When to Beaver

In backgammon a beaver is an immediate redouble by a player who just accepted a double. A player who beavers turns the cube up one level and retains possession of the cube. A rule often used in money play (but never in match play) states that a player who accepts a double may immediately redouble (beaver) without giving up possession of the cube. The opponent (the player who originally doubled) may refuse the beaver, in which case he resigns the game and loses the current (doubled) stakes. Otherwise, he must accept the beaver and continue the game at quadruple the stakes prior to the double. But when is the right time to beaver?

For bear-offs, there is a theoretical minimum beaver point of 37.5%. This corresponds to the analogous minimum take-point of 18.75%. The minimum take is realized in the position where each player has one man on the 6-point.

The minimum beaver doesn't come up in a real position. However, in the following position players can beaver with 39.6%.

The opponent (doubling) has 2 men on the 3-point and the player (beavering) has one man on the 6. The "continuous model" gives a take-point of 20%, and a corresponding beaver-point of 40%. Just as players usually need more than 20% to take, players usually need more than 40% to beaver. In a short race it depends a lot on what effect the specific position has on the cube efficiency. It is very commonly correct to beaver with a 44% or greater cubeless chance of winning. In a long race the beaver point approaches the theoretical 40%.

Of course this becomes a bit more complex with gammons.

For raccoons, it is usually true that a player should raccoon (immediate redouble by the player who just accepted a beaver) if their opponent shouldn't have beavered. But there is a class of exceptions called the Kauder Paradox positions. The sequence double/beaver/raccoon may be correct.

Finally, there are positions which a player should beaver if and only if their opponent can't (or won't) raccoon.