You’re playing a 5-point match, and you lead 3-to-1. You need two points to win, your opponent needs four. The next game starts out favorably for you. What’s your proper cube strategy?

This scenario is among the most common in tournament backgammon, and among the most frequently mishandled. The leader’s doubling strategy can be succinctly summarized in these two rules:

Rule 1: If there is any significant contact in the position, don’t double, no matter how big a favorite you are. Play for the gammon instead.

Rule 2: In a non-contact position, double when you are better than 80% to win a cubeless race. In races, this usually occurs with about a 13% or better lead in the pip count, or in short bearoffs with a slightly more favorable than normal 3-roll position.

To understand these rules, we first need to look at the situation from the trailer’s point of view, and understand his taking point. If the trailer drops a cube, he will need to win four points to the leader’s one, starting with the Crawford Game. To win the match, the trailer will most likely need to win three games in a row: the Crawford game itself, the next game after an automatic immediate double, and the final game at double match point. The trailer’s chances are actually a bit better than this, since a gammon in the Crawford Game leave him needing only one more game, while a gammon in the post-Crawford game also wins the match. The effect of all this is that the trailer’s chances if he drops at 2-away 4-away are in the neighborhood of 17% to 18%, depending on whose Match Equity Table you use.

If the trailer takes a cube, he will of course automatically redouble the following turn. From the leader’s point of view then, a double will result in one of two outcomes: the leader will win one point, or the leader will own a dead 4-cube next turn.

So what should the leader do? If there is contact in the position, he should usually play on for an undoubled gammon with any kind of advantage. Consider this position:

White on roll, leading 3-to-1 to 5.

Here White would have a nearly optimal double in a money game, with a strong anchor and plenty of threats to make a prime. (Black would have a small pass.) At this score, however, White can’t consider doubling. Black’s raw winning chances in a cubeless game are in the 27% range, far above his dropping point. If Black has such a trivial take, and there are reasonable gammon chances, White doesn’t have a good double. Instead, White should simply play on to see if his gammon chances develop.

In a non-contact position, White can use the cube effectively. He simply has to reach a position where he’s a big enough favorite to double. In practice, this point comes when he’s very close to Black’s take point, with some market losing sequences. The next diagram shows an example of a position of this type.

White on roll, leading 3-to-1 to 5.

White leads in the race by 100 to 114, or 14% of the pip count. His cubeless winning chances are a little over 81%, which gives him almost an optimal double and Black a narrow take (with a forced redouble next turn, of course). In most medium to long races, this 13% to 14% lead indicates winning chances in the desired range.

In effect, White’s ability to use the cube is severely crippled when he is two points away from winning and his opponent needs four or more points. An analysis of empirical tournament results by Kit Woolsey in Inside Backgammon showed that at these scores the leader is only winning about 42% of the games!