Do you know how to calculate the odds for Exalted 3e style dice rolls- i.e. cases where the highest number is a double success? I used to think that it was equivalent to just rolling a d11, because one tenth of the time you get an extra success, but I don't know if that logic actually holds water.
In general, the odds for a dice pool system where a given die can produce varying numbers of hits need to be calculated as though you were calculating the odds for a sum of identical dice (i.e., NdX) where the faces have non-standard numbering. For example, the odds for an Exalted dice pool are equivalent to taking the sum of Nd10, where each d10 has six faces marked "0", three faces marked "1", and one face marked "2". Effects which change the target number to something other than 7, or which allow doubling of results other than 10, adjust these proportions accordingly.
Calculating the odds of a sum of arbitrarily numbered dice by hand is possible, but it's a big pain in the butt, since you need to convolve the generating function of the die's result distribution. (Don't worry if you don't know what that means – they don't cover it in high school!) Fortunately, most dice calculator apps have a simple notation for such dice. For example, on anydice.com, an unmodified Exalted die can be notated as "d{0,0,0,0,0,0,1,1,1,2}". Thus, the program:
output 5d{0,0,0,0,0,0,1,1,1,2}
... would give you the odds for a pool of five dice with target number 7, doubling 10s. If you have a TN of 6, change one of the zeros to a 1; if you're using a Charm that lets you double 9s, change one of the 1s to another 2; and so forth. This even works for dice pools subject to effects that cause certain results to subtract hits; for example, if your enemy has whammied you with a Charm that causes your 1s and 2s to cancel successes, just replace a couple of 0s with -1s.
(It gets slightly more complicated for effects where 1s cause you to discard dice rather than subtract successes, since you could theoretically be discarding a die that generated multiple successes. That's a rare enough edge case that it almost never comes up, though.)
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