SIMULATION EXAMPLES

1 / 3

# SIMULATION EXAMPLES - PowerPoint PPT Presentation

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.

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

## SIMULATION EXAMPLES

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

### 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