Beaver - Backgammon double
Some players have introduced a fascinating but dangerous new twist to the doubling cube. If the rule is agreed (it is never played in tournaments), a player who is offered a double may beaver. This means that he immediately redoubles before the doubler has thrown, and yet he retains the cube on his side of the board. So if, for instance, the original double was from 1 to 2, he accepts it and redoubles to 4, while still retaining the normal right to offer a double (which is now to 8) in the usual way. Obviously, a player who is doubled should only wish to beaver if he considers that the doubler made a mistake in doubling. There is otherwise no point in his voluntarily doubling the stakes. But it does not follow that, just because the double was a bad one to give, it is a good one to beaver.
Look at the position in Diagram. Black may be tempted to double. He is definitely favourite and he will win more games than he loses. However, he is actually wrong to double because too often he will throw a 2 and then be unable to take a redouble. This will cause him to lose a number of games which he might have won later by throwing a double himself. He lost that chance by allowing you the opportunity to redouble when he could not accept. So, in fact, the double is a bad one to give. Black wins more points in the long run by playing on undoubled, and doubling you out the next turn, if nothing dramatic happens, than by doubling at this stage. But it would be idiotic to beaver. The game is still one where on average you are going to lose money, and so what on earth is the point of doubling the amount that you expect to lose?
But people do sometimes give doubles which are bad enough to justify your beavering and so, if you can afford the big swings which this kind of game produces, you should be happy to play the rule.