I'm afraid I don't understand your math. I'm not saying it's wrong, as it may very well be just over my head.

Why are you using ^? Shouldn't you just be using multiplication?

I mean, in the original example, if each bolter shot has a 17/18 chance of not killing the terminator, which translates into each shot having roughly (by my math) a 5.55% chance of killing the terminator. 5.55% * 18 shots = 100%, which is basically just saying that 1/18 * 18 = 1. I don't see what bringing it to the power of 18 proves.

No, you don't use multiplication.

To get the chance of, for example, two shots killing a Terminator, using the example chance of 10% per shot, you do:

10% chance for the first shot.

You get the remainder of the 100%, which is 90%, and then get 10% of that (the chance of the next shot doing it), which is 9% of the original 100%.

So you have a 19% chance of killing one Terminator with those two shots.

If you want the chance of killing two Terminators with two shots, you do the opposite.

You get the chance of killing one, 10%, and get 10% of that, which is 1% of 100%.

So a 1% chance of killing 2 Terminators with 2 shots.

If you have different chances, of for example 3 shots but you want the chance of killing 2 Terminators, it doesn't really matter how you order them.

It gets pretty complicated sometimes, but that's how I do it, the manual way