Double Trouble

Taking the Cube in Money Games

In this week’s position analysis, we have a cube dilemma. It is a money game and Black is on roll. Should Black double? If Black does double, should White take?

This is a very interesting type of position that comes up frequently. Black is behind in the race 15 pips, but he clearly has a positional advantage. There are many good numbers black could roll on his next roll that could cause big problems for White. For example, with a 5-3 black hits and makes the 4 point and that could easily lead to a gammon victory for black. A 5-4 does the same, but does give White a slight chance to roll a 6-2 and get back in the game. But just about any hit is a problem for White. 

So if you are Black, and thinking about doubling, here’s one way I approach it: “How would I feel if I don’t double and roll one of those wonderful numbers?” Pretty bad. Then I ask myself another question: “If I were White, would I want to see the cube here?” I’m pretty sure that anyone playing White would be relieved if Black did not turn the cube, and that tell me, more than anything, that Black should double.

So the first half of the answer is yes, Black should double. Things could go wrong…he might not be able to hit White, and White could escape and win the race, but when that happens he loses 2 points. If he doubles and things go well, he wins 2 point, but sometimes he also wins 4 points…so that potential for gammons add a lot of reason to double. By the way, if you put this into GNUBG or Snowie (backgammon computer programs) to get the answer, they will confirm that it is right to double and it would be a big blunder not to.

For me, this was a much tougher decision. Even if Black doesn’t roll one of his good pointing or hitting numbers on the next roll, White would still have to roll a 6 to get out and to have a chance in the race. Since the odds are against rolling a 6 on the next roll (25 to 11 against), it looks like a tough take. 

In the actual game I was playing, which was a chouette (several people playing at once against me), I doubled and 3 or my 4 opponents dropped. The one opponent who took, happened to be a very fine player, so all of us wondered if maybe he was right, and that is why I took a picture of the position and ran it through the computer. 

Sure enough, it is a clear take. And it’s a take because White is ahead in the race; because he might well get a shot and could win that way; and primarily because of the total math involved. If White drops, based on the total number of likely wins, losses, and gammons, he is giving away .50 of a cube equity. What that means is that if he is playing for $1 a point, he has thrown away 50 cents by dropping, in the long run, as opposed to taking. What this means is that he will still, in the long run, lose money if he takes… he is clearly an underdog, but he will lose half as much, statistically, by taking, than he would be dropping.

Another way to say this is that if he played this game 100 times and dropped every time, he would lose 100 points, or at $1 a point, $100.00. But if he took it every time and won about 1/3 of the games, as he should, he would only lose 50 points, or $50.

So the decision to take a cube, in money games, really boils down to whether or not you can win over 25 percent of the time or not, and in this case, you certainly can.

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