around me black bats dive up from the dark.

Not quite, no.

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.)

e.g., one dungeon might allow characters to advance by progressively enbodying mythic archetypes to produce something resembling a conventional class-and-level system, save that the "character classes" are specific to that dungeon, and a different dungeon which nominally has the same advancement schema would have a totally different set of playbooks; another might have fully randomised advancement in which player characters acquire weird body-horror mutations that grant mildly game-breaking super powers with no ability to influence which ones they get; and a third might have wholly extrinsic advancement based on acquiring golf-bags full of magic items with oddly specific functions. In each case, progression through the relevant advancement schema would be extremely rapid, such that exploring its full gamut in the span of a single adventure module is feasible, and player characters would "reset to level 1" once that module is complete.

The cheap lethality of some of these games would absolutely work better in a roguelite kinda thing

For once I'm not actually doing a bit; those "any resemblance to real persons living or dead" disclaimers genuinely exist because of Rasputin.

children of any species are very good at being annoying and very cute while doing that

a sphinx child based on this post