by Douglas Zare
1 May 2010
A key idea in backgammon is equity, the average value of a position assuming perfect play. This is a weighted average over all of the possible sequences of rolls, giving the sequences appropriate weights assuming the dice are fair.
We are rarely able to check the true equity of a position. The main reason is that the set of all possible sequences is extremely large, in fact, infinite, so we can't list all sequences and check them. In addition, we don't know how to play perfectly, but even if there were no arguments about how to play in each later position, it would still be difficult to determine the equity of a position.
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