Backgammon

We return to the game where we left off last week. White on roll - should he double? Should Black take or drop?

Edward O Thorpe is famous in the world of blackjack for his theories, published in Beat the Dealer. What is less well known is that he also studied backgammon, and developed a formula for accurately evaluating racing positions which takes into account distributional features as well as the pip count.

Calculate the leader's (L) adjusted pip count as follows:

(1) Calculate the normal pip count. (2) Add two for each remaining man. (3) Add one for each man on the 1-point. (4) Subtract one for each point in the home board with at least one man on it. (5) Add 10 per cent to the total if it is less than 30.

Do the same for the trailer (T) but omit step (5). If T > L-2 the leader should double. If T > L-1 the leader should redouble. If T > L+2 the trailer should pass.

In the problem above, White's count is 38.5 (21+16+2-4+3.5). Black's count is 38 (29+12+0 - 3). Thus, according to Thorpe's formula, White should double and Black should take. Checking against the Sconyer's CD of bear-off positions shows this to be the correct answer.

Thorpe's formula is remarkably accurate for this type of position, and it fails only when it comes up against really strange distributions.

Use of Thorpe's formula will strengthen your doubling decisions in races and bear-offs. In the chouette from which this position was taken White, the box, redoubled to 4. Two of my team-mates passed, the other two of us took and we were rewarded when we threw a timely set of double fives on the last roll.