From Dark and Darker Wiki
Whether luck works or not isn't confirmed. SDF recently stated that "it should work". If for whatever reason it doesn't work, we have a bug on our hands.
But proving it doesn't work requires testing, which few people are willing to do rigorously as it takes a lot of effort.
There have been numerous anecdotal experiences where people have been exceedingly unlucky. Promoz had a stream where he killed 70 Elite Skeleton Champs in a 440 Luck kit but received 0 keys.
The odds of not receiving a single key in that span is on the order of 1 in a 1 million. That is, assuming luck works. If you assume luck doesn't work, the odds are a much more reasonable 11.8%.
There are a few contexts that need testing: crush, unchained harmony, regular interaction/lock picking, and killing mobs. Regular Interaction and Lock Picking have very similar structures and presence in game files, so testing one is likely good enough for covering both.
Repeating Promoz's attempt at Golden Keys is ideal for testing mobs since the supposed effect luck has on key drops is incredibly strong.
The other contexts are harder to test though. There are no container loot tables where luck has such a strong effect as with Skeleton Champion and Golden Keys. So to make up for that one would need to collect a larger sample size for good confidence.
An additional complication is that the devs have not confirmed the wiki's loot tables are accurate.
We create them on a set of assumption that feels reasonable to us given what information we can find in the files. From playing the game and reflecting on anecdotal experience, the assumptions feel correct.
But there may be edge cases where we are wrong. So if you want to be completely certain, not only does a luck sample need to be collected, we also need a control sample too.
As of yet no one has made an attempt to test luck rigorously.