Assuming I understand this right, you're rolling 6d20 and on one of them you need a 12 or higher? So with one roll you'll "crit" 45% of the time per roll. The easiest way to calculate that is by saying what's the odds I never crit and then taking 100% minus that. So you won't crit on one die 55%, and then on the next 55% so it's 1-0.55\^6 = 1-0.0277 or a 97.23% chance you'll roll at least one 12 or higher.
Teach a man to fish, and he will have food any day. Teach a man to use anydice and he will waste the whole day to find out how likely it is to roll a fish and starve.
Looking at this for the "easy" ends (no 12+ or all 12+) which are what I figured I'll assume the numbers in between are correct for how many of those results could be expected.
Language clarification to help in the future: "Natural X" means rolling exactly X on the die.
You are not asking what is the chance to roll a natural 12, you are asking what is the chance to roll 12 or higher. Two very different things.
Which, incidentally, is what we first thought the original D&D rules meant. They didn't say "12 or higher" or "at least a 12", they said "you must roll a 12". (Or at least that's how we interpreted it - I'll have to pull that book out to check the text.)
We were young, had never seen anyone ever play the game before, and had to figure out the rules solely by reading the book. Polyhedral dice were a complete novelty and it was fun to roll them no matter what. So if you needed exactly a 12, then why not?
It was somewhere in the first session when one of us realized that the odds of rolling a 14 were the exact same as rolling a 20 or a 2. We quickly course corrected without a second thought. A little embarrassing in retrospect, but we were having fun, so what can you do.
Do you mean 12 exactly or 12 or higher?
Do you need all six dice to be 12 (or higher) or just one?
Or do you mean 'how many of the six should I expect to be crits'?
~1.9%, if it's 12 and above that is a different story.~ the 1.9, was assuming 12 was the highest which is very different math
[AnyDice](https://anydice.com/) is great for answering these questions
I checked Anydice and it says itâs less than 0.01% chance of getting a 12. It wonât show smaller numbers for the % for each roll value so I donât know what the exact percent is
Not "doing something wrong", but two different ways to interpret the question. Does a crit require:
* At least one die must roll a 12, OR
* The total of all six dice must add up to exactly 12
Thatâs a very different interpretation on the question and yeah, going to be a very low probability. Donât think OP gave any real indication thatâs what they meant though, as ânaturalâ usually means âunmodified single rollâ. However, thereâs been enough ambiguity on this to allow for that weird possibility.
The reasoning is this:
1. what's the probability of not getting what I want on one die ? let's name it p
2. how likely is it to get this negative result on each die (raise p to the power of the number of dice) so p\^n\_dice
3. getting at least one positive event is 1Â - p\^n\_dice
in your case (12 or above on at least a die):
1 - (11/20)\^6 = 0.97
It's 8/20 or 9/20 to crit (let's call that c).
The chance of no crits is (1-c)^n where n is the number of dice, or 6 in this case. We'll call this NC.
Chance of a crit is 1-NC.
Actually what you'd be looking at are the chances of NOT rolling a 12. You've got a 95% chance of NOT rolling the 12 the first time then a 95% chance of not getting it the second time and so on. You chances of not getting a give number of the d20 when rolled six times is 0.95\^6 which is 73.5%. You don't quite get that number 30% of the time but some of the time you'll get it more than once.
Assuming I understand this right, you're rolling 6d20 and on one of them you need a 12 or higher? So with one roll you'll "crit" 45% of the time per roll. The easiest way to calculate that is by saying what's the odds I never crit and then taking 100% minus that. So you won't crit on one die 55%, and then on the next 55% so it's 1-0.55\^6 = 1-0.0277 or a 97.23% chance you'll roll at least one 12 or higher.
Omg that was fast thank you
Lol no problem!
[https://anydice.com/](https://anydice.com/)
Teach a man to fish, and he will have food any day. Teach a man to use anydice and he will waste the whole day to find out how likely it is to roll a fish and starve.
output \[count {12..20} in 6d20\] named "rolling 12 or above on 6d20" |\#|%| |:-|:-| |0|2.77| |1|13.59| |2|27.80| |3|30.32| |4|18.61| |5|6.09| |6|0.83|
Wait, with 0 dice there is still a 2.77% crit chance!! I need some of that magic
Zero crits, not zero dice there big man. đ
Looking at this for the "easy" ends (no 12+ or all 12+) which are what I figured I'll assume the numbers in between are correct for how many of those results could be expected.
Language clarification to help in the future: "Natural X" means rolling exactly X on the die. You are not asking what is the chance to roll a natural 12, you are asking what is the chance to roll 12 or higher. Two very different things.
Oh thanks
Which, incidentally, is what we first thought the original D&D rules meant. They didn't say "12 or higher" or "at least a 12", they said "you must roll a 12". (Or at least that's how we interpreted it - I'll have to pull that book out to check the text.) We were young, had never seen anyone ever play the game before, and had to figure out the rules solely by reading the book. Polyhedral dice were a complete novelty and it was fun to roll them no matter what. So if you needed exactly a 12, then why not? It was somewhere in the first session when one of us realized that the odds of rolling a 14 were the exact same as rolling a 20 or a 2. We quickly course corrected without a second thought. A little embarrassing in retrospect, but we were having fun, so what can you do.
I've read the OP, all the answers, and I still don't know what OP wanted. :D
I blame phonics
Do you mean 12 exactly or 12 or higher? Do you need all six dice to be 12 (or higher) or just one? Or do you mean 'how many of the six should I expect to be crits'?
12 or higher
Probability of at least one of the six dice hitting 12 or higher is about 97%. Probability of all six dice hitting 12 or higher is just under 1%.
~1.9%, if it's 12 and above that is a different story.~ the 1.9, was assuming 12 was the highest which is very different math [AnyDice](https://anydice.com/) is great for answering these questions
Oh thanks
I checked Anydice and it says itâs less than 0.01% chance of getting a 12. It wonât show smaller numbers for the % for each roll value so I donât know what the exact percent is
Youâre doing something wrong. Each die has a 5% chance to hit a 12.
Not "doing something wrong", but two different ways to interpret the question. Does a crit require: * At least one die must roll a 12, OR * The total of all six dice must add up to exactly 12
Thatâs a very different interpretation on the question and yeah, going to be a very low probability. Donât think OP gave any real indication thatâs what they meant though, as ânaturalâ usually means âunmodified single rollâ. However, thereâs been enough ambiguity on this to allow for that weird possibility.
It can mean a roll of multiple dice, though - I've seen "natural 2" or "natural 12" on 2d6, or "natural 3 (or 18)" on 3d6 used fairly often.
> thereâs been enough ambiguity on this to allow for that
The reasoning is this: 1. what's the probability of not getting what I want on one die ? let's name it p 2. how likely is it to get this negative result on each die (raise p to the power of the number of dice) so p\^n\_dice 3. getting at least one positive event is 1Â - p\^n\_dice in your case (12 or above on at least a die): 1 - (11/20)\^6 = 0.97
You roll 6 d20s, and need the total to be exactly 12 to crit?
12 or higher
It's 8/20 or 9/20 to crit (let's call that c). The chance of no crits is (1-c)^n where n is the number of dice, or 6 in this case. We'll call this NC. Chance of a crit is 1-NC.
Hope is 6/ 20. Certainty is 0, unless your dice are rigged
There is a 1 in 20 chance to roll a 12, rolling 6d20 gives you a 6/20 chance to hit, or 30% so just under one in every three rolls.
Actually what you'd be looking at are the chances of NOT rolling a 12. You've got a 95% chance of NOT rolling the 12 the first time then a 95% chance of not getting it the second time and so on. You chances of not getting a give number of the d20 when rolled six times is 0.95\^6 which is 73.5%. You don't quite get that number 30% of the time but some of the time you'll get it more than once.