Combat in lopsided encounters

[Jonathan]

I am interested in the probabilities of success in encounters that are not evenly matched. I produced a table of win percentages using Monte Carlo simulation for encounters featuring two allies versus one opponent.

The raw data can be downloaded right now. I am still working out interesting visualizations.

My experimental setup has a fixed damage per hit and a chance of hitting per each swing. Combat is round-based. Initiative is determined randomly per player for each encounter. I looked at both increasing the damage done by the lone opponent and increasing his accuracy. I simulated each encounter 1000 times and record the number of wins for each side, the maximum number of rounds combat took, and the total number of rounds simulated (divide by 1000 for the average number of rounds per encounter) for each possible configuration.

I was hoping to find some combination of accuracy and damage that would result in an evenly matched one on one encounter but still give the loner in the two v. one encounter a decent shot at winning. Unfortunately, I didn't find one. Yes, if you let everyone kill with a single hit and give them a low probability of hitting, the loner will win sometimes. Even with a 10% chance of hitting, the chance of the loner winning is only 15%.

If the loner does the same amount of damage per round as two allies combined, he can have anything from a 0% to a 38% chance of winning depending upon the damage and accuracy. It is not strongly dependent on the absolute damage per round (product of damage and accuracy). High damage per hit will tilt the odds towards the loner more than high damage per round. It is better for the loner to have higher accuracy than to have higher damage per hit, though. This falls out from probability theory, of course.

If the loner does 3 times as much damage per round as one opponent (1.5 times as the two combined), then he can have an even chance of winning. I need to scrub my data so that damage > 100% or accuracy > 100% is forced to 100% so the sorts come out correctly.

This prompts me to do some further experiments. First, I'm going to take a look at very low accuracy, to see what the numbers look like. I can't imagine a system where each attack takes a millisecond, but I'm curious nonetheless. Second, I'm going to experiment with giving the two attackers a damage bonus and giving the defender an accuracy bonus. I may be able to find a combination that is equal damage per round in an one on one engagement, but gives the loner a decent chance at fending off two foes. I'm also going to generalize to larger groups.

Eventually, I'd like to repeat these experiments with more detailed players and actual skills instead of probabilities.

[Peijen]

I was thinking about this today. How about having increased regeneration rate?

I suspect in this situation the loner has to do shitload of damage and maybe sacrifice attack speed in the process. The character design goal should probably focus on getting the first hit and do massive damage with the first hit in hopes of dropping one of the opponent quickly.

Other than that you will have to employee stun like abilities.

[Jonathan]

I will add rate of attack and regeneration to my model.

I haven't had a chance to examine the data regarding low accuracy or uneven attackers/defender in depth. Suffice it to say that very low accuracy is not all that interesting, and with even damage per player per round, the loner gets the crap beaten out of him, even with 6x accuracy.

One possible solution I've thought of is to give a player an accuracy bonus for each player beyond the first in the 180 degree arc in front of him. The reasoning is with that many targets in front of him, it is harder to swing and miss. You'd want to limit the radius and max bonus.