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Shouldn't a perfect game be flagged automatically?

Yesterday I played a blitz game against someone with a rating of ~1500 or so (mine was 1750 or something at that point). I felt very pressured during the game, and ended up losing in what felt like a clear, brilliant way. I became suspicious, used the computer analysis and - lo and behold - my opponent had zero inaccuracies, zero mistakes, zero blunders. I made a report and the user was banned for cheating.

This led me to think, shouldn't perfect games be flagged automatically (i.e. shouldn't a moderator be alerted to take a look)? If I hadn't become curious to see the analysis, perhaps I would've missed this.
To establish perfect play, somebody must first request an analysis. It would be overwhelming to the server if lichess had to analyse all games. So it is up to the loser to request an analysis and then to report if suspicious. Not all 0 0 0 games are suspicious. E.g. if you blunder it may be easy to defeat you 0 0 0.
I know this is a silly example, but I don't think a moderator should be alerted for black playing perfectly accurately in this game: 1. g4 e5 2. f4 Qh4#.
Ah, I didn't think of that (that an analysis must be requested). You're right about overwhelming the server.
On the other hand games where the standard deviation of time per move is smaller than some pre-set percentage of the average time per move could be flagged automatically as suspect. That would not take up too much processing I guess.
So at least what could be done then is being sure to use the game analysis with Lichess' cheat detection software in an automatic way in those cases where either player does happen to request an analysis. If the work is already done why not use it?
The point about short games is also a good one. There could be a minimum number of moves requirement before it kicks in.
One unintended and kind of humorous consequence to this though would be that people that tend to worry a lot, like myself for instance, might start worrying that if they shoot for a perfect game they're gonna be flagged as a cheater. They do happen occasionally even to players like me that hover in the 1800-1900 range.
One time after analyzing a game that was a good size number of moves I was shocked to see 0 0 0 for me! So of course I had to show it off in the forum. Even then someone said the game showed my understanding of openings was not good and my play was uninspired lol.
I don't think that a perfect game should automatically be flagged; in fact, I have played dozens of perfect games in atomic when my opponent makes checkmate unavoidable in the first dozen or so moves. This would probably bring in a thousand reports a day of innocent players.

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