What is the average result of rolling two dice, and only taking the value of the higher dice roll?
To make sure the situation I am asking about is clear, here is an example:
I roll two dice and one comes up as a four and the other a six, the result would just be six.
Would the average dice roll be the same or higher than just rolling one dice?
Answer
The number of ways to roll a number x under your definition would be 2(x−1)+1.
Therefore the expected value would be
E[X]=6∑x=12(x−1)+136x=1366∑x=1(2x2−x)=16136≈4.47
So the average is considerably higher than the average of a single die, being 3.5.
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