8/5/2023 0 Comments Dieroll 21 12![]() 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). The expected value of a dice roll is 3.5 for a standard 6-sided die (a die with each of the numbers 1 through 6 appearing on exactly one face of the die). (You can also watch a video summary of this article on YouTube!) What Is The Expected Value Of A Dice Roll? In this article, we’ll talk about the expected value for various dice rolls: 4, 6, 8, 12, 20, and N-sided dice. Of course, we can also look at products, minimums, and maximums of dice rolls and get different expected values for these as well. ![]() Dice with a different number of sides will have other expected values. The expected value of the sum of two 6-sided dice rolls is 7. This assumes a fair die – that is, there is a 1/6 probability of each outcome 1, 2, 3, 4, 5, and 6. So, what is the expected value of a dice roll? The expected value of a dice roll is 3.5 for a standard 6-sided die. However, it is often presented in the context of dice rolling, where probabilities are uniform and calculations are easier to perform. Expected value is a useful tool for analysis in business and in game theory.
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