Doubling Duplication Tactic May Triply Assure a Victory
Paul Magriel, 1979
New York Times, November 18, 1979
Backgammon Often in backgammon the game reaches a critical position in which the outcome will be decided in the next few rolls. In such positions accurate tactical play is essential. A key ingredient for precise tactics is an awareness of specifically which numbers are good for your opponent each roll.

In the diagrammed position, Black had doubled several rolls ago but failed to improve his position. Furthermore, the roll of 3-1 is a disappointment — Black had hoped for a 5 with which to hit White’s blot (exposed man) on the 18-point. Indeed, with this roll, Black is unable even to safety his own blot on the 13-point.

Black to play 3-1.
Black’s first consideration is to try to avoid being hit next roll. In order to minimize this possibility, Black can play 13/10, 7/6, moving his blot closer to White’s men on the 9-point.

Before making this play, however, Black must examine the placement of all of White’s men. Next roll, White has other objectives besides hitting Black — White also wishes to cover his man on the 18-point and so form a strong five-point prime (from the 22-point to the 18-point). This prime would blockade Black’s two back men (on the 23-point) and significantly reduce Black’s chance to win.

Black is aware that to make the 18-point White needs a direct 4. This observation opens up new tactical possibilities. For example, Black might consider leaving his blot on the 13-point. By remaining there, Black puts White in a position in which White needs a direct 4-shot to hit — the same number, 4, that White needs to cover. Black is said to have “duplicated” White’s good numbers: 4’s to hit and 4’s to cover. Notice that if Black plays 13/10 he would allow White to hit with 1’s or to cover with 4’s. Thus, White would have a much better chance for a favorable roll.

Black has an imaginative way of applying the same logic and carrying it one step further. The correct play is 7/4, 5/4, making the 4-point but giving up the 5-point.

(a) 13/10, 7/6
(b) 7/4, 5/4
This play exposes a second man and so appears dangerous. The open man on the 5-point, however, is exposed only to a 4-shot and so entails essentially no extra risk. By again duplicating 4’s, Black seizes the opportunity to take a poor roll and still make a strong offensive play. If White fails to roll a 4, Black may be able to make the 5-point to complete his prime.

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Tom Keith 2013 
Money play
Centered cube
Black rolls 3-1

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

3-1: Game BG   Equity
1 13/10, 7/6 W
−0.0290 x  (a)
2 13/12, 7/4 W
−0.1222 (0.0932) 
3 7/4, 5/4 W
−0.1275 (0.0985)  (b)

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