Oddgamer

11-16-2015, 02:12 AM

I have a pair of opponents, A and B. Each round they go in random order. Both have a chance to score 0, 1, 2, 3, or more points against the other, which I would call A0%, A1%, A2%, A3%, A4% and the same for B0 to B4. 4 points wins the game. How do I work out the odds of A winning?

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.

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.