It's Old and Trite, but True: Rules Are Made to Be Broken
Paul Magriel, 1980
New York Times, March 23, 1980
Backgammon Many rules of thumb have been developed to guide backgammon players through standard game situations. An advanced player, however, will not hesitate to deviate from the guidelines if the circumstances demand it.

In the diagrammed position, Black has all his men in his home board and is ready to bear off. Meanwhile, White is sitting on the 1-point, hoping for a last-minute shot at Black. If he fails to hit Black, he is in jeopardy of losing not only the game, but possibly a gammon (double game).

White’s chance for a shot is much better than most players realize. Trial and error have shown that, even with the best play, Black will leave at least one shot a surprising 90 percent of the time while bearing off against the 1-point. For Black, therefore, it is critical to play carefully in order to minimize this risk. Nothing is more frustrating — and costly — than being robbed of victory in this manner.

Black to play 5-1.
With the roll of 5-1, the obvious play is 6/off, simply removing a single man from the 6-point. This play gives Black a perfectly “smooth” position: He has an even number of men on all the higher points, and no gaps (or empty points) between the points he is holding. Nevertheless, Black has a better and safer alternative.

The correct play is 5/off, 5/4, completely clearing the 5-point. Black is left with three men on the 6-point and a gap on the 5-point. Thus the best play paradoxically violates two basic precepts in bearing off against opposition: Always leave an even number of men on the highest points, and try to avoid leaving gaps. Why are these rules disregarded in this case?

(a) 6/off
(b) 5/off, 5/4
By examining the reasoning behind these rules, it may be seen why they don’t apply here. First, the injunction against leaving an odd number of men on the higher points is designed to avoid giving an immediate shot. In many situations, this protects against rolling two high numbers or a high double. In this position, however, the correct play (5/4, 5/off) is absolutely safe next turn; no numbers leave shots. By contrast, after 6/off, Black is immediately vulnerable to 6-5 or 5-4. Either of these disastrous numbers forces Black to leave a double direct shot.

Secondly, the gap rule is designed to avoid difficulty in safely clearing points in back of the gap. In this position there is only one such point — the 6-point. Although the correct play does increase somewhat the difficulty of clearing the 6-point, this is compensated for by never having to worry about clearing the 5-point.

Finally, notice that the correct play gives Black a flexible position with spares on each of his remaining four points. By contrast, the attractive, “smooth” position resulting from 6/off is deceptive because Black is stripped down without any spares on the higher points. His position lacks flexibility, which may result in many dangerous sequences of rolls in the next two or three turns.

XG logo
Tom Keith 2013 
Money play
White owns 2-cube
Black rolls 5-1

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

5-1: Game BG   Equity
1 5/4, 5/off W
+0.9560 x  (b)
2 6/off W
+0.8534 (0.1026)  (a)

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