So the basic idea is that we first compute a "level" for whatever interaction, by adding beneficial modifiers and subtracting harmful ones. Imagine most modifiers are smallish integers like 2 or -3 (though they can be non-integers too). Each level can be thought of as making things twice as good/bad, although this only applies directly when they're balanced. The actual formula starts with a 50/50 chance of "success" at level 0, and then each positive level halves the chance of failure, or if the levels are negative, each negative level halves the chance of success (note that halving the chance of failure is not the same as doubling the chance of success).
The intuitive explanation is that you start with a coin flip. Then if the level is positive, you flip that many additional coins and succeed if any single coin succeeds, but it the level is negative, you have to flip that many additional coins and succeed only if *all* flips succeed.
For example, if I have a dagger with 5 crit chance, and I attack an opponent with no armor modifiers, I'd have to win any 1 of 6 coin flips to score a crit (p = 1 - (1/(2^6)) = 63/64. Increasing my crit modifier by 1 ups my chances only slightly, to 127/128. This is obviously pretty poor return, indicating that the 5 I already have is very strong. If the opponent had armor with -3 to crits, the interaction is now level 2, so the crit chance is 7/8, which is still pretty good. We can see from these examples that the basic system
rewards a small level advantage a lot, but the rewards diminish rapidly. The system has a few avenues for tweaking how it works though, that can let us modify this. There's also a potential benefit (though sometimes drawback) that no matter what the level gap, there's an effective limit to how much the interaction swings.
@drbruced@aus.social
