I tried this out last night, and players seemed to like it a lot:
On a natural 20 a player must make a quick decision before rolling damage:
1. Double the result of the roll, or
2. Roll double damage dice
The player is choosing between a flat distribution and a bell curve. This has very real strategic implications, and there are definitely situations where one would be preferred over the other. This is a nice little way to introduce some abstract strategy without bogging things down.