Uberlager, yes, that example is clearly correct. Not sure what your point is though, because the issue with the program is with the “Must take territory” button, which is not needed for that particular battle you just gave. I’m pretty sure that the prog works fine if you don’t use that button.
@Uberlager:
I will reiterate that you need to look at the probability of 0 units remaining as not being part of the distribution. It is merely the chance of losing the battle. The chance of winning the battle is actually greater, but is distributed over the number of units you can expect to survive. Therefore, each row will individually be less than the ‘0 units’ line.
Yeah, I basically agree with this, I think I just worded my previous post poorly. So I’ll try again. :-)
I understand that the 0 units result will often have a higher probability than each of the other individual rows. I’m saying in the particular battle DY gave, the 0 unit result should be much, much lower, since it’s at the extremity of the curve. It should not have a big spike because the probability of getting 9 or more hits as the attacker (i.e. 0 defending units left) is very low.
What I was trying to point out though, is that 0 unit result is not “merely” the chance of losing the battle and should be ignored as part of the distribution. It has meaning if you realize that the probability distribution for the surviving defenders is really just a reflection of the probability distribution of the number of hits the attacker rolls.
Specifically, the 0 units remaining result is the chance that the opposing side rolls a number of hits equal to or greater than the number of units you have. So, if the attacker rolls 10 hits and you only have 9 units, its counted under the 0 unit result (since you can’t have -1 units), just as if he had rolled only 9 hits. Thus, the 0 unit result is the sum of multiple probability events for the attacker, all of which have the same meaning in game terms: 0 units surviving. This is in contrast to the other results, which represent only one specific number of hits rolled.
That’s basically all I was getting at when I said the 0 units result was the rest of the distribution curve crammed into one category.