Taking Count

by Douglas Zare
4 January 2013

Douglas Zare

A fundamental difference between backgammon bots and people is that people try to find the right play, while bots try to evaluate each position. We look at a position and find criteria for safe play versus bold play, for example, while bots simply evaluate each possible result of making a move. Our approach may be more effective for identifying patterns which let us generalize from a smaller experience, but occasionally it is good to try to think like a bot.

One type of position where it is better to try to think like a bot is volatile cube decisions in the endgame. In some of these positions, the easiest way to decide whether you have a take is to try to count 9 wins out of 36 rolls. You go through the rolls, counting each nondouble twice, and evaluate each of these as some fraction of a win, grouping similar rolls.

If you try to find the right move and err, you might have the wrong rule of thumb, or your heuristics might not apply to the particular example. These are qualitative and are hard to analyze directly with mathematics. However, if you try to evaluate positions and err, your error can be put into at least one of the following categories.

  • Evaluation: You misevaluated subsequent positions.
  • Counting: You miscounted the groups of later positions.
  • Arithmetic: Your evaluation of this position does not match the average of your evaluations of later positions.

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