Don't Allow Danger to Blot Out the Odds
Paul Magriel, 1977
New York Times, December 29, 1977
Backgammon is a game of calculated risk. When your opponent has a 5-point home board, it is especially important to reduce danger to a minimum.
Black to play 6-2.
In the diagrammed position, Black, with three exposed blots, faces White’s 5-point board. When Black rolled a 6-2, there was no way for him to play completely safe. He decided to evaluate the possibilities with respect to the danger of being hit immediately:

  1. Black could play 7/1*, 3/1, hitting White on the 1-point and covering. This would not give White any direct return shots, but it would leave him several indirect shots from the bar. Specifically, White could reenter and hit Black with 3-2, 3-3, 3-4, 3-6, 4-2, and 4-6, for a total of 11 combinations out of 36.

  2. Black could play 18/16*/10, hitting White and continuing on to make his own 10-point. This move would leave White a direct shot at Black on the 3-point (11 combinations out of 36). In addition, after this move, White could also reenter and hit with 4-2 or 1-2 (4 combinations out of 36), for a total of 15 combinations out of 36 with which to hit Black.
Option 1: 7/1*, 3/1
Option 2: 18/16*/10
Based on this analysis, Black decided that the first choice was the less-dangerous play. In evaluating the danger, however, Black neglected a major consideration — he took into account only shots (number of combinations that hit), not blots (exposed men).

The correct play is actually the second choice, 18/16*/10. This move leaves only one blot (on the 3-point). Now if Black is hit, he will still retain significant winning chances. White will have no other blots to attack. To insure a victory, White would have to make the 22-point for a closeout. Because White has no builders bearing on the 22-point, Black will have several rolls in which to come in and get back into the game.

On the other hand, with the first choice, if White hits back, Black will be in a desperate position. Unless Black reenters immediately, White will probably hit Black’s other blots, not only eliminating Black’s winning chances, but gammoning him.

Very often, the play that reduces the chances of being hit is not necessarily the one that reduces danger to a minimum.

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

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

6-2: Game BG   Equity
1 18/16*/10 W
+0.4947 x  Option 2
2 7/1*, 3/1 W
+0.2357 (0.2590)  Option 1

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December 22, 1977
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January 5, 1978

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