Let’s first enumerate the different types of cube actions. It’s customary to describe the action for both players for a given position. The common1 cube decisions are as follows:
- No double / Take (ND): Your position is stronger than your opponent’s, but it could stand to be stronger before giving up the cube. In a gammonless situation, this would correspond to a win percentage below ~70%. For example, if you only have 55% win chances, you would certainly be increasing your expected winnings by doubling; however, you are taking on more risk than necessary because you could certainly double with an even stronger position later and your opponent would still be willing to take. As for your opponent, if offered a cube in this position, they should take it in this situation.
- Double / Take (D/T): Your position is much stronger, and now you should double to maximize your winnings. Your opponent still has a take, because by accepting the cube they will lose fewer points on average, as we’ve discussed previously. This corresponds to win percentages between 70 – 77% and is what is known as the doubling window. If you don’t double now, your position might improve too much in the next roll (say, by rolling a joker 66) for your opponent to continue to be willing to accept a double.
- Double / Pass (D/P; also called Double / Drop): Your position has become too strong for your opponent to take, but probably will not result in enough gammon wins to justify playing on for more than 1 point. It’s worth doubling if only to guarantee ending the game with a win. In a sense, the existence of this category implies that once you have 80% win chances, you have reached the “finish line” in a backgammon game. You don’t need to keep playing the game out. If you do, you’re merely giving your opponent a chance to win (albeit a slim chance). This is known as “cashing the game” or “doubling out” your opponent.
- Too good to double / Pass (TG; also called No double / Pass): Your position is so good that you are expected to win more than 1 point thanks to significant gammoning chances. Here, doubling is a mistake, and your opponent will be relieved to be able to pass and lose only 1 point. A “Too good” cube is only possible in games with no Jacoby rule.
- No double / Beaver: If you’re actually in a losing position, and you make the incorrect decision to double, your opponent’s correct response would be not only to take the cube but to beaver (that is, in unlimited games that permit beavers).
These decisions lie on a spectrum, illustrated below:
As you go left from right, the strength of your position is improving: at first you shouldn’t be considering doubling; eventually, your position is strong enough that you should be considering doubling, but not so strong that your opponent wouldn’t take; beyond this, your opponent will start rightfully refusing the cube. Right in the middle of the spectrum, shaded in blue between points ② and ③, we have the famous doubling window, the sweet spot where you are ready to double and your opponent is willing to take the cube. In every other region, someone is making a mistake if the doubling cube is exchanging hands.
Further reading
- A highly recommended classic article by Peter Bell that discusses the doubling window and equity.
- Other than the cube actions listed here, there is also Too good/Take and Double/Beaver, which are both rare and too complicated to explain. At certain match scores you can also be Too good to double and No double at the same time. These situations all tend to be more of mathematical curiosities than of any practical use. ↩︎
Next lesson: Cubeful and cubeless equity
Leave a Reply
You must be logged in to post a comment.