Evaluating Positions in Backgammon Strategy

The backgammon doubling cube forces you to decide whether you want to play at double the stakes or concede the game at single stakes. Novice players do not have an explicit backgammon strategy in such situations but go on their gut feel. However expert players systematically evaluate their position using a concept known as backgammon equity.

You can win a normal backgammon game and get the points at stake. You can gammon your opponent and win twice the staked points. Or you can backgammon your opponent and win thrice the staked points. Similarly you can lose in three ways giving a total of six outcomes in the backgammon game. As a part of the backgammon strategy of evaluating positions using equity you need to assign percentages to each of these options.

Not all six options will be possible at any time. Suppose you are playing for 1 point at $1 per point and you have a 30% chance of winning a single backgammon game and winning 1 point, a 40% chance of losing a single game and losing 1 point and a 30% chance of losing a gammon and losing 2 points. Then your backgammon equity becomes 0.3(+$1)+0.4(-$1)+0.3(-$2), which is -$0.7. If your opponent now plays the backgammon doubling cube what should your backgammon strategy be. If you refuse the double you lose the backgammon game at single stakes, that is $1. If you accept the double then the stakes get doubled and with it your backgammon equity and you expect to lose $1.4. Hence the correct choice when the doubling cube is played in this situation is to quit.

This is how the concept of backgammon equity is used to evaluate positions and formulate the correct backgammon strategy when faced with the play of the backgammon doubling cube.