Problem 143 Solution

The probability of a win for A, or of rolling a 12 on any given roll is (1/6)*(1/6) = 1/36.

The probability that the (x-1)^th roll will be a 7 is 1/6 and the probability the x^th roll will be a 7 is 1/6, thus the probability of the x^th roll being a win for B is also (1/6)*(1/6) = 1/36.

Thanks to Extra Stuff: Gambling Rambling by Peter Griffin for this problem. See chapter 6.

Michael Shackleford, ASA, August 19 1999

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