TTRPGs, die rolls, and how often things happen

There's this great joke d20-based tabletop roleplaying game that we do not know the name or author of, but which has very simple mechanics:

• If you do something, then roll a 20-sided die.
• If you roll 2 or better, you succeed; if you get a 1 on a die roll, then you die.

So, your character wakes up (die roll), gets out of bed (die roll), puts on clothes (die roll), opens their bedroom door (die roll), walks down the stairs (die roll) ... you see where this is going. And where this is going is approximately a twenty-minute life expectancy. This character is gonna die.

And that doesn't really make sense, right? Your typical person has a lifespan of at least half an hour, and often much longer. However generous the checks look on paper, the frequency of the checks tells a different story.

...so in the name of not beating around the bush, lemme put a formula in front of you:

If consequence rate is how often (times per day, week, year, whatever) you want a given thing to happen, check rate is how often you want someone to make one or more die rolls that could cause that thing, and check probability is the chance that any given check will lead to the consequence, then:

consequence rate divided by check rate equals check probability.

If you want to tell a story in which something has a chance to happen, and you want to defer that chance onto random luck, it's very easy to make that chance way too high or way too low. And that's kind of why we want to talk about it, because it felt like that came up in an actual-play we were listening to today.

( What happened was: ... )

Like, it's easy to miss this in the language of rulebooks, but numbers tell stories. And when players and GMs know what stories they want to tell, it can help them to know what stories their numbers would tell.

So, consequence rate divided by check rate equals check probability.

(Oh, and something like AnyDice to do the arithmetic to find check probabilities, if you don't know them already.)