1. GAMBLER’S RUIN in a FAIR GAME
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