Win by the Easiest Way Out, or Work for Glorious Victory
Paul Magriel, 1980
New York Times, January 6, 1980
Theoretically, a backgammon player should always strive to obtain the maximum advantage from a position. But in practice, as soon as a clearly winning line of play is found, a player will often look no further. Sometimes, however, a little extra effort may reveal a refinement that increases the player’s equity at little or no extra risk.

In the diagrammed position, Black missed the opportunity for an unusual play.

Black to play 4-1.
With the roll of 4-1, he played 8/7, 8/4, making his bar-point (7-point), and bringing a builder onto the 4-point. By making the 7-point, Black trapped White behind a full prime (from the 2-point to the 7-point). The victory was now routine: Black hit White on the 1-point, closed White out, and bore off safely. Black’s winning procedure was safe and simple; how could Black have possibly done better?

Black shortchanged himself by settling for just a simple victory. To extract the most from the position, he should attempt to win a double game, or gammon, from White. If Black closes out one man, he can expect to win easily. But if Black wants to gammon White, he must somehow hit a second man.

The correct play is 11/7, 2/1*.

(a) 8/7, 8/4
(b) 11/7, 2/1*
Black again makes the bar-point, and then hits White by breaking the 2-point. Although Black is leaving a double direct shot by this unusual 2/1* play, there is no risk involved. The new prime (from the 3-point to the 8-point) prevents White’s escape. Indeed, Black hopes to be hit as White reenters so that he can “circle back” and possibly capture a second man.

To see how the “circle back” might work, consider what happens if White immediately rolls 1-3 or 2-3. He is forced to reenter, hitting Black and simultaneously breaking the 21-point. This gives Black a direct 4-shot at the needed second man.

But Black is not just relying on White’s rolling 1-3 or 2-3. By opening two points in his home board, Black can prolong the game for many rolls. Black will continue to hit White with a single man on his 1- and 2-points. As White reenters he will repeatedly be forced to hit Black back. This gives Black additional time to pick up another man as White breaks the 21-point. In fact, he may even be able to wait for shots as White breaks the 22- and 23-points.

All this may seem like a lot of work for Black. The game is already won, and even with the best play his chance for a gammon is still not great. However, as long as Black maintains a prime, he is in no jeopardy of losing. In effect, he is taking a “free shot” to gain additional points.

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Tom Keith 2013 
Money play
White owns 2-cube
Black rolls 4-1

5184 games with VR
Checker play: 3-ply
Cube play: 3-ply

4-1: Game BG   Equity
1 11/7, 2/1* W
+0.9352 x  (b)
2 8/7, 8/4 W
+0.9281 (0.0071)  (a)
3 11/7, 8/7 W
+0.9217 (0.0135) 

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