Discrete Probability Distributions — Grinstead & Snell
Mathematics — Probability · simulation-discrete-probabilities
Problem
You are offered the following game. A fair coin will be tossed until the first time it comes up heads. If this occurs on the jth toss you are paid 2j dollars. You are sure to win at least 2 dollars so you should be willing to pay to play this game---but how much? Few people would pay as much as 10 dollars to play this game. See if you can decide, by simulation, a reasonable amount that you would be willing to pay, per game, if you will be allowed to make a large number of plays of the game. Does the amount that you would be willing to pay per game depend upon the number of plays that you will be allowed?