Monday, March 1, 2010

Monday Probability 8: N Gamblers

In a game of N gamblers, the i-th gambler starts the game with a_i dollars. In each round, two gamblers selected at random make a fair bet, and the winner gets a dollar from the loser. A gambler losing all his money leaves the game. The game continues as long as possible, i.e., until one of the gamblers has all the money. What is the expected number of rounds played?

Answer: 1/2 * [(SUM(ai))^2 - SUM(ai^2)]

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