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.

  • $\begingroup$ There is a similar question asked recently. Please look up $\endgroup$ – Shailesh Oct 11 '15 at 3:08

Player 1 has probability $A$, all the others have probability $B$.
Player 1 could win now, or later.
$A=(1/6) + (5/6)B$

  • $\begingroup$ Could you please explain the second equation deeply?? I can't understand where that 5/6 comes from. Thank you $\endgroup$ – Samantha Oct 1 '15 at 17:55
  • $\begingroup$ Player 1 has $1/6$ chance of winning immediately, and $5/6$ chance of missing, in which case she becomes just 'one of the others' with a chance $B$ of winning. $\endgroup$ – Empy2 Oct 1 '15 at 19:05

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