In a certain game, Players 1 through 5 take turns rolling a standard six-sided die, beginning with Player 1 If a six is rolled, that player wins. If any other number is rolled, the die is given to the player whose number corresponds to the number rolled, even if that is the player whose turn it currently is. What is the probability that Player 1 wins? Express your answer as a common fraction.
Player 1 has a 1/6 (1 in 6) chance of winning because there are 6 numbers that he can roll but only one that he wants to roll.