GAMBLER’S RUIN in a FAIR GAME

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Presentation transcript:

GAMBLER’S RUIN in a FAIR GAME 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. 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?

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