Warlight's explanation of luck: http://wiki.warlight.net/index.php/Luck_Modifier
The number of armies killed can be generalized as (Expected Value)*(100%-Luck)+(Random Value)*(Luck).
The expected value for 20 armies at 100% killrate is: 100%*20 = 20 kills.
As for the random value, well, we can do that quite easily. We take 20 rolls of 1-100. If the number is 100 or less, the army kills. If it's more than 100, then your RNG broke.
(If you're lazy, here's a link that makes 20 random numbers between 1 and 100: http://www.random.org/integers/?num=20&min=1&max=100&col=5&base=10&format=html&rnd=new
Anyway, you'll quickly notice that the random value constantly gives 20 kills, so...
20*(100%-Luck)+20*(Luck) = 20*(100%-Luck+Luck) = 20*100% = 20 kills, regardless of luck value.
Luck value also doesn't matter at 0% killrate (Defense only).
Personally, I think the idea would be a nice twist :) Uservoice is pretty slow though, unfortunately, as I have no votes still :(