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Saturday, August 22, 2026
Edge cases of the d20 system
I am still playing Pathfinder: Wrath of the Righteous, over 200 hours into the current run and approaching the end of act 3. Now Pathfinder, like D&D, runs on a d20 system. That is to say that the success of an attack, or whether whether a spell is resisted or diminished in effect, is determined by rolling 20-sided dice. At the start of the game you might have an attack bonus like "+5". That means you roll the d20 and add 5. If for example the enemy has an armor class (AC) of 16, you need to roll 11 or more on your d20 to hit, and only if you hit you deal damage. In this example your chance to hit is 50%, because 11 or more is 50% of the results of a d20. This is how the whole game scales. I'm level 14 now, and my attack bonuses are more like "+25". But then the armor class isn't 16 any more but 36, and I still need to roll the same 11 on the d20 to hit.
But in these higher levels I also frequently encounter the two possible edge cases: Enemies with armor class so low, I only need to roll a 2 to hit (a 1 is always a failure, regardless of the math of attack bonus and AC); and enemies with armor so high, I need to roll a 20 to hit, which is always a hit. So the game sometimes puts boss monsters in my way, where the AC is incredibly high for the level. Even with all the optimization of the world and taking the character classes with the highest to hit bonuses, and wearing magical gear, the to hit bonus can only get so high at a certain level. And if the AC of the boss is then higher by 20 than this optimized to hit bonus, my chance to hit goes down to 5%. That ends up being pretty long and miserable fights.
So over the course of the game I collected various means to break that problem: I have now 3 characters in my core team that can apply a -2 to AC onto the enemy. Ember the witch has the Evil Eye hex, which gives -2 AC for at least 1 round, and can then use Cackle every round to keep that debuff going forever. Lann has a relic belt, Malander's Penance, that gives monks the ability to spend a Ki point for a -2 AC debuff. And Arueshalae has the Big Game Gloves, that adds a -2 AC debuff to her quarry ability.
The result is significantly easier boss fights, as long as the main difficulty of the boss fight was the high armor class. If the AC of the boss is 20 above my to hit bonuses, I only have a 5% chance to hit. If I spend one round to apply three times -2 to AC, the AC is now only 14 above my to hit bonuses, and I have a 35% to hit. Making it 7 times more likely for me to hit means the boss goes down quickly.
One tends to think of the d20 system as being linear, with every +1 or -1 changing the probability by the same plus or minus 5%. But if you consider the edge cases, and the absolute chance to hit, if you have only a 5% chance to hit, a +1 bonus to to hit, or -1 malus to AC, doubles that chance to hit to 10%. So I can see why many Pathfinder players are so obsessed with minmaxing their builds. If you have regular enemies which you already hit half of the time, another +1 seems irrelevant. But if boss monsters have too high armor, that +1 might be the difference between being able to beat him or not.
- posted by Tobold @ 9:44 AM Permanent Link
