As far as I know, I have created a new dice battle mechanic. Because I am not great at statistics theory, I was wondering if someone could compute some probabilities for me. Here is how the battle mechanic works. Each player rolls a number of dice equal to his or her attack or defense value and checks the value of his or her highest valued die. Whoever has the highest die value wins. If there is a tie, each player checks the value of his or her second highest die, and whoever has the highest value on their second die wins. If there is still a tie, the players check their third highest die and so on. If all dice are ties, the defender wins (I doubt this will be rare). If players tie, but another player have more dice leftover, the player with more dice wins.

Here is an example of a battle. Player One has an attack value of 3, so he rolls three dice. The values are 6, 5, and 4. Player Two has an attack value of 4, so he rolls four dice. The values are 6, 5, 2, and 1. Both of the player’s highest dice are 6s, so each player checks his second highest die. The second highest dice are both 5s, so each player checks his third highest die. Player One has a value of 4, and Player Two has a value of 2. Therefore, Player One wins the battle. Here is one more example. Player One has six dice, and Player Two has 1 die. Player One rolls five 1s and one 2. Player Two rolls a 6. Player Two wins the battle.

I’m wanting to know what the nuances are of this battle system, and I’m wondering how drastically the number of dice each player has effects the probability of winning a battle. I’m assuming that the chance of winning or losing will be 50:50 when players roll the same amount of dice, but what is the probability of winning when one player has 1 die, and the other player has 2? What about 1 vs 3, 1 vs 4, and 1 vs 5? Is the chance of winning with 4 vs 5 the same as 1 vs 2? A probability table would be very helpful. I don’t know how to compute values like these, and I would be very grateful if someone could help me with this.

Thanks guys! I didn't realize it would be as complicated as it turned out to be when I first posted this question. I was in the process of writing my own simulation, but Zag beat me to it. Anyway, it will be nice to see if my program comes up with the same percentages.