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A game is played with the following rules. Two ordinary number cubes, each with six sides labeled 1 to 6, are rolled. After each roll a player is given a certain number of points depending on the outcome.
If the sum is 2 or 12, the player receives +6 points
If the sum is 3 or 11, the player receives +2 points.
If the sum is any other number, the player receives –1 point.
What is the expected value of the number of points a player will receive after a roll?
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Having 36 possible outcomes;
2 = 6 points
4 = 2 points
30 = -1 point
The expected number of points received is
(2*6 + 4*2 + 30*-1)/36