Problem 33 Solution

The probability the first player will lose is 1/6 * Sum for i=0 to infinity of (5/6)2i = 1/6 * 1/(1-25/36) = 6/11.

Mark Perkins suggested an alternative solution:

p = 1/6 + (5/6)*(1-p)
6p = 1 + 5 - 5p
11p = 6
p = 6/11

Michael Shackleford, A.S.A., Jan. 6, 1999