Dice probability formula question

I am trying to work out the formulas for group rolls. Assuming I have a group of mooks with the same stat, what are the chances  that a certain number of them will succeed their roll? X chance of success per die, Rolling Z dice. What is the chance of zero successes, what is the chance of 1 success, what is the chance of two successes, etc. Like, with a 17% chance of success per dice, what are the odds that exactly 4 out of 7 dice will succeed? If different values of Z require different formulas, I’m specifically looking for Z=3 to Z=7.

To get the probability of what you're describing, you'd want to use the Binomial distribution . Here is a Binomial distribution calculator you can use in the future for looking up the odds for similar things in the future. It also shows the propabilities of rolling up to, or below the number you want, so you can use it for figuring out probabilities for a range of results, like what's likelihood of rolling 5 or more successes. Chances for rolling exactly Z successes with 7 dice, where probability of success is 0.17 (17%): Z, number of successes Probability of Event Z = 3 8.16% Z = 4 1.67% Z = 5 0.21% Z = 6 0.014% Z = 7 0.00041% If you're calculating the odds of a 1d6 roll, using 0.166666 instead of 0.17 would be more accurate, but doesn't change the result too much. You could also use Anydice.com for getting the probabilities of various rolls, and has a pretty solid notation that enables to figure out odds for even complex things, as long as you're able to figure out the dice notation. To figure out the same thing there, try output 7d{0, 0, 0, 0, 0, 1} named "dS" on anydice, and then look at the "Transposed" results, which gives the odds of each individual success, but does so only to an accuracy of 0.01%, anything less and it will say 0%

Andreas J. said: Here is a Binomial distribution calculator you can use Thank you. This was exacly what I needed. I can now make group of roll tables and resolve the group checks with a single macro.