You play a gambling game with a friend in which you roll a die. If a 1 or 2 comes up, you win $10. How much should you lose on any other outcome in order to make this a fair game? $

Question

You play a gambling game with a friend in which you roll a die. If a 1 or 2 comes up, you win $10. How much should you lose on any other outcome in order to make this a fair game?

$ 

Answer 1

In order to answer this question, you have to make two assumptions. The first is that this is a standard six sided die (there are other shapes possible). The second is that this is a fair die (each side has the same probability of coming up). Given those two assumptions, in order to make this a "fair" game, this means that the average outcome is zero (over the long run, you win as much as you lose). The problem states that if you roll a 1 or 2, you win $10.

Number Outcome

1 +10

2 +10

3 -x

4 -x

5 -x

6 -x

Therefore, 20 - 4x = 0, so x= 5. Therefore, if you lose $5 if you roll a 3, 4, 5 or 6, the game will be fair.