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March 15th, 2011, 03:48 AM   #1
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Probability question with dice

Dear all
I have a problem which seems very easy, but I still can't wrap my head around the math of it.

If I roll a large series of 6-sided dice, the average should be ca. 3.5. So far, so good.
However, if I were allowed to always roll two dice, and pick the highest for each cast, what would be the new average?
Surely, this isn't the same as rolling a certain amount of dice and simply crop the higher half of the results -- or is it? I may be confusing myself with the procedure.

Looking forward to your help!
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March 15th, 2011, 04:23 AM   #2
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Re: Probability question with dice

Throwing two dice and taking the maximum:



Each entry in the table has the same probability, so sum them and take the average.
The array is symmetrical.
Twice the upper-right triangle + the leading diagonal =
2 (1.2 + 2.3 + 3.4 + 4.5 + 5.6) + (1+2+3+4+5+6) = 161
161 / 36 = 4.47222...
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March 15th, 2011, 04:55 AM   #3
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Re: Probability question with dice

Thanks, aswoods, it's quite clear now
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