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Early Beavers

by Bill Robertie
1 August 2001

Bill Robertie

The beaver is an interesting addition to backgammon which dates back to the 1960s. It allows players to punish an opponent for a grossly incorrect double, while also setting a trap for the player who is too eager to raise the stakes. Beavers are not allowed in tournament play under any circumstances.

The basic idea of a beaver is this: In a money game in a more or less even position, your opponent suddenly doubles you from one to two. You can, if you wish, simply keep the cube on two, satisfied that your cube ownership now makes you a favorite in the game. But you can also beaver, turning the cube another notch, from two to four, but still keeping it on your side. Now if the game turns solidly in your favor and you redouble, the cube will be moving to the 8-level.

Beavers certainly juice up the game, which is why serious money players love the rule. But beware: The beaver rule contains a subtle drop of poison. Most incorrect doubles are not proper beavers. A beaver is only correct if, in the position after the beaver, you are actually the favorite in the game, owning the cube. That's a tall order. In most cases, incorrect doubles reduce the doubler's equity, but leave it positive. In that case, beavering is a blunder which makes you a bigger underdog in the game! Let's take a look at a practical example.


		Pip: 157

		Pip: 157

This position arose from the opening sequence White 3-1, Green 4-3 (splitting), White 4-2, Green 4-3. White now decides to double. What should Green do?

The answer is that Green should just take - he should not beaver. Although White's double is incorrect, White remains a favorite in the game even with Green owning the cube, so a beaver would not be profitable.

In the old days before Snowie and Jellyfish, we had to make rough, educated guesses in these positions, but now with can quantify these positions much more precisely. If White doesn't double in Position 1, but plays on with the cube in the middle, his equity is about 0.35. (In other words, White would win about 35 points in 100 games played from this position with the cube in the middle.) If White doubles to 2 and Green takes, White's equity drops to 0.20. White would be making less money than before (that's why his double was a mistake), but he'd still be making money. If Green does beaver from 2 to 4, White's equity doubles from 0.20 to 0.40. Oddly enough, a beaver would make White's double correct, since he would now be earning more money with the cube on Green's side at 4 (0.40 points per game), than with the cube in the middle at 1 (0.35 points per game).

There's a wide range of positions with are incorrect doubles but not beavers. In fact, most incorrect doubles fall into this category:


		Pip: 167

		Pip: 160

Green wins the opening roll with a 5-2 and brings two checkers down. White decides to juice up the game and doubles. Now Green has a beaver. In fact, the beaver is huge, earning Green more than 1/3 of a point. In fact, any time your opponent doubles after you win the opening roll, you have a proper beaver.


		Pip: 137

		Pip: 137

Symmetrical positions in the early going tend to be beavers. Being on roll makes you a slight favorite in a cubeless game played to the end. (Here White is about 52% to win, cubeless.) But the advantage of holding the cube for the rest of the game more than compensates for that. Here Green should beaver if doubled.


		Pip: 162

		Pip: 165

Incorrect blitz doubles tend not to be beavers. The gammon chances inherent in even an unfavorable blitz tend to keep the attacker in positive equity territory. Here Green opened with a 4-1, playing 13/9 24/23, and White responded with a 4-1, hitting two checkers. Green danced with a 6-6 and White doubled. Although the double is incorrect, Green should not beaver but should just take.

The positions we've looked at so far would only be doubled by a very weak player, or someone who was trailing on the score and steaming. Beavers in the opening between good players who are playing well are quite rare, since most early game positions are pretty well understood. Here's a position where even a good player might go astray:


		Pip: 166

		Pip: 146

A White player might double here, thinking that his game is positionally much stronger than Green's, and Green may have to start exposing some new blots in the near future. Indeed, White is a favorite in a cubeless game, or with the cube in the middle. But if Green owns the cube, he becomes a solid favorite, based mainly on his lead in the race. Beware of early positional doubles, unless accompanied by a racing lead.

Next time in Part 2: Beavers in later positions.

Editor's Note: This article was written by Bill Robertie at the request of GammonVillage reader Steve Baedke who was curious about when it is proper to beaver. If you have a concept you would like to see more information on, please request it by writing to editor@gammonvillage.com