Duplication Duplicity Increases Chances
Paul Magriel, 1977
New York Times, September 29, 1977
Awareness of which numbers are good for your opponent is crucial. For example, when you leave a man exposed, you should, of course, be aware of which numbers will hit. This does not mean, however, that you should mechanically minimize the total of all your opponent’s favorable rolls.

Black to play 2-1.

In the diagrammed position, Black has just been hit and now has a 2-1 to play. He must reenter from the bar with the 2, then decide how to play the 1. One obvious consideration is to avoid having White hit his other exposed man, the blot now on the 14-point. Black cannot safety this blot; he must leave a direct shot (a shot 6 or less points away). The slightly safer play is 14/13, moving closer to White. (When leaving a direct shot, the closer you are, the less likely you are to be hit.)

(a) bar/23, 14/13

Black, however, has other considerations besides simply minimizing his chances of being hit. To discover what these are, he should examine the position from White’s point of view.

White has two major, independent objectives: to hit Black’s outfield blot and to cover his own blot on the 21-point. Whether White hits a second man or not, he will have a strong position by making his own 21-point. White can close this point with a 2. This simple observation is the key to Black’s decision.

The correct play is bar/23, 6/5. By staying on the 14-point and “wasting” the 1 in his home board, Black duplicates White’s good numbers. That is, White needs the same number, a 2, both to hit on the 14-point and to cover on the 21-point. By duplicating this number, Black greatly reduces White’s chances of getting a productive roll. If, instead, Black had played 14/13, then White would have many extra good rolls; both his 1’s (to hit) and his 2’s (to cover) would be good.

(b) bar/23, 6/5

Technically, hit-and-cover duplication offers two benefits. Primarily, it reduces your opponent’s chances of either hitting or covering. It also reduces his chances of hitting and covering. In this example, through duplication, Black reduces White’s hitting-and-covering chances from 3 combinations out of 36 to only 1 out of 36.

The concept of duplication, although a fundamental tactical principle of backgammon, is neither known nor used extensively. In its most general form, the principle says: When your opponent needs specific numbers for different tactical objectives, duplicate these numbers to reduce his chances for success. The most common application of this is hit-and-hit duplication, in which you duplicate the number your opponent needs to hit in different parts of the board.

Once the idea of duplication is grasped, many variants become possible. Hit-and-cover is one of the more refined variations. Others include duplicating the number that hits and escapes from behind a prime, or the number that hits and reenters.

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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 BG   Equity
1 bar/23, 6/5 W
−0.1590 x  (b)
2 bar/23, 2/1 W
−0.1661 (0.0071) 
3 bar/23, 14/13 W
−0.2263 (0.0673)  (a)

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