"Paradoxes and Probabilities," New Barclay Cooke Volume
Paul Magriel, 1978
New York Times, November 23, 1978

Barclay Cooke
Barclay Cooke, a veteran of 30 years of competition over the backgammon board, has long been considered one of the world’s best players. With his enthusiasm, he has done much to enhance the stature of the game and has always endeavored to keep it on a high level. In addition to his playing, he is also known to the backgammon world as a teacher and a writer.

His latest contribution is a book of problems entitled, “Paradoxes and Probabilities,” which has been published by Random House this month. This varied collection illustrates the complexities of backgammon strategy by presenting several situations where even experts may frankly disagree about the correct play, as well as examples where the average player will often go astray.

The diagrammed position drawn from this book shows how easily an error can be made. Mr. Cooke warns that the first play to come to mind, the obvious “reflex action” play, is not always the best move strategically.

Black to play 5-1.
With the roll of 5-1, Black is given the opportunity to attack White on his 1-point by playing 6/1*, 2/1. This play also makes ideal use of Black’s spare men on the 6- and 2-points to close a fifth point in his home board. Most players, with such a strong home board, would be happy to put White on the bar.

However, as Mr. Cooke points out, a more effective strategy for Black is simply to leave White alone and play 24/18 putting a third man on the 18-point.

(a) 6/1*, 2/1 (b) 24/18
By not hitting, Black forces White to move. If White now fails to roll a 4 immediately, he will be forced to relinquish a vital point. For example, if White rolls a 5 or a 6, he is placed in a dilemma of either giving up the 5-point or the 12-point, each of which is essential to hold. Or, if he rolls two small numbers without a 4, he may be forced to further destroy his already weakened home board.

Black should resist the temptation to automatically attack and should give White the possibility to self-destruct. Failure to project ahead may allow White to keep his position intact and be a threat when he reenters later.

Rollout

Tom Keith 2013
Money play
Centered cube
Black rolls 5-1

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

 5-1: Game G BG Equity 1 6/1*, 2/1 W L .6761 .3239 .2091 .0586 .0030 .0022 +0.7534 (a) 2 24/18 W L .6770 .3230 .2199 .0624 .0067 .0018 +0.7135 (0.0399) (b)

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