MathDB
Miklos Schweitzer 1965_10

Source:

September 25, 2008
probabilityprobability and stats

Problem Statement

A gambler plays the following coin-tossing game. He can bet an arbitrary positive amount of money. Then a fair coin is tossed, and the gambler wins or loses the amount he bet depending on the outcome. Our gambler, who starts playing with x x forints, where 0<x<2C 0<x<2C, uses the following strategy: if at a given time his capital is y<C y<C, he risks all of it; and if he has y>C y>C, he only bets 2C\minus{}y. If he has exactly 2C 2C forints, he stops playing. Let f(x) f(x) be the probability that he reaches 2C 2C (before going bankrupt). Determine the value of f(x) f(x).
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