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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

SIMULATION EXAMPLES

GAMBLER’S RUIN in a FAIR GAME

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
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