I agree that, in your first two points, there would appear to be an error. Your last point, though, is affected by the “Details Cutoff” slider, whatever that does. Move the slider to 0.0% and look at the details again.
D’oh! I didn’t even notice that slider, thanks for the info. That would explain why some probabilities are not listed. As you say, though, there are still some errors.
The skewed distribution is correct, I believe. I have seen this shape many times before when using the sim during previous games and in battles with several different unit types (when not using “Must Take Territory”).
I don’t think it is correct. Usually with these sims, the “meat of the curve” is clustered around the most likely result. A normal-ish looking distribution, in other words. In this case, the most likely result (at least the one this program says is the most likely) is 0 units remaining for the defender. So, we would expect the probabilities for various other results to cluster around this point. Obviously since the defender can’t have negative units, we only see the tail-end of the distribution, with the result for 0 units spiking up since it represents the “rest of the curve” crammed into one result.
However, looking at the actual distribution of results for surviving defenders, we see that the high point occurs in the 5-7% range around 5 units remaining, and actually declines for fewer units remaining. I think this is probably what the actual distribution should look like, but somehow the result for 0 units is messed up. It would be correct I think if the results for 0 units remaining were fixed so that it’s less than the result for 1 unit remaining, and the probabilities were all increased proportionally so that they equal 100% again.
The chance of 0 units surviving (losing the battle) coincides with the chance of victory for the attacker - with some small apparent error.
If I’m not mistaken, the difference arises because the chance of 0 units surviving for the defender equals the sum of victory for the attacker and and the chance of a draw (both sides destroyed). If you add up those 2 numbers it should be the same as the probability of the defender having 0 units remaining.
The number of units remaining if the defender wins the battle then takes a normal-looking distribution. So you have to first separate winning and losing the battle, then think of how many units you have left.
Yes, this has to do with only getting the “tail-end” of the curve if you are favored to lose the battle, as I mentioned.