The ante one game involves k players, with initial integral fortunes w1, . . . , wk.
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The ante one game involves k players, with initial integral fortunes w1, . . . , wk.
At each play each of the players whose current fortune is positive puts 1 in the pot, which is then equally likely to be won by each of them. That is, if there are currently r players with a positive fortune then each has probability 1/r of winning the r dollars in the pot. This continues until one of the players has a fortune of w =
k i=1 wi. Find Pj , the probability that player j is the one with final fortune w.
Hint: Let Zn be the fortune of player j before game n.
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