The goal of this game is to get your opponents life points down to 0 before he gets yours down to 0. You take turns hitting each other until one persons health is at 0. The variables are: Attack (accuracy of hitting instead of missing) Strength (how high you can hit) Defense (determines opponents hit / miss ratio) Life points (How much health of yours is to take away. Now, I'm going to leave the formulas of the game out. But usually, you miss around 30% of the time. Out of the times you do hit, a random number is generated between 1 and your max hit determinant on your strength. A common max hit is 8, so the hitting range would be 1-8. Now, let's assume that we have already calculated both opponents hit/miss ratio and max hit and that we know their life points. The average number of hits the match will last is easy to calculate. However, my goal is to determine the probability of each player winning. Assume P1: Misses 35% of the time Has a hitting range of 1-8 Life points are 60 and P2: Misses 30% of the time Has a hitting range of 1-10 Life points are 55 So, P1 has to hit a total of 55 or more damage against P2 before P2 hits a total of 60 damage against P1 for P1 to win. What is the probability of P1 winning? I've thought about ways to do this, and I imagined that we had two overlapping probability distributions of the number of turns it would take P1 to hit 55, and P2 to hit 60. If we knew these distributions, we could calculate the % chance of either one of them winning with relative ease. The hard part for me is getting the probability distributions. Any insights on how to do this?