Sum of 5 Dice

If you roll a six-sided die, the expected value for the number rolled is 3.5. 3.5. If you roll 5 six-sided dice, what is the expected value for the sum of the numbers rolled?

15 17.5 18 20

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1 solution

Maggie Miller
Sep 3, 2015

The expected value of one die roll is 1 + 2 + 3 + 4 + 5 + 6 6 = 3.5 \frac{1+2+3+4+5+6}{6}=3.5 . Then the expected sum of five die rolls is 5 3.5 = 17.5 5\cdot 3.5=\boxed{17.5} .

While 17.5 is the mathematical answer, it is actually IMPOSSIBLE to roll 17.5 on 5d6. Thus, the correct answer should actually be 18.

Kevin Bishop - 5 years, 9 months ago

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No, 17.5 is correct - in general, you should literally expect the expected answer over one simulation! 17.5 gives the appropriate value to consider for gambling over a large number of trials.

Maggie Miller - 5 years, 9 months ago

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While I agree from a statistical point of view, that 17.5 is the correct mathematical answer; I can not agree that its the correct answer to the question as it is presented. As an avid tabletop wargamer (who happened to take a lot of math in school), I have never ever seen anyone roll 17.5 on 5d6.

Kevin Bishop - 5 years, 9 months ago

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