I already did this question earlier in the thread "I did a limiting sum, so Pat can win on his 1st, 2nd 3rd,... role. 1/36 + (35/36)^2(1/36) + (35/36)^4(1/36) + .... Factorise 1/36 out and you should get 1/36{1 + (35/36)^2 + (35/36)^4 +....). Sum to infinity, 1/36{1/(1-(35/36)^2)} = 36/71."