So I've been working on this problem related to World of Warcraft, and I'm just not able to solve it.
Basically, let's say player 1 has $500$ health, does $100$ to $200$ damage, and has $5%$ miss. Player 2 has $1000$ health, does $50$ to $100$ damage, and has $5%$ miss. What's the probability of player 1 winning?
The way I thought of solving this would be by coming up with a function that gives the probability of player 1 killing player 2 in $0,1,...$ seconds (weapon speed is $1$ second in both cases). I would do the same for player 2 and then the probability of player 1 winning would be the probability of player 1 killing player 2 in $0$ seconds times the sum of the probability of player 2 killing player 1 in more then $0$ seconds, and then repeat for all in player 1.
But the problem is that there are infinitely many probabilities to check and I don't know how to get to a precise probability. Also I need to take into account the proability of a tie which I believe is just a coin toss in World of Warcraft. So anyone have any ideas? Also ideally I would need to be able to solve this problem for any stats on players.