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Very nice, but just a tad conservative for raw pip counts

Posted By: Timothy Chow
Date: Thursday, 4 February 2010, at 1:51 a.m.

In Response To: Very nice, but just a tad conservative for raw pip counts (Bob Koca)

Bob Koca wrote:

Isn't the problem small enough that an exact recursive algorithm could calculate equities for all those positions?

Hmmm...maybe you're right. There are about 17 million ways to distribute up to 15 checkers across 12 points. So if we restrict attention to races in which both players have all their checkers on their own side of the board (and if we assume that, say, White's pip count is lower than Black's), then there are about 150 trillion positions to consider. Either player could be on roll and the cube could be in three different positions, so that's another factor of 6. This puts us close to 1 quadrillion. But this is an overestimate because we would be satisfied with considering only positions with pipcounts of less than (say) 120. So yes, it looks feasible, although the fastest algorithm would probably need a large amount of memory.

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