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I might be quite worried about the stats...: But I wasn't cheating

your opponents played bad .
When your opponent play so is easy do bit o any mistake.

I played a 37-move perfect game last week. ...and, like you, instead of enjoying it, I immediately thought - "Oh, great. They're going to think I'm cheating! ".
en.lichess.org/liHjcbgf/black

At the end, some of my moves were slightly > .3, but not considered an inaccuracy because it was a winning position. To me, it felt like all my moves were just the most logical and not difficult to find in the position.

I'd like to know how cheating is determined too. There was a guy on YouTube who said to do an analysis and if it says 0 inaccuracies, 0 mistakes, 0 blunders, they're cheating. My game above meets that criteria (with Avg. Centipawn loss of 6!) but I was really not cheating.
The moves made were not like really hard to see. You played quite simply and would be quite surprised if you were banned for this game.
I'm pretty sure the anti-cheating mechanism won't flag anyone for one 0/0/0 or 1/0/0 game - it happens to quite a few people, even low rated players like me.... if the opponent blunders early, or the moves are "obvious" then it's quite easy to play a perfect game.
The world is strange if you have to worry for playing well.
Don't worry, the cheat detection system is sophisticated enough to distingue players who are playing well from cheaters.
@Solal35 It really interests me how a anti cheating system can make differences between playing a perfect game and winning with an engine. I mean if someone uses an older version of a top engine like e.g. Hiarcs 8, and lets say he cares about his time per move management so that it is not obvious for a cheat after, how the hell can a system make a difference there!? Often it has been said there are human like and non human like moves. Ok i think a 3000+ engine can make such decisions in gameplay which no human would go for, but again: with an older engine there has to be a gameplay style which could be similar to a strong human player. Remember what exciting moves world top players like Naka make happen in their games sometimes, and also remember that every chess player on a decent level has a quantum on recognizable style at least where you know who you play after a couple games with him.
@TombRaiderIII Since I'm not a moderator, and so I don't know what it is possible to say and what's not, I would just add that there are others factors that enter in considerations. But nothing is perfect and if a really clever man would liked to cheat, he wouldn't be labeled for a long time. But I hope clever mens are smarter enough to don't cheat :)
i hope so too @Solal35 :), yeah definetly there is a big point in the tecnique of summarizing many factors of suspicious behaviour in game data. I was anti cheat moderator for 2 years on a another chess site, but that took place in a time where my team had very limited possibilities to check them. This job was in its childhood there you could speaking. I think we have to trust this system and iam sure the lichess team wont give us a reason to worry there :)

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