The Value of a Rerolled Die

I’ve seen a couple of blogposts about the advantage/disadvantage mechanic in WotC’s playtest materials that suggested some interest in the underlying math.  I actually find these functions useful to have around in other situations, too, so I’m reposting this bit I wrote up for our campaign wiki.

Average Value Re-rolling a N-Sided Die, Taking the Highest Result

Average Value Re-rolling a N-Sided Die, Taking the Lowest Result

So, for a D20…

The highest of two dice averages 13.825, the lowest of two dice averages 7.175.