To make the game fair, who should gain points if a 1 is rolled, and how many points should they gain?

Question

A single six-sided die is rolled and point values are assigned to each outcome. The dice is rolled once and if the dice shows a 5 or a 6, Joe gains 6 points. If the dice shows a 2,3 or 4, Fred gains 1 point.

Answer 1

Die Reward Probability Probability * Reward

1 +x 1/6

2 Fred +1 1/6 1/6

3 Fred +1 1/6 1/6

4 Fred + 1 1/6 1/6

5 Joe + 6 1/6 1

6 Joe + 6 1/6 1

To be fair both Joe and Fred should have same expected outcome. Expected outcome = sum of Probability * Reward. So far joe has expected outcome of 2 and Fred has expected outcome of 1/2. This means Fred has to make up 1.5 point in expected value. so expected result (x) * 1/6 must = 1.5, so Fred must be able to get 9 points for getting a 1.