|> Make a histogram of the results. Compare it to what the analyzer says should happen.
Unfortunately that is utterly pointless. The analyser uses the exact same code as the game engine itself (this has been stated on multiple occasions by Fizzer). The analyser comes up with its **estimates** by simply simulating the attack a lot of (1000??) times and simply counting how often the attack succeeds. In other words, what you're doing is essentially manually simulating a run of the analyser. Even if the calculation / code / whatever *did* change, this experiment will not confirm it.
If you want, you can use my analyser (link below) which actually calculates the success chance. When I first wrote it, it either agreed with the WL built-in analyser fairly closely, or it disagreed (but only in cases where the built-in analyser was known to get it wrong; the reason I even started that little coding project).
If it suddenly starts disagreeing with the built-in analyser now, that would be an indication something has changed. Note, if you find such a disagreement, please post number of attackers, number of defenders *and* offence kill rate and luck percentage (if it happens to be an X-vs-X attack, equal numbers of attackers and defenders), you should also include the *defence* kill rate.
***Warning:** as pointed out by Fizzer the last I posted this link, you're downloading executable code; essentially you are blindly trusting me to not have put any viruses or other nasty stuff in there.* (If you have even a tiny bit of programming experience, you don't have to trust me; [here](http://warlight.net/Forum/Thread.aspx?ThreadID=3153&Offset=19
) is the important part of the code; feel free to copy-paste it into your own program.) If you choose to trust me, you can download my analyser [here](http://dl.dropbox.com/u/12477348/AnalyserGUI.exe
Do you mean three attackers kill two defenders and only lose a single army themselves? That is a combination of 3-killing-2-(or-more) and 2-killing-1. Assuming 60% offence, 70% defence and **100%** luck (that's a bit easier to calculate :p ) that works out to:
60% * 60% * 40% * 2 nCr 3 = 0,432
60% * 60% * 60% * 1 nCr 3 = 0,216
70% * 30% * 1 nCr 2 = 0,42
( 0,432 + 0,216 ) * 0,42 = 0,27216
For **0%** luck (also easy to calculate) the result is:
3 * 60% = 1,8 -} 80% chance of killing both defenders
2 * 70% = 1,4 -} 60% chance of killing one attacker
0,80 * 0,60 = 0,48
So at 100% luck that's better than a 1 in 4 chance and at 0% it's virtually 1 in 2; either way not exactly "extraordinary" if you ask me. (A 1 in 4 chance is flipping a coin twice and having it come up heads both times, a 1 in 2 chance is flipping a coin once and having it come up heads.)