382.Alternating Die Duel

Two players alternate rolling a die, Player 1 first. Player 1 wins by rolling a 1 or 2 on his turn; Player 2 wins by rolling a 3, 4, 5, or 6 on his turn. The game continues until someone wins. If $p_1$ and $p_2$ are the players' winning probabilities, find $\max\{p_1, p_2\}$.