Complementary Dice

Two players are playing a game by rolling a single standard die. Player $1$ rolls first. If the top surface of the die shows $1$ or $2$, then he wins. If not, then Player $2$ will roll the die. If the top surface of the die shows $3$, $4$, $5$, or $6$, then he wins. Else, the game is continues until there is a winner. Let $p_1$ and $p_2$ represent the probabilities that the two players win, respectively. Find $\text{max}\{p_1,p_2\}$.