D20 vs. 2d10 vs 3d6

Christina Freeman

There is another key difference between a d20 system and a 2d6 system - the bell curve created by the die roll. A +1 bonus actually has a difference in effect depending upon the roll, simply because it is NOT a flat +5% chance. As such, you might find that changing from d20 to 2d10 might also work (or even 3d6, as suggested by monte cook).. I actually prefer a 2d10 system myself... the bell curve isn't as steep as with 3d6, \

Matt Miller

Bell curves are both good and bad. They make the expected range of numbers more predictable, adding bonuses to them shifts the peaks out of phase by changing the mean.

Matt Miller

The intersect between the two curves is when the blue player can reasonably expected to beat the red player. Assuming that area is equal to a third of the area under the curve, the blue player must roll in their top 1/3 at the same time the red player rolls in their low 1/3, which will only happen 1/9 of the time. This is for a difference in means of 2. The case is even more severe if the difference is larger. 

d20 has a 'flat' distribution, with much more variance. d20+2 will beat d20+4 fully 20% of the time. d20 still has a 1/400 chance of beating a d20+19. I also like the d20 'explode' rule, where 20 hits and 1 misses, better; there is always a chance of success or failure, regardless of other conditions. Opposed rolls (d20 vs. d20 or 3d6 vs. 3d6) are analogous to 2d6, where the resulting roll is very much a bell curve. 3d6 vs. 3d6 creates a very strong, very regular bell curve, where the difference in medians is decisive a very large amount of the time. Using one mechanic for 'tests' vs a DC and one for opposed rolls would not be a terrible idea...

Simplicity in mental math is its own virtue. Rolling 3d6 vs 3d6 for every roll is 7 mental operations. d20 vs DC is 1.

Julian Stanley

For the record, Monsters & Magic is 3d6 vs. Difficulty or an AC score.