[debacle]

Let me see if I can work through this.

Player 1 wins based on the following series:

Chance to get a 1 (turn 1): 1/6 Chance to be allowed to roll: Previous chance to be allowed to roll * 5/6 (Chance player 1 didn't roll a 1) * 5/6 (Chance player 2 didn't roll a 6) Chance to get a 1 (turns 2+): Chance to be allowed to roll * Chance to get a 1

So... summation( 1/6 * (25/36)^(n-1) )

I don't know what that comes out to be.

[kurumo]

It's actually 1/6 * Sum_n (5/6)^2n = 1/6 * 1 / (1 - 25/36) = 6/11. The first move provides a small advantage, as intuition dictates.