Today I feel like looking at probability distributions for ttRPGs. Going to thread some plots and observations.

Of course the most popular is D&D in all its iterations. The basic rule is roll a d20, add your bonus, compare it to a target number. 5e added the innovation that if you have advantage, you roll twice, take better; disadvantage, you roll twice, take worse.

A major problem with d20 games has been that the targets typically scale with your skill. Your chance to succeed never really goes up as you level, and your chance to succeed at things you aren't specialized in just goes down.

And the numbers just inflate. Worse math no benefit

We're playing Red Markets right now. The rules are:
Roll a black d10 and a red d10. If the black + skill exceeds red, you succeed.

If you rolled doubles, evens is a critical success, and odds is a critical failure.

You can expend additional resources to improve your skill.

This is a good system. You can't start with more than 3 in a skill. That's about a 70% success rate, which is sort of the psychological sweet spot for feeling competent.

The game is billed as a game of 'economic horror', and building in diminishing returns adds to the theme.

There are also multiple ways players can expend resources to improve their odds. (They can also spend a will point to switch red/black face values). This is one of the best ways to help players not get frustrated with a run of bad luck, while still carrying consequences.

In World of Darkness games, you roll a number of dice based on your skill + attribute. Each roll above a 7 is a success. If you get a 10 it's a success and you roll another die.

Exalted is basically the same, but succeed on 7 or higher.

I like Storyteller (WoD) dice rules, but they can drag a little. It's fun to throw lots of dice. It's exciting when the dice explode on 10s. There are pleasant distribution curves that account for variable levels of success. There's no adding numbers together. It's good.

I will say, it was a pain in the ass to code out the probability mass functions for storyteller dice.

Shadowrun is basically the same as world of darkness, but you have to hit a 5 on a d6 instead of an 8 on a d10.

As you might expect, the probabilities look very similar too.