Cube Handling

The Expert's Error
Kit Woosley, 1983

From Backgammon Times, Volume 3, Number 1, Winter/Spring 1983.

An expert sits down to play a long match (say 15 points) against weaker competition. He says to himself: "I am virtually sure to win this match if I can keep the cube low and grind out 1-point victories. The only way I could lose would be to lose a couple of large games. Consequently, I will only double when my opponent has a clear pass, and I will never take a double if it is remotely close. In this way the cube will almost never get above the 1-level, and I am sure to win because we will play so many games."

This assessment of the expert's chances in the match would be correct if there were no cube in play. My computer simulations show that a 55–45 edge in every game would make a player better than 70% to win a 15-point match with no cube, and a 60–40 edge in each game would make him better than 85%. However, there is a cube in play. It would be nice if the weaker opponent were to adopt the same super-conservative cube strategy. In fact, we all know that the easiest kind of opponent to play against is one who never takes and, more important, never doubles. But if the weaker opponent is using reasonably good cube strategy, then the super-conservative approach by the expert will reduce his chances of winning the match rather than increasing them, and if he overdoes it he may actually become the underdog.

Let us see why the "grind 'em out" approach doesn't work. Suppose the expert always waits until he is an 80% favorite to double, at which point his opponent will pass. Suppose further that his opponent is doubling fairly normally, at about a 70% favorite on the average, which the expert passes since he is playing his super-conservative strategy. We won't see many 2-cubes, but the expert won't win as many of the 1-games as he thinks he should. If the expert is a 55–45 favorite in the starting position, he must increase his equity by 25% in order to reach the 80% mark where he claims. His opponent, on the other hand, also needs only a 25% increase, for he claims at the 70% mark. The super-conservative strategy by the expert has the effect of equalizing the match.

Another drawback to never playing a game out is that the expert does not have the opportunity to fully exploit his superior skill with the checkers. These days, anybody can play the opening moves fairly accurately. The expert's advantage in play is largely his superior technique which safeguards the win or squeezes a gammon out of a good position, which the weaker player might misplay, or his ability to make the most of his chances from an inferior position, which the weaker player will not do as effectively.

An interesting illustration of this principle occurred in a recent 5-point match I played against a weak player. In the first game, I took a double which was a very marginal take in a complex position. One of my students was watching, and he was shocked that I had made such a questionable take against a weak player in a short match. As the game progressed, my opponent handled the position badly, and I eventually turned the game around. My student said to me later, "I see—you took that double because he was a weak player." This was correct. The possibility of his misplaying the position brought my winning chances above the 25% mark. Against a strong player, passing would have been correct. In general, it pays to be more aggressive in cube action against weak players, so games have to be played to the finish. Also, you never know when he might pass one of your loose doubles.

Another argument against the super-conservative approach is that the expert is relinquishing one of his advantages—superior cube judgment. If he plays his normal game he will make better cube decisions than his opponent, but if he never takes and never doubles he is throwing this advantage out the window. In this day and age when most tournament players can move the checkers reasonably well, superior cube judgment should be the expert's main advantage.

The prospect of a high cube against a weak player scares the expert. It shouldn't. Take this example at 0–0 in a 7-point match.
12 11 10 9 8 7 6 5 4 3 2 1
13 14 15 16 17 18 19 20 21 22 23 24
Weak Player (7 away)
Black redoubles to 4.
Should Expert take?
Expert (7 away)
Most experts playing a weaker player will fold a redouble to 4 when the opponent has a man on the 3-point and a man on the 2-point and a 1-roll bearoff (25 wins, 11 losses), although taking is theoretically correct.

I think they are wrong. The weak player is far more likely to make a terrible cube blunder at a lopsided score (4–0 either way) than he is at a relatively close score (2–0 his favor). If the score is close, normal money cube actions are generally correct, but lopsided scores involve unusual cube actions which the weaker player might not be familiar with, so the expert can increase his advantage.

A classic case of cube fear occurred in a much discussed position from a match at the Holiday Tournament between an expert and a weaker player. In a 19-point match, the expert was ahead 8–2, but was redoubled to 8 in a very complex position in which it was not clear who was the favorite. The expert chose to pass. When I was shown the position and given the conditions I said I would take—how could I pass when I might be the favorite (subsequent rollouts proved that the expert had, in fact, given up 4 points when he was winning). When Bill Robertie, one of the few other takers, was asked how he could take an 8-cube in a match, his simple answer was, "It's the only cube there is." This is the kind of attitude which allows the expert to realize his full advantage.

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