The "math" of RPGs

[GMMichael]

But it also makes it more likely that in some of the combats you experience, you will have very one-sided roll.

Ah. The argument I was referencing suggested that TPKs happen more often. Which was incorrect. Happening more or more often are two different things.

I'm no good at the math thing, but does a single die even have a "average" result, mathematically. I know that like 3d6 has a bell curve, but a d20 doesn't. Just curious as I'm am whatever the opposite of a math geek is...

Average roll of a d20 is 10.5. Chance of any one result: 5%. The d20 gets called "swingy" because of that 5%. Odds of rolling a sum of 10 are significantly greater with 3d6 than on 1d20, for example.

 

[Fenris-77]

The swingy-ness of the d20 is significantly reduced by the way most system add bonuses to various rolls. The basic roll is no swingier that percentile (duh) but the mods in d20 systems work from 5% and go up. 5E, as an example, is not really significantly swingy on any roll that matters for a given PC given the mods in play. Frankly, I think a lot of people don't realize how constricting mechanics like the 2d6 bell curve is in terms of useful results and the resulting design space for modifiers. PbtA as a chassis is great, but also distinctly limited in a bunch of ways because the 2d6 roll has far more concrete limits on how it can be modified as compared to a d20.