A Case of Too Little Being Just Enough
Paul Magriel, 1978
New York Times, March 9, 1978
Every game of backgammon ultimately becomes a race. In a pure racing game, in which no contact is possible between the opposing sides, high numbers are, of course, favorable. However, the outcome of many games is determined by which player most effectively blocks his opponent and prevents him from racing. In such cases, high numbers may be quite disadvantageous.

Consider the diagrammed position. Both sides have constructed full 6-point primes. As the position stands, neither Black nor White can escape from behind the other’s prime.

The game, however, is not a stalemate. Both sides must continue to move forward until, inevitably, one or both primes break. In order to delay breaking first, each side wishes to advance as slowly as possible.

Black to play 2-1.
Black was delighted when he rolled a 2-1, the smallest combination on the dice. The obvious play now is 6/3, maintaining his full 6-point prime. Black took a deeper look at the position with respect to priming and found a better play.

The correct play is 8/7, 8/6, “clearing” the 8-point. Black voluntarily relinquishes his full prime before he is forced to do so! Black leads and White, with a spare man on the 12-point, is quite unlikely to be forced to break his own prime on the next roll. Thus Black must plan on maintaining an effective blockage for at least one more roll. The key to an effective blockade against White’s men on the 1-point is to hold the 3- to 7-points as long as possible.

Killing 6's: 8/7, 8/6

With the correct play Black sacrifices the 8-point in order to slow down his forward progress. Black deprives himself of 6’s. That is, on his next roll, Black will not be able, legally, to play a 6, because he no longer has any men on the 8-point. Sixes are ordinarily the largest, and so the worst, number for Black in terms of unwanted forward progress. Now 6’s become his best numbers — he can’t play them at all.

Many players are familiar with the idea of saving 6’s in certain holding positions. The related concept of depriving oneself of 6’s is often overlooked, even though it occurs at least as frequently. In fact, whenever one is trapped behind a prime, the opportunity to avoid playing certain numbers may be a vital consideration.

Rollout

Tom Keith 2013
Money play
White owns 2-cube
Black rolls 2-1

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

 2-1: Game G BG Equity 1 8/7, 8/6 W L .4972 .5028 .1192 .1356 .0059 .0079 −0.1680 2 8/5 W L .4947 .5053 .1185 .1422 .0060 .0090 −0.1981 (0.0301) 3 8/7, 6/4 W L .4850 .5150 .1126 .1445 .0059 .0092 −0.2260 (0.0580) 4 6/3 W L .4838 .5162 .1139 .1414 .0059 .0091 −0.2264 (0.0584)

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