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Probability of hitting a checker from a long running start

Posted By: ah_clem
Date: Tuesday, 1 July 2025, at 5:31 p.m.

In Response To: Probability of hitting a checker from a long running start (ah_clem)

Forgot to include line breaks:

I'd approach this recursively. Let n be the number of pips that the black checker is away from the white checker, and p(n) be the probability of hitting from there

p(1) = 11/36.
p(2) = 12/36.
p(3) = 14/36.
p(4) = 15/36 + 2/36 * p(1).
p(5) = 15/36 + 3/36 * p(1) + 2/36 * p(2).

In this tedious manner, one could recursively calculate p(n) for any n. The answer would be the limit of p(n) as n -> ∞, assuming it converges.

I'll leave the actual calculation as an exercise for the reader. (c:

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