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How Hard Is It To Get A 'Perfect' Game?

How hard is it to get a 'perfect' game (according to a chess engine)? I ask this because I'd like to know the statistical probability of someone cheating. I myself have had one 'perfect' game according to the websites engine, a Caro-Kann that I was pretty much playing defense until just before my opponent resigned... but by and large I have multiple inaccuracies and mistakes per game and usually a blunder or two for good measure. By my thinking, unless the player is FM level or better 'perfect' games are few and far between, or at least games with minimal inaccuracies and mistakes, much less blunders. But I see players all the time wiping the field in tournaments here on Lichess with minimal to no inaccuracies, mistakes, or blunders.

So the second question is what is a good criteria for reporting a player as cheating? I was looking at a player earlier who had a couple perfect games, a couple really good games (an inaccuracy or two, maybe a mistake), and a couple really bad games (which, lets face it, either means something is really fishy or someone has multiple personalities and Biff took over at the wrong time).

Weigh in people, give me some ideas.
1) It depends on your opponent and on the length of the game. It is easy to play a perfect game against a weak opponent. He lets you take pieces, you take these. You cannot go wrong. Perfect game. Sometimes an opponent walks into an opening trap, you play out previous analysis, perfect game.

2) I do not know and have never reported any player. I did get some rating refunds because an opponent was found cheating. So even without reporting the anti cheating measures work fine. a player with good and bad days/ moments is not necessarily cheating. If you feel like reporting anybody, then do so.
Getting a perfect game is doable if games goes into some semi forced situation and does not get into complex endgame. So short game with lots of exchanges should be sometimes possible
It's not that hard in my opinion. You just have to play longer time controls and play with care, patience, and attention to detail.
From my experience it is nearly impossible to play a perfect game outside of slower, more positional games. This should be true for at least games against opponents who don't blunder really fast and bad. But I'm pretty sure that rather than just looking at the summary of blunders/mistakes/inaccuracies the game itself in how it is played points towards a cheater. For more statistical information you would need to have someone from the team telling you more.
I get one perfect game for each 10 games I play, more or less. It's not really that hard.
I play perfect games all the time, it is just that the computer doesnt understand them.
"I was looking at a player earlier who had a couple perfect games, a couple really good games (an inaccuracy or two, maybe a mistake), and a couple really bad games (which, lets face it, either means something is really fishy or someone has multiple personalities and Biff took over at the wrong time"

how incorrect you are... people have bad days... you are too inexperienced apparently to know this but there will come a time when you play like utter crap and wonder just what went wrong... it's called being human, ironic isn't it?
#8 ok, but there are limits. If a 1400 plays like a 2000 then something is wrong.
"#8 ok, but there are limits. If a 1400 plays like a 2000 then something is wrong."

There are different sorts of 1400-leveled players. Some may be stable, some may mix 2000-level games with 1000-level blunders. I think a detective work is necessary in each particular case. I would check the complexity of positions, the number of complexities in the game (it is ok to solve a hard puzzle a couple of times per game, but if there are more and all decisions are accurate despite limited time, then it may be a cheating)

I am the 1400 player (in classical; blitz and bullet are much worse) and I do have many games with average centipawn loss less than 20.

What can I say: I can play really accurate when an opponent plays weakly (doesn't set inevident traps or complex puzzles), when I know the opening very well (there are some of that kind), when I get advantage in the beginning. So a perfect play is possible at this level in some situations, but if a game lasts more than 50 moves with complex positions, having no mistakes is a bad signal. The more such signals - the higher probability of cheating.

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