Modular Dice, Revisited
In retellings of D&D, people tend to remember very good and very bad rolls (even though in principle, a very close roll should be just as exciting). How can we craft a dice mechanic so that these more exciting outcomes are more common? What can replace the d20? We can use modular dice rolls to achieve this effect.1
6d6-1 mod 20 gives you an “inverted” bell curve (slightly favoring success). 
In general, you can do this by starting with any bell curve and “centering” the expected value around 20. But a sharper bell curve, like 10d4+15 mod 20, gives more exaggerated results. 
We can do better: 10d2+25 mod 20 excludes many of our “boring” results completely. 
In fact, the inevitable caboose on this train of thought is 1d2+19 mod 20: a coin flip. 
Obviously, these are all very silly.↩︎