So let's say I am about to roll a certain number of dice, how can I know the probabilty of scoring crits and successes? Like I want to know, for example, If I roll 6 dice I have this and this chance of getting 3 success and this and this chance for getting a crit
Ok so for crits, here are the probabilities of rolling one given a certain number of dice rolled:
1 dice: 10% chance to roll a crit.
2 dice: 19% chance to roll a crit.
3 dice: 27% chance to roll a crit.
4 dice: 34% chance to roll a crit.
5 dice: 41% chance to roll a crit.
6 dice: 47% chance to roll a crit.
7 dice: 52% chance to roll a crit.
8 dice: 57% chance to roll a crit.
9 dice: 61% chance to roll a crit.
10 dice: 65% chance to roll a crit.
11 dice: 69% chance to roll a crit.
12 dice: 72% chance to roll a crit.
How did I calculate those? Well simple. You calculate the chance that the crit will NOT roll, and you subtract from 100%.
For 1 die, there is 90% that I do not roll a crit and 10% that I roll a crit. That's a very simple case. But we will use this case for the next ones.
Now, let's move on to 2 dice. On the first die, I have a 90% chance of NOT rolling a crit. on the second die, I again have a 90% chance of NOT rolling a crit. so I multiply .9 by .9 to get the chance of not rolling crits on BOTH dice, which gives me 81%. Now I subtract from 100% which leaves me 19% to roll at least 1 crit.
For 3 dice, you multiply .9 by .9 by .9 to get .73, or a 73% chance NOT to roll a crit in any dice. So the chance of rolling a crit is 27%
And so on. So basically the formula is to first calculate .9 to the power of the number of dice you are rolling, and then subtract that result from 1
Calculating the probability of rolling a number of successes based on number of dice rolled is a bit trickier. But I am working on a document which will have the chart of all the probabilities when I am done I will send it to chronodev so he can put it on this site somewhere.