Yes, I could brute-force this and run a computer program to test it out 100 times or whatever I felt was sufficient, but that won't help with my problem of trying to find an A that wins against B x% of the time since the number of trials could well get unmanageable

*and*there are other factors in the eventual competition when I'll be forced to go to brute force to check anyway (for instance, if an opponent has a point scored against them their chances of scoring points against the other decreases by an amount specific to the chance they had in the first place and another factor). I am using this to get

*close*before I need to start trying brute force to discover an answer. It gets

*very*bad when I need to consider teams of opponents on both sides. I think the problem above can have a (fairly) simple answer I can plug into an equation and get close before I start fiddling with specifics, groups, and so on to give a more comprehensive look. And, of course, all of

*this*is even going to be only close to reality as it'll ignore lots of other factors that come up in the real thing which I can't model.