Question

You are at a Casino and have two dices to play with. You win $10 every time you roll a 5. If you play till you win and then stop, what is the expected payout?

Answer 1

Let’s assume that it costs $5 every time you want to play.

There are 36 possible combinations with two dice.

Of the 36 combinations, there are 4 combinations that result in rolling a five (see blue). This means that there is a 4/36 or 1/9 chance of rolling a 5.

A 1/9 chance of winning means you’ll lose eight times and win once (theoretically).

Therefore, your expected payout is equal to $10.00 * 1 — $5.00 * 9= -$35.00.