i have checked the wiki for it , and i think luck do not affect that graph.
but unfortunately i also found this :
"The Army Loss graph presents the most likely outcome of the attack. The actual outcome may be off based on the random factor, but since that's impossible to predict it's logical to assume that the most likely outcome is what will happen when forming your plans."

what are the random factor(s) ? , why is it impossible to predict(in case it really do not depend on luck) ?

one more thing : i think that The army loss graph only depends on "the offencive kill % and defensive kill %" : which is 60 and 70 respectively(standard).

Uhm no....they do also calculate luck and whether or not it's straight/rounded mode

the random factors are luck and weighted random rounding. With the latter, if an attack kills 1.2 armies, there is a 20% chance it will kill 2 and an 80% chance it will kill 1. straight round, however, makes it 100% that 1 would die.

then there's luck %, which sometimes means you attack with a bajillion armies and it doesn't kill a single one. however, the graph continues to show the most likely outcome nonetheless, it's only the range of deviation that changes.

with 0% luck and straight round, you can predict exactly how many armies will die in a given attack. on standard kill rates, 3v2 always succeeds with one leftover army, i think.

<i>i have checked the wiki for it , and i think luck do not affect that graph.</i>
Luck does not affect this graph. The most likely result is still the same no matter what percentage of luck is present. As a result, the only things affecting the army loss graph is the offense/defense kill rates.

<i>i have checked the wiki for it , and i think luck do not affect that graph.</i>
Wait, if you read the wiki, then you should have seen this point: "Both graphs are affected by the offense and defense kill rates set for the game you are looking at. The top graph is also affected by the luck percentage set for the game."
That implies that the bottom (Army Loss) graph is not affected by luck percentage.

<i>with 0% luck and straight round, you can predict exactly how many armies will die in a given attack. on standard kill rates, 3v2 always succeeds with one leftover army, i think.</i>
3v2 leaves 2 on the captured territory, as 1.4 armies rounds down to 1.

>.> My bad, I'm too used to formatting with <> symbols instead of brackets. It's still readable, though.