Decisions, Decisions — and Playing the Odds
Paul Magriel, 1977
New York Times, September 22, 1977
Backgammon combines the elements of luck and skill. Because the dividing line between the two is elusive, players’ perceptions of these elements are often distorted.

In backgammon, as in many other games, the more skillful player appears to be luckier. In bridge, for example, the good players seem to hold the better cards; in backgammon, the good players seem to get the better dice. This illusion is in part created because the luck factor in backgammon is highly visible, whereas the skill factor, although significant, is disguised.

Backgammon is a deceptive game. Players of all levels invariably underestimate its profundity; it is a complex game of tactics and strategy. On every roll, a decision must be made, and the cumulative weight of these decisions is a vital factor in winning. One critical aspect of such decisions is trying to minimize your opponent’s number of good rolls. A basic principle by which this is accomplished is the duplication principle.

Black to play 6-1.
In the diagrammed position, Black is well ahead in the race but still has one major task — to escape with his last back man from behind White’s 5-point prime and come home safely. Black has a 6-1 to play. With the 6, he seizes the opportunity to leap out by playing 22/16. The other half of the roll, the 1, must be played with great care.

Black’s objective is to avoid being hit next roll. If White misses, Black will be well on his way to winning the game — he can soon redouble. If he is hit, Black will be in even worse shape than before the roll. So his concern is to minimize the number of combinations that hit him.

First consider what White needs to hit Black if Black uses the 1 to continue on to the 15-point. White can hit Black on the 8-point with a 5 and on the 15-point with a 3. White will then have a double direct shot.

(a) 22/15 (b) 22/16, 8/7
Now consider the position after the correct play, 22/16, 8/7. This move also leaves two blots, one on the 7-point, one on the 16-point. However, now White needs the same number, a 4, to hit in either place. The number that White needs to hit with, 4, is said to be “duplicated.” By duplicating White’s good numbers, Black greatly reduces his chance of being hit — he is effectively leaving a single direct shot instead of a double direct shot.

In general, if you must leave blots exposed in different parts of the board, leave them exposed to the same number, thus minimizing the amount of combinations that hit.

Rollout

Tom Keith 2013
Money play
White owns 2-cube
Black rolls 6-1

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

 6-1: Game G BG Equity 1 22/16, 8/7 W L .4236 .5764 .0588 .1474 .0012 .0048 −0.3920 (b) 2 22/15 W L .3065 .6935 .0586 .1972 .0017 .0085 −0.8243 (0.4323) (a)

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