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.