The game goes this way:
There are 6 players, numered 1 to 6 (Player 1, Player 2,...,Player 6).
Player 1 starts the game, he rolls a dice with six faces. If the result (x) of rolling the dice is 1 then Player 1 wins. Else the player number x starts his turn. The game goes on and the Player x rolls the dice, if the result (y) is equal to x then Player x win, else it's the turn of Player y. And so on.
What is the probability of the Player 1 to win?
Thank you.
Player 1 has probability $A$, all the others have probability $B$.
$A+5B=1$
Player 1 could win now, or later.
$A=(1/6) + (5/6)B$