All or Nothing at All — A Basket of Eggs
Paul Magriel, 1978
New York Times, March 16, 1978
Crockford’s Club in London is one of that city’s oldest gaming establishments. It was founded in 1828 by William Crockford, and included among its original members the Duke of Wellington and Prime Minister Benjamin Disraeli.

Its most famous contribution to modern society can be traced back to the night that the Earl of Sandwich, not wanting to interrupt his gaming, slapped some beef on two slices of bread and so created the sandwich.

Today, Crockford’s actively supports backgammon at all levels. In addition to a major international tournament once a year, the club also holds local tournaments three times a week for beginners, intermediate, and advanced players. The diagrammed position occurred at one of the tournaments.

Black to play 4-1.

Black has already doubled and now has a 4-1 to play. White has a single blot on the five point, which Black was tempted to hit. However Black is unable to do so without exposing himself to a direct return shot by White. Black was deterred by White’s formidable home board — with six inner board points closed, a return hit would instantly be fatal. Indeed, Black reasoned, “I’m winning, so why should I risk losing the whole game on a single roll?” Accordingly, Black played 7/6, 7/3, safely bringing two men into his home board.

Black’s reasoning was seriously in error. The correct play is 10/5*, hitting loose (unprotected) on the five point. Black failed to appreciate that by attacking he could also win the game on a single roll. If he fails to come back in immediately, White will have virtually no chance. Black also fails to properly assess the danger of not hitting and allowing White to race.

(a) 7/6, 7/3 (b) 10/5*
In fact, neither play is truly safe. To determine which one is best, the chances of winning in each case must be compared.

1. By hitting, the game is basically reduced to a one-roll proposition. Numerically, White’s chance of rolling a 5 to hit Black is 11/36. Thus White will win approximately one third of the time.

2. By not hitting, Black allows White to race. Before Black plays his 4-1, the pip count (the total number of units left) is identical. Therefore Black’s lead in the race is very small indeed. In fact White’s possession of the doubling cube effectively nullifies Black’s lead altogether.

Rollout

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

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

 4-1: Game G BG Equity 1 10/5* W L .6587 .3413 .0250 .0557 .0003 .0003 +0.2623 (b) 2 7/6, 7/3 W L .5446 .4554 .0016 .0018 .0000 .0000 −0.0647 (0.3270) (a)

 Previous Column March 9, 1978
 Next Column March 23, 1978