I don't know the formula for this particular situation, but by simulating it, it only goes wrong 10% of the times.

Didn't remember the theory right either. Sat down and actually separated the problem into 17 simple binomial cases and did each case by hand. (6 hits on reisen straight -> 0.0013. One on either snake -> 1/3^7*6*2 = 0.0054 (etc etc)). Add everything up and it comes up at 0.11265; For the two cases where one of the snakes dies, I ended up just considering 7 possibilities of in which hit they die separately and adding all those in. Adding up all 17 cases ends in a total of 11.265%. Looks a lot more plausible. Simulating can help point out math mistakes, turns out.

I think multinomials and adding a 10th phantom hit and just counting the number of sequences that end with reisen isn't the right solution; it's more weighted towards hitting the snakes in actuality.

This'd make for a nice math test as a single problem by itself. Kind of neat. Think I'd still have decided to leave the enemies up at 11%.