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there is some degree of truth to what @chess240 said but he should not go around and spread miss information especially to beginners who might take his words as fact.
If you really don't think it's possible for a 1300 to play a single perfect game against another 1300 then go do a search for the term "sample size."
I think this is going nowhere so I'll say one LAST thing...
Your point was that it was easier to play a perfect game versus phlegm cause he's a 1300.
My point was that your rating doesn't change depending on who you're playing. eg if a 1300 plays a 1300 he won't play like a 1500
or a 1300 versus a 2800 won't play like a 1100, you always play at your rating.
So no it won't be easier for a 1300 to play a perfect game versus another 1300.
It WILL be easier for a 2000 to play a perfect game versus a 1300 but that's because there's 700 points difference!

Hmm...I think I see chess240's point. Think of it this way, CafeMorphy. Suppose I'm a 1500 player: the question is, would it be easier to play a 'perfect game' (0-0-0 according to the Lichess engine) against another 1500 player than, for example, a 2000 player? If by 'easier' we mean 'more likely to occur' then the answer is obviously 'yes.' The lower rated player will pose fewer problems, make more obvious moves, hang pieces, etc. Perhaps he'll even give up a mate-in-one after 25 moves (something, we'll assume, the 2000 player would never do). In short: at many, many points in the game, it will easier to find the best moves against a 1500 player than against a higher-rated player. And it will be easier even for other 1500 rated players. (Just think of your experience playing people all over the rating range. Isn't it easier to find good moves against lower rated opponents than higher rated?? This is because of their range in ability, not yours.)
Even my most "perfect" games contain lots of non-perfect stuff. It is possible but practically impossible to play perfect games. Of course you can play lots of impeccable moves but your fingerprint catches you out. So after a couple of games it's clear.

Even distributing 0's and 1's randomly will trap you - a human being delivers a fingerprint. So one can clearly distinguish man and machine.

@dmsv I've said (I think in all my posts) that the stronger player will find it easier to play the perfect game. That's not the question.

So let's not forget the context here, I'm talking about the cheater who played perfect games against phlegm and is (we assume) the same strength.

Imagine this... the cheater, a 1300 player, after playing 2 perfect games in a row says "it was easy to play perfect games against you because you're just a 1300".
Does that statement sound right to you? I would go "what the hell are you talking about you're a 1300 player too!"

I think we're talking about different things...

I'm talking about does the 1300 cheater have a good argument for saying he played perfect games cause his opponent was also just a 1300.
This is where I kept saying a 1300 will play like a 1300... if he found his fellow 1300 opponent easy he wouldn't be a 1300, he'd be stronger.

So, 1300 Cheater says;
"It was easy to play perfect games versus this 1100" -Yes I agree. It was easier cause he's more skilled.

But then the douchebag says;
"It was also easy to play perfect games versus this 1300" -Umm no. How can it be easier to beat him if they are the same strength...
A 1300 won't find another 1300 weak and easy to play against.

I have a funny feeling this might be a misunderstanding... probably my fault :)
Just play your natural game , If you are suspicious , then Report the Mods . They are Amazing .
@CafeMorphy--Yeah, I was ignoring the present context. For me the interesting question isn't whether X was or was not cheating, but rather whether it's easier to play well against low-rated competition. I suspect it's easier regardless of one's rating, for the reasons I mentioned. Simply put, a 1300 player is more likely to play 'well' (according to the engine) against a fellow 1300 player than he is against a 2000 player. That's all I meant to suggest.
It is certainly easier to play against a consistently lower rated player, but I'm still not sure that you would be able to find 0/0/0 except for a short combination.

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