He Who Hesitates May Lose Gammon
Paul Magriel, 1977
New York Times, October 20, 1977
Nothing is more exasperating in backgammon that to have a gammon within your grasp, only to be hit in the bearoff. By making the proper percentage play, the skillful player finds himself less often bemoaning such accidents. The situation described here occurs frequently in practice, yet, surprisingly, few players know the correct procedure.

Black to play 4-2.

In the diagrammed position, Black, with all 15 men in his home board, is ready to begin bearing off. Black has a 4-2 to play which gives him two options:

  1. He can play 4/off, 2/off, bearing two men off.
  2. He can play 6/off, using the whole roll to bear a single man off the 6-point.

The novice may choose option 1, simply to remove his men as quickly as possible. This approach is superficial. Black’s objective is to bear off all his men as safely as possible, not necessarily as quickly as possible. As long as he avoids being hit, both the game and the gammon as assured.

The problem confronting Black is to find the safest procedure. Because White holds the 5-point, the danger lies in clearing the 6-point. Thus the only relevant difference between the two options is the number of men that would remain on the 6-point after each play. A more experienced player will attempt to assess the options by using his knowledge of the odds. He computes how many ways, in each case, Black would be forced to leave a man exposed on the 6-point on the following roll:

Option 1: 4/off, 2/off
Option 2: 6/off
Option 1. This leaves three men on the 6-point and forces Black to give a shot only if Black rolls a 6-5 (two ways out of a possible 36).

Option 2. This leaves two men on the 6-point and forces Black to leave a shot next time with either 6-1 or 5-1 (four ways out of 36).

Based on this comparison an experienced player, like the novice, would also choose option 1, for its apparent safety value. However, the expert sees a flaw in option 1. In backgammon, sometimes a little knowledge of the odds can be misleading.

The safety of option 1 is illusory. This play is safer only on the very next roll. Black must instead consider the overall problem of removing all his men from the 6-point. Option 1 is ultimately more dangerous because Black only delays clearing the 6-point. Unless Black is lucky enough to roll a double, he will eventually reach the option 2 result anyway — two men on the 6 point. He is merely postponing the same danger he was trying to avoid. Thus option 1 places Black in double jeopardy; that is he exposes himself both to the risk of rolling a 6-5 in the three-man position immediately and later to the risk of rolling a 6-1 or a 5-1 in the two-man position.

The correct play, 6/off, immediately prepares Black to clear the 6-point, without first incurring an additional risk. This play, even though twice as dangerous on the next roll, is safer overall. In fact, a refined mathematical analysis shows that Black is actually 30 percent more likely to be hit sometime during the bearoff by exposing himself to double jeopardy with the incorrect play.

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Tom Keith 2013 
Money play
White owns 2-cube
Black rolls 4-2

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

4-2: Game BG   Equity
1 6/off W
+1.8814 x  Option 2
2 4/off, 2/off W
+1.8640 (0.0174)  Option 1

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