he has no board.

4-1:  12/8, 7/6 5-1:  ?
White to play 5-1.
White moves from white’s 0 point to white’s 8 point, and from white’s 11 point to white’s 6 point, refusing to hit, of course.

5-1:  11/6, 9/8
21. 2-2:  8/4, 7/5, 6/4 6-1:  ?
White to play 6-1.
White moves from white’s 9 point to white’s 8 point, and from white’s 9 point to white’s 3 point. A good shot, but black’s timing is still excellent.

6-1:  9/8, 9/3
22. 3-3:  15/3 6-4:  8/4
23. 5-4:  18/14, 13/8 3-1:  ?
White to play 3-1.
White doesn’t hit. He does not want to delay black.

3-1:  8/5, 4/3
24. 5-4:  14/5 5-3:  8/5, 8/3
White has now brought all of his men into his inner board, but black’s timing remains nearly perfect.

25. 3-1:  18/15, 8/7 5-2:  6/4, 5/off
26. 4-1:  15/10 1-1:  6/5, 6/3
27. 6-2:  10/2 5-1:  ?
White to play 5-1.
White bears one off the 5 point and plays 4/3, keeping his men as diversified as possible.

5-1:  5/off, 4/3
28. 5-1:  7/2, 5/4 4-2:  5/3, 4/off
29. 4-1:  23/18 5-4:  ?
White to play 5-4.
White bears two men off and leaves a triple shot which endangers two blots.

5-4:  5/off, 4/off
30. DOUBLE
Black doubles to 4.
Should White take?
Should white take? In all money games, the answer is yes. Black can hit with any 2, 3, or 4, which means that 27 shots hit and 9 do not, making him exactly a 3 to 1 favorite. You will recall that 3 to 1 is the dividing line on whether or not one accepts a double. In this instance, white is neither over nor under. But the determining factor here is that if black misses, white has good double-game possibilities, since he has five men off already. But because this was a tournament match, and due perhaps to the score at the time or the psychological blow he had just been dealt, white thought it expedient to drop.

PASS
 2 points
When a position like this arises — that is, when you leave a triple shot — do not throw up your hands in the belief that your cause is hopeless. How many times, for example, have you failed to enter a three-point board? In this instance the odds are exactly the same. But black may have bluffed white here. The psychological setback of suddenly leaving two blots may have caused him to drop without considering the position carefully.

Nevertheless, overall this is a superb game by two great strategists, and it demonstrates the essence of backgammon.