I'm trying out different systems for a board game, and my (weak) probability skills are failing me.
The basic mechanic is as follows: you roll a number of six-sided dice (d6). Any die showing 5 or more is a success. A specific bonus can "upgrade" part of your pool to a larger die (let's say a 10-sided dice, or d10).
So for example:
regular roll: roll 7d6; any die showing 5 or more is one success.
same roll with bonus: roll 4d6 and 3d10; any die showing 5 or more is one success.
I'd like to learn how to calculate the chance of getting X successes with the mixed pool (either "X" successes or "X or more" successes).
this thread thaught me how to find the probability for the homogenous pool, but I have no idea how to change the formula to accomodate the differently-sized dice.
I would like to learn the general formula, to be adjusted for different size of dice (such as d8 and d12) and for a larger or smaller pool of mixed dice as well.
Thanks in advance, sorry for any English mistake I may have made.