Three people, A,B,C play a game. A rolls the die.

Then, in order of "B,C,A,B,C,A..." they each roll the die. They keep going until someone wins. To win, you have to get the same number as the previous number rolled on the die. ( A can't win with his first roll because there was no roll before to compare it too.) What is the probability that each person will win?

Ok so I used Excell after comming up with equations, is that cheating. Anyway.

P(B) = SUM (5/6)^(3n-3)*(1/6) = 36/91
P(C) = SUM (5/6)^(3n-2)*(1/6) = 30/91
P(A) = SUM (5/6)^(3n-1)*(1/6) = 25/91

(1/6) is the prob of matching any given role, thereby winning.
(5/6)^(3n-3) is the probabilty that no one will have won by B's turn in round 'n'. For every round each player roles die once, if no one wins first.

B has the best chance of winning because he is the first one to role with a chance of winning (i.e after A roles).

Posted by wonshot on 2003-11-12 15:56:41