# What's the closest I can get to simulating critical hits with a dice pool, without relying on the total sum?

I'm making a game that uses a dice pool rolling system (for my purpose it's always a d12 and no other dice), and I wanted to figure out if making a 'critical hit' mechanic was possible, that is rewarding rolls roughly 5% of the time.

Playing with anydice this set up:

output 1d12 >11
output 2d12 >21
output 3d12 >29
output 4d12 >37
output 5d12 >45


Gets this output for 'criticals':

Dice pool size % chance of a crit
1 8.33333333333
2 4.16666666667
3 4.86111111111
4 4.82735339506
5 4.63083526235

I admit with one die of less that 20 sides 5% is impossible. But the others are close and seem to fight a pattern of getting over the maximum results (12, 24, etc) - some number (1,3,7,11,15) (possibly $$\(n-1)\times4-1\$$ for all but the first).

I cannot say this is the easiest to calculate as you need to sum all dice faces and as your dice pool goes up, so does the total sum.

Is there a way to simulate this without summing all dice faces?

The answer needn't use anydice, but I have and might be relevant.

• What happens on a critical hit? How does the pool work; especially how do you determine how many dice to roll and the success of that roll? The answer might be "like most white wolf products", "like Exalted", "like In Nomine", "vaguely like Weapons of the Gods", or something else entirely. Commented Jun 24, 2022 at 14:04
• @fectin Answering in order: I don't know yet, I don't know yet, I don't know yet. However, had I known and thought it relevant I would have included it in the question. If you think it's relevant, please let me know and I'll try and update my question. Commented Jun 24, 2022 at 14:08
• :D fair enough! Commented Jun 24, 2022 at 14:09
• Will it always be d12? Guess not but I think this question can use clear description of what dice sizes and numbers are needed to be taken into account, can you mix dice in a pool, et cetera. Commented Jun 24, 2022 at 15:53
• @Mołot d12 is my dice of choice. I don't know if there's a generalisable system of isolating 5% of the rolls and calling them a critical success, out there. Commented Jun 24, 2022 at 16:25

## 3 Answers

If you want a fun way to do it and you're in person, you could have someone call a pair of the dice which have to add up to exactly 8 (e.g. 1+7, 2+6... 7+1) which is 4.86% according to anydice (though this would require identifiable dice, or rolling them separately to make them your lucky dice). Having a fixed number (eight) like that is fun and lets players have more "control" over their criticals.

If playing a game with arbitrary sized dice, this could be used by players to use dice closer to whichever "lucky number" you choose to cause criticals more often too, though still with the limit of 2dx unless honed further.

Naturally this only works with a minimum of 2dx but without involving heavier mathematics during play than you've stated you likely can't get more exact.

Barring something like that, there's also the possibility of having a "crit dice" that you always include, though that probably goes against the fun of it.

• Hi and welcome! Good answer! I'm guessing you don't need to but there is always the tour and help center if you want to know more. I'm not clear on this part "call a pair of dice d12 which will add up to 8 which is 4.86% according to any dice" Is this saying both individually must both be $>8$? Because my calculation on anydice says that's ~11%, and as per my post, to get 5% from the sum you need to be $>21$. Commented Jun 24, 2022 at 10:52
• Hi, I meant as in the sum of the 2 dice is 8 (1+7, 2+6, 3+5, 4+4, etc) Commented Jun 24, 2022 at 11:02
• Oh, equals 8 exactly. Commented Jun 24, 2022 at 11:04

## You could count up a number of successes

You can set a success cutoff number for each pool size, count all rolls equal or higher than that cutoff as successes and demand a given number or more of successes per pool. This gets you around summing, you just look up success die.

To be honest, I think this is a horrible experience, because you essentially need to have a table at hand to remember the cutoffs, and it is not very exact either but here you go:

Pool Cutoff Successes Needed (at least) Probability
1d12 12 1 8.33%
2d12 10 2 6.25%
3d12 9 3 3.7%
4d12 10 3 5.08%
5d12 12 2 4.53%
• +1 for the use of the much neglected d12, and the easy to read table. Commented Jun 24, 2022 at 15:05

## You need to figure out what you want your system to do

There are a few general models for dice pools and criticals, which I can briefly describe to help you out. Be aware that everything ties into your basic mechanic: the feel of the game, the character stats, etc.

Roll Under Stat: Traveller (and and many other systems) have a fixed target number which is derived from your stats. You roll a handful of dice. If the sum shown is less than the target number, you succeed. Traveller has had a lot of versions, and different versions let the GM adjust difficulty in different ways: sometimes it's a bonus/penalty to the target number and the number of dice is fixed; sometimes the number of dice changes (more is harder). It's a swingy system for low-skill characters, but much more predictable for high-skill characters. It feels "realistic", and is good for systems where there really is a wide difference between untrained and trained checks, but everyone is similarly dangerous. Target numbers are (usually) in the range you'd expect to see for rolled D&D stats.

For something like this, you want to either look at how much the check succeeded/failed by, or just ignore "critical" effects altogether.

Count Successes: Probably what most people think of when they hear "dice pool". The traditional exemplars of this were games using White Wolf's Storyteller system, but there are a bunch of new and old variants. Your stats determine how many dice to roll; each dice generates a success if it shows certain faces (example: roll Xd10, count the number of faces showing 7+). Some games also have failures (example: Fate has you roll specially marked d6 dice, sum the "+" results and subtract the "-" results). After counting, the total is your result, which you compare to a target difficulty (or to an opposed roll... one advantage of this system that opposed results are easy to implement). Most systems like this change the difficulty by changing the number of successes needed to succeed. The original Mage: the Ascension did that PLUS changed the target number for each die to be a success. That was mechanically neat, but too much headache; you should stick to varying the number of successes needed.

Depending on how large you allow the dice pools to be, this is a good system for super-hero stuff. People rolling 1-2 dice are going to have a very swingy output (especially if you include criticals); people with 8+ dice are quickly going to converge to expected values. The sweet spot for variable outcomes is around 3-8 dice, and a 3-4 die advantage in pool size is very hard to overcome in opposed rolls: a plucky kid from the Bronx will never outrun the Flash.

Criticals get handled four main ways:

1. Some specific roll result ("if the number of 10s is more than the number of 1's, and the roll is a success", etc). This is... okay. It gives you a mechanism for critical hits, but it's too fiddly to give the little dopamine hit that "natural 20" does. It also usually feels bolted on.

2. In relation to the target number of successes ("if you get 2 more successes than the target number..."). This is actually pretty good, but it means experts will regularly crit and untrained will regularly fail; the window for regular success is narrow (and you need to balance the game carefully around that, or define crits in a way that you're okay with it). If Bobby Nobody and Superman each try to lift a car, Bobby will fail and Superman will crit. But maybe Superman juggling cars at-will isn't a problem?

3. Exalted. I'm sure it's not just Exalted, but that's where I ran into it first, and I really like the simplicity: on each die, 7+ is a success. For heroic characters, 10 is two successes. The big barrier for untrained people is right around 2-3 successes. Your system is probably set up so that everyone rolls at least one die any time they get to roll, so there's a 50% chance of getting a success (or whatever%, based on die size and success criteria). Having a 10% chance of getting 2 successes suddenly makes rolls around 2-3 difficulty a lot more plausible. 1 die hits Target Number 2 (TN2) 10% of the time; 2 dice hit TN2 73% and TN3 5%, etc. It puts desperate attempts back on the table for low-skill characters, which is very much where criticals are good. Exalted gates this for special characters only; keeping mooks off criticals isn't a bad plan.

4. Special Die: when you roll dice, one of the dice in the pool is special (one red in a pool of black, or whatever). That die determines if the result is critical. Pretty easy, but it means that there are no non-critical successes/failures for only one die. Joke systems like In Nomine work just fine with this mechanic; serious systems work less well.

Best Result: Roll some number of dice. The best result is your result. Blades in the Dark does this especially well. You do need to keep the pools small to make it work though (four dice is starting to push it). For BitD, the results go like this. Roll a number of d6 equal to your stat:

• All dice less than 4: failure.
• Highest die shows 4-5: partial success (the thing happens, but it's complicated).
• Highest die shows 6: look at the rest of the pool:
• If all other dice are 5 or less: success.
• If there are TWO sixes: critical success This works very well in a narrative game (incidentally, I just noticed that BitD has an SRD and very permissive licensing...), meaning the game is mostly improv theater/storytelling with some mechanical prompts. It would not work in a crunchy game with tactics that mattered. I like both BitD and D&D 3.5, but they are very different beasts: Resolution mechanics will absolutely drive the feel of your game.

Finally, Roll and Add: Is there anyone who didn't love West End Games' Star Wars? If so, I haven't met them. This is really simple: your stats tell you how many dice to roll, you roll that many dice and add them up. Compare that number to the target number, and you're done. This makes for enormous gaps between trained and untrained, and may make your character building... complicated. But there is a visceral appeal to rolling a fistful of dice and shouting "30!". The major downside is that it can take players a long time to add up a fistful of dice.

There is at least one open-source variant of the system (http://opend6project.org/), which you could just lift wholesale. As ever, there are plenty of other similar systems though.

Criticals for roll-and-add are similar to count-success systems:

1. If you exceed the target number by ____, you have a critical success.
2. Exploding: some (or all) dice explode: if the die shows a specific result, add another die to the pool (usually, "if any d6es show '6', add them to the result, then reroll those dice and add the results'). This adds much more swinginess, and means that anyone might be able to succeed on any task, however unlikely. Will definitively affect the feel of your game. Unfortunately, details on how exploding dice affect things are too expansive to fit in this answer.
3. One die in the pool is special; add the result normally but criticality is based on that specific die result.

Bottom line, you have an enormous number of options. How you set up the rest of your system and what your goals are for criticals will strongly affect which options are better or worse.

• You've definitely listed a bunch of systems that already use a dice pool (and poked fun at one of my favourites), but none of this changes the statistics of my question. In theory I could use 'roll under stat' and still mark a critical by adding up faces (as per my question). It's not how the existing system works, but there's no reason a new one couldn't. Because of that mismatch I'm going to say this doesn't answer my question, but makes some interesting points for discussion. Commented Jun 24, 2022 at 16:22
• So this isn't a bad post (it's very interesting!), but it definitely doesn't get me any closer to answering my question. Commented Jun 24, 2022 at 16:23
• @AncientSwordRage I think your question needs a lot more detail to be answerable. I probably should have voted to close based on that, but it didn't seem like a helpful approach. I posted this instead as a frame challenge, in that you need to make a number of other decisions first. Commented Jun 24, 2022 at 16:43
• @AncientSwordRage I think the specific die result is a good answer, in fact you can get exactly 5% by rolling a d20 "Crit Die" with the rest of your pool. Since it's your own system, you could even add other things to it, like critical failure (1) and allowing them not to roll the d20 (avoiding either critical result). You could even attach special temporary events to specific numbers, like in a given combat, the first to roll a 7 on their crit die triggers an event... Commented Jun 24, 2022 at 20:44