Backgammon Game Theory

by Douglas Zare
2 June 2014

Douglas Zare

This column is about the mathematical theory of backgammon, but we have hardly seen anything about the part of mathematics (and economics) called game theory. The reason is that game theory says almost nothing directly about backgammon. There are some situations which occur in backgammon where game theory is relevant, but usually not over the board.

One part of game theory studies games with simultaneous play or hidden information. Rock-paper-scissors and poker are games analyzed well by game theory. In poker, there is a mathematical theory of deception to get the most out of the fact that you know your cards but your opponent does not. In backgammon, both players can see the whole board and plays are sequential, so this part of game theory doesn't apply directly.

Combinatorial game theory studies games with alternating moves, perfect information, but no chance. For example, chess can be studied within combinatorial game theory, although it's hard to say much. A great deal can be said about the game of go, where many endgames decompose into pieces, each of which can be analyzed and quantified using combinatorial game theory. Due to the dice, combinatorial game theory does not apply to backgammon.

Money play.
Red redoubles.

White entered two checkers from the bar, so Red stopped playing for the gammon and redoubled. White thought for a long time, then passed. "What did you think of the position?" "I hoped you would take." "Do you think it's a big pass? Would you pay me 1.2?" (Rollouts say 1.2 is reasonable.)
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