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SIMULATION EXAMPLES

SIMULATION EXAMPLES. GAMBLER’S RUIN in a FAIR GAME. Gambler’s Ruin in a Fair Game. In a fair game, let player A has a fortune of k and player B has a fortune of l . At each iteration of the game, the winner takes one unit from the loser. The game ends when one player loses everything.

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SIMULATION EXAMPLES

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  1. SIMULATION EXAMPLES GAMBLER’S RUIN in a FAIR GAME

  2. Gambler’s Ruin in a Fair Game In a fair game, let player A has a fortune of k and player B has a fortune of l. At each iteration of the game, the winner takes one unit from the loser. The game ends when one player loses everything. • What is the probability that player A will lose everything? • What is the expected duration of the game in terms of total number of iterations?

  3. Analytic Solution vs. Simulation Applying “First Step Analysis” • Player A will lose everything with probability • The mean duration of the game is What about simulation results for k = 4 and l = 6? • A typical game • Estimation after 1 Million Games

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