Banned for cheating

What is the probability that a person who is banned for cheating, didn't cheat?

Extremely high

zilch, nada, niente, zero, nil....

Once in a blue moon.

But, sometimes when I play Stockfish I think a human is intervening.

@ChessLearning2020 That's shocking.

Cause stockfish is just other humans playing against the same stockfish level 50% of the time.

(Lol)

I'm experiencing a similar problem at work, where I want to train a model based on previous PREDICTIONS (rather than observations)... People who are flagged get a probability of cheating, and say only near-certain cases are flagged, then lichess could use these new "observations" (which aren't certain) to further train their model...

I don't know if that's what they're doing, but I'm sooooo interested in cheat-detection models

I think this is an interesting classification problem, so it would be nice to discuss a bit. Almost every classifier has some non-zero error rate and you can tune it to have either false positives (the person didn't cheat but got flagged) or false negatives (the person did cheat and the system didn't detect it). On Lichess, of course, there's also a human in the loop so the reports are reviewed.

It would be interesting to know, for example, how many appeals are upheld. Assuming the process is fair (which I do assume) then that would give you some data to try and figure it out from. My guess, because of the human in the loop, is that while mistakes happen it's pretty rare. Not zero, but rare. It's an interesting academic exercise to try and put some bounds on that number.

I don't even know why you'd cheat; if you're only playing chess to win, you're not enjoying it anyway. My guess is people get caught up in their rating.