Cube Handling in Matches

Playing the Score:
Cube Decisions at 2-away 4-away

Kent Goulding, 1981

From Backgammon Times, September 1981.

For the most part, cube strategy is the same in match play as in money play. However, as a long match nears a conclusion, or in a short match (5 points or less), there are numerous situations where the score compels a total reevaluation of cube decisions. Take this familiar position:

13 14 15 16 17 18 19 20 21 22 23 24
12 11 10 9 8 7 6 5 4 3 2 1
White (4 away)
Should Black double?
Black (2 away)

Every money player knows (or could calculate) that Black is a 17:19 underdog in this position. Should Black be lunatic enough to double in a money game, White would laugh at him as he beavers. With cube play like that, Black will soon be playing in the penny chouette at the Salvation Army soup kitchen.

Having rehabilitated himself, Black now runs into the identical position leading 23–21 in a match to 25 for the world’s championship; i.e., he is ahead 2–0 in a four point match. His experience as a money backgammon player tells him this is not a double. Furthermore, like most players nurturing a lead in a match, he will tend to double less and pass more than usual. After all, why voluntarily risk your hard-earned advantage in marginal situations or, as here, when you are an underdog?

Why? Because you significantly increase your chance of winning the match!

The key to understanding why Black should double as an underdog leading 2–0 in a match to 4 is that the extra point risked by doubling is far more valuable to Black than it is to White. By winning two points instead of one, Black’s equity increases from 81% (his chances if he wins a single point and leads 3–0) to 100% (his chances if he wins two points and therefore the match). White, by contrast, increases his equity from 41% (his chances if he wins one point and trails 1–2) to 50% (his chances if he wins two points and ties the match at 2–2). In other words, by putting two points up for grabs instead of one, Black stands to gain 19%, or more than twice as much as White’s potential 9% gain. This is ample reason for Black to double in this one-roll position, even though he is a slight underdog.

For the skeptics among you who cannot believe it is right to double when you are behind in the game (and leading in the match, yet!), let’s compare Black’s chances of winning the match if he doubles with his chances if he doesn’t.

If Black doubles:  Black wins the match outright by winning this game 17 times out of 36, or 47.22%, and loses this game 19 times out of 36 but wins from 2–2 half the time, 1/2 × 19/36, or 26.39%. By doubling, Black wins the match 47.22% + 26.39% = 73.61%.

If Black does not double:  Black wins one point and leads 3–0, 47.22% of the time. It is generally agreed among experts that a 3–0 lead in a match to 4 is enough to win 81% of the time. (The exact calculation is quite involved.) 47.22% × 81% = 38.25%. He loses one point and leads 2–1, 52.78% of the time. It is also generally accepted that a 2–1 lead in a match to 4 wins about 59% of the time. (Some players say as low as 55%; a few say 60–61%.) 52.78% × 59% = 31.14%. By not doubling, Black wins the match 38.25% + 31.14% = 69.39%.

These calculations carry an appearance of precision which some may consider overstated in view of the imprecision in evaluating a 3–0 and 2–1 lead. Even if you disagree slightly with the 81% and 59% figures, however, the bottom line remains the same: it is clearly correct to double.

What has all this proven? Well, in this particular situation, it is correct for the person who is leading in the match to double, even though he or she is an underdog in the position. This is an extreme case that demonstrates the differences between match and money cube strategy. More stubtle are some of the decisions about taking a double at this same match score: many money passes are takes because of the distortion of cube equity. These situations are too numerous to present here, but I suggest that the reader construct some positions and examine them carefully.

More articles by Kent Goulding
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