Making Every Roll in the Race Count
Paul Magriel, 1978
New York Times, January 5, 1978
Atlanta, one of the country’s fastest-growing urban areas, is also rapidly becoming a major United States backgammon center. The Atlanta Backgammon Society, under the direction of Bette Breiman, is actively developing local interest in the game. The diagrammed position is taken from the intermediate section of one of the society’s recent weekly tournaments.

The position appears to be simple. Both armies have bypassed each other and so the game has evolved into a pure race. Nevertheless, even in such a straightforward situation, Black, an inexperienced player, made a fatal error.

Black to play 6-2.
First, how should Black evaluate the position to determine who the favorite is? Note that the standard pip-count method is no longer reliable when there are only a few rolls left on each side — especially with men piled up on the 1-, 2-, and 3-points. To assess this position, Black must estimate the exact number of rolls each side needs to finish bearing off. White has already borne off five men and so has 10 left on the board; by bearing off two men at a time, White will need precisely five rolls to complete his bearoff. Black has already borne off six men and has nine men left.

Black has just rolled a 6-2. After he completes this move, he will have eight men left. In order to beat White in the race, Black must bear these remaining eight men off in four rolls. That is, Black must make sure he doesn’t “miss” — he must take two men off every roll.

The correct play is 4/2, 3/off. By playing the 2 first and then taking a man off, Black insures that he can indeed take two men off on every roll. With this play, Black fills the gap on the 2-point, and thus avoids the possibility of missing if he rolls a 2.

(a) 4/2, 3/off (b) 4/off, 3/1
In the actual game, Black played carelessly, moving 4/off, 3/1. By taking the 6 off and then moving the 2, Black left a gap on the 2-point. Then, on his next turn, when he again rolled a 6-2, he could bear off only one man. White, now one full roll ahead, redoubled, and Black conceded. (Black was theoretically still in a position to accept the redouble.)

Even during the bearoff, when the outcome is usually determined almost entirely by the dice, a player can throw away a sure victory with careless moves.

Rollout

Tom Keith 2013
Money play
White owns 2-cube
Black rolls 6-2

1296 games with VR
Checker play: 2-ply
Cube play: 3-ply Red

 6-2: Game G BG Equity 1 4/2, 3/off W L .6590 .3410 .0000 .0000 .0000 .0000 +0.2278 (a) 2 4/off, 3/1 W L .5525 .4475 .0000 .0000 .0000 .0000 −0.0633 (0.2911) (b)

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