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

I don't think there is anything to be afraid of. I've had flawless games before. I don't know how they find cheaters but I don't think accuracy is going to make them think you're cheating. Personally, I think some of the biggest indicators that somebody is cheating (though I don't understand how one can be completely sure) would be these: 1) The time taken between every move seems to be the same no matter how drastically the position changes. 2) The player never seems to make risky decisions. (If you're not Jose Capablanca, you're going to take a risk now and then to be successful). 3) The player seems to play a capture as most of his/her refutations. (This is my opinion, and it's based on my personal experience playing against computers. If the computer thinks you are worse positionally, it likes to capture things). In any case, I don't think you have anything to worry about.

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