A Maximum Gain in Control with a Minimum of Danger
Paul Magriel, 1978
New York Times, December 7, 1978
Roger Low and Paul Magriel blindfolded
Roger Low and Paul Magriel play blindfolded
in a demonstration match with
Denise Hemingway and George Plimpton
In the last five years, the enormous growth in popularity of backgammon has resulted in many significant theoretical advances. Even though the game is thousands of years old, many fundamental concepts have only recently been discovered. A new generation of talented young players is spearheading this advance.

Foremost among this new breed is 21-year-old Roger Low. His play combines exceptional analytical ability with a tough competitive spirit. He alone, among all the world’s best players, seems to have the uncanny capacity to effortlessly remember whole series of games roll-by-roll and move-by-move. This same capacity has helped make him the uncontested top player in the world of blindfold backgammon.

After attending Cornell University, where he learned to play, he is now on Wall Street, training to be a broker, so that he can divide his time between playing on the backgammon board and on the Big Board.

Black to play 1-1.
In the diagrammed position, Low showed his ability to visualize all the possible plays. With the roll of 1-1, Black seemingly has little choice because he cannot move the men on the 20-point or 13-point. The routine play is to hit 24/23* with the first 1, and then break the 16-point and move 16/13, putting another man safely on the mid-point (13-point).

Low discovered a better play, which many players would have overlooked — 24/23*, 16/14, 16/15. Again Black hits with his first 1 and then breaks his 16-point, but now he intentionally leaves two blots in White’s outfield.

(a) 24/23*, 16/13
(b) 24/23*, 16/14, 16/15
By leaving spare men on the 14- and 15-points, Black is able to exert more control over his own outfield. Specifically, Black gains one extra builder to make his 8-point and two extra builders for his 9-point. Black and White are engaged in a 2-way holding game — in which both sides have anchors in each other’s home boards. In such positions, outfield control is often a vital winning factor.

The additional danger incurred by leaving two blots is minimal. Surprisingly, the probability of being hit is only slightly increased (8 chances out of a possible 36, instead of 7) by this play. (Note that the duplication principle is at work here: White needs 2’s and 3’s to reenter and 2’s and 3’s to hit.) Even if White does reenter and hit, Black has little to fear because he has the security of owning the 20-point and the prospect of return shots at White’s blot on the 21-point.

XG logo
Tom Keith 2013 
Money play
Centered cube
Black rolls 1-1

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

1-1: Game BG   Equity
1 24/23*, 16/15, 16/14 W
+0.4198 x  (b)
2 24/23*, 16/13 W
+0.3849 (0.0349)  (a)

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