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At chess.com, my daily rating is 1500+ (my puzzle rating: 2400+; my blitz rating: 1600+ and my rapid rating: 1700+) and I played two games with the same opponent whose daily rating is much lower than mine (his daily rating: 1200+; his puzzle rating: 2000+; blitz rating: 1300+; rapid rating: 1500+). I was not only defeated in both games, but I also did not even have any chance of winning or even drawing. Of course, the accuracy of all his moves is not 100%, but I can hardly imagine me standing no chance playing against a player whose rating is a few hundreds below me. I suspect he made some moves by himself, but also received help, either from a much stronger player, or from some engine at least several times during each game. However, I have no black-and-white evidence supporting my suspicion.

Here is the first game (I play black):

    8/4k1p1/4p2p/1pp1B3/2p5/P1P5/5P1P/6K1 b - - 2 30
   1. d4 d5 2. c4 c6 3. Nc3 Nf6 4. Bg5 dxc4 5. Nf3 b5 6. a3 Bb7 7. e4 Nbd7 8. Be2
h6 9. Be3 e6 10. Ne5 Bd6 11. Nxf7  Kxf7 12. e5 Nxe5 13. dxe5 Bxe5
14. Qc2 Bxc3+ 15. bxc3 Qd5 16. O-O Rad8 17. Rad1 Qe4 18. Qb2 Rd7 19. Bf3 Qf5 20. Bxa7 Rhd8 21. Rxd7+  Rxd7 22. Bb8 Ne4  23. Re1 Rd2 24. Qc1 c5 25. Rxe4 Bxe4 26. Qxd2 Bxf3 27. gxf3 Qxf3 28. Qf4+ Qxf4 29. Bxf4 Ke7 30. Be5 1-0

I was really impressed by his key move 24. Qc1. It was hard for me to imagine a 1200+ player can find such a surprisingly good move. I have a coach who is rated 2200+ and he did not see this move when he was analysing this position.

Here is the second game (I play white):

5rk1/7p/1pRp2p1/p2Pb3/3pP2q/P2Q2PP/1P4BK/8 b - - 3 25
1. e4 c5 2. c4 Nc6 3. Nc3 g6 4. g3 Bg7 5. Nge2 Nf6 6. Bg2 e5 7. O-O O-O 8. d3 d6
9. Rb1 a5 10. a3 Be6 11. h3 Qd7 12. Kh2 Nh5 13. f4 f5 14. Be3 Nd4 15. Bxd4 cxd4
16. Nd5 fxe4 17. dxe4 Bxd5 18. cxd5 exf4 19. Nxf4 Nxf4 20. Rxf4 Qe7 21. Qd2 b6
22. Rc1 Be5 23. Rxf8+ Rxf8 24. Rc6 Qh4 

Here black has a clearly winning position. I feel completely overwhelmed in this entire game. Again, I do not understand why a 1200+ player can play so well.

So my question is, did my 1200+ rated opponent play honestly in these two games, or is it likely he cheated by receiving external help?

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    I think no one here can answer whether someone is cheating or not. There are reporting systems on almost all chess platforms. If you suspect someone is cheating, I suggest reporting them instead of speculating here or in another place.
    – Minot
    Nov 8 '21 at 6:35
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    As a rank amateur, on the first game Qc1 is basically the only move; my thought process. Qa2 leaves a possible revealed attack, Qa1 is putting the queen in the corner, Qb4 invites c5 then I'm just getting my queen pushed around.
    – JeffUK
    Nov 18 '21 at 18:26
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I have no way of knowing for sure whether your opponent cheated - however, I suspect he did not.

In the first game, Qc1 could easily have been luck. Keep in mind that your opponent isn't choosing from dozens of possible moves here. The queen is threatened and it only has a few reasonable squares to move to; I could see him choosing that square for his queen even if he didn't see the follow-up at that time (and I don't think it's totally unreasonable, especially in a correspondence game where you can legally take notes and play out the position on another board, that he could see the follow-up.)

As for the second game... Well. Out of 24 moves, the chess.com analysis says Black made 2 blunders, 3 mistakes, and 2 inaccuracies. That's pretty much a third of the moves after the book moves. In contrast, he only played a "excellent" or better 8 times. That really doesn't look like cheating to me. (Not that you can't cleverly play "blunders" when you're winning that leave the game solidly in your hands - but he didn't even do that; the first blunder, according to the analysis, took the evaluation from -1.56 to +0.61, which seems like an odd thing to allow if you're cheating.)

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    Thank you! I just find it hard to explain why he beated me so easily when his rating is far below mine. To me, he plays like a 1800+ player, who still makes mistakes but plays much more accurately than a 1200+ player.
    – Zuriel
    Nov 8 '21 at 11:32

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