I've looked on the wikipage for how luck works, but they won't give me a full algorithm. I want to be able to calculate how likely it is with a certain luck modifier that X troops will be able to kill Y many enemies. They say that there is a luck roll which is multiplied by the luck modifier, but they don't say how the luck roll works.

BTW I just finished a game on 75% luck where on the first turn I lost a bonus because somebody attacked me with 4 troops and killed my 4 defending troops without losing a single man. 4v4 ended with 4v0. I would like to be able to calculate how likely that is.

Just read the wiki descriptions, and I think it has sufficient information to explain how luck modifier works. It's just a pretty convoluted algorithm that doesn't fit a simple formula.

I get probability of the event above = 0.07776 * 0.00768 = 0.06%.
Or once per 1674 trials.
Pretty rare.