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What Is The Expected Value Of 2 Dice Rolls? Let’s start with 2 rolls of a 6-sided die (or rolling 2 6-sided dice) and taking the sum of the outcomes. Of course, multiple dice rolls (or dice rolls for a die with more or less than 6 sides) will give us different expected values. However, if we roll a 6-sided die many times, the average outcome will be 3.5.Īs an example, if we roll a 3 and then a 4, the average of the two die rolls is (3 + 4) / 2 = 7 / 2 = 3.5. Note that an outcome of 3.5 is not possible with a single die roll.

(EV) This table illustrates the concept of The table below illustrates the concept of expected value of a 6-sided die roll in another way: with outcomes, probabilities, and their products. We take the product of each outcome and its probability and then add up those products to get the expected value (EV) of rolling a 6 sided die:

The possible outcomes are the numbers 1 through 6: 1, 2, 3, 4, 5, and 6. In this case, for a fair die with 6 sides, the probability of each outcome is the same: 1/6. The expected value of a single die roll is 3.5, assuming a fair 6-sided die (the numbers 1 through 6 are printed on the sides and appear exactly once each, and the probability of each outcome is 1/6).