Magriel's NYT Columns

Skillful play in backgammon depends on two factors: determining the proper strategic plan by assessing the overall board positions — and then using the most effective tactical means to carry out this plan.

Black to play 5-1.

In the diagrammed position, Black has a single exposed man slotted on his 4-point. With the roll of 5-1, he is not able to safely cover this man. Therefore, he must now decide whether to risk keeping it there or else play 4/3, 11/6, lifting it and leaving no exposed men for White.

Strategically, the risk of leaving the man slotted on the 4-point is justified. If Black is able to make this point, he creates a dangerous home board that will inhibit White’s play later on. This extra point will be decisive in many possible future variations. Furthermore, White’s home board at present is still not strong, but will rapidly become so. Therefore, it is to Black’s advantage to take risks early to strengthen his own home board.

Once the strategic decision to leave the man slotted on the 4-point has been made, Black must still exercise care. The obvious play for Black is now 11/5, bringing the spare man into his home board to try to cover the 4-point next roll.

Black, however, has a superior tactical play that accomplishes the same strategic objective — 13/8, 11/10. With this move, Black brings into play two additional builders, and so increases his chance of covering the 4-point. Black’s men are now much more actively placed than if he had simply played 11/5.

By putting an additional blot on the 10-point, Black seems to be taking an extra risk. However, the Duplication Principle shows that his chance of being hit remain precisely the same! Notice that White needs the same number, a 3, to hit in either place. This number, 3, is said to be “duplicated.” Because of this duplication, Black is able to play with a second blot, yet effectively leave only a single direct shot instead of a double direct shot.

The Duplication Principle is a valuable tactical tool that increases the range of possible plays. Indeed, in the diagrammed position there is yet another play that is almost as good as the recommended: 13/8, 5/4, duplicating 4’s.

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