That's certainly nice improvement. But it's nowhere near the fastest improvement in history. I'll bet I'm not the only one who can attest to much greater improvement in as little as one or two games, not 4.
The Fastest Chess Improvement in History: my Opponent goes from Patzer to GM in just four games
No need for public shaming, but I agree you could report. As a strong human player, my eye immediately goes to 28.Nxf6+ +-, not 28.Qxe8+. However, that's not proof of anything, by any stretch of the imagination. Just an observation.

No need for public shaming, but I agree you could report. As a strong human player, my eye immediately goes to 28.Nxf6+ +-, not 28.Qxe8+. However, that's not proof of anything, by any stretch of the imagination. Just an observation.
I think the thing that strikes me is all the incredibly easy tactics he missed in the first two games - like in the second game where, already losing, he blunders his rook. I already knew he was cheating before Qxe8+, but seeing as how I was already dead lost I thought I'd give him the opportunity to play it as the cherry on top.
But beyond all that, in the third game, every move from move 12 was an engine move. Playing the Nd8 was something you'd see from Kramnik. He put up an incredible defense.
In the last game, he didn't win immediately due to any blunder on my part - even though I am 400 points stronger, he won a war of attrition, blowing me completely off the board. Once the game was over I found that every single single move with only one of two exceptions was an engine move - either first choice or second choice. His average cp loss was better the GM level from move 12 on the third game (when facing the prospect of losing three in a row to me), and the final game.
I understand that there are a lot of poor sports who make excuses and accuse innocent people of cheating. But this is the real deal, and sadly, I don't think Chess.com will do anything about it, because he is a subscriber.

You can report suspicions of cheating here:
https://support.chess.com/customer/portal/emails/new
Its against the site rules to name, and shame, and to accuse someone of cheating in the main forums.
https://support.chess.com/customer/portal/articles/1444772

I agree that does seem suspicious.
Out of 32 moves, White in the last game had 30 Excellent moves and 2 Inaccuracies (both in the early stage of the match). That’s the only part where I can see anything suspicious (the sheer amount of Excellent moves given his rating), but nonetheless, you should still report this to the website instead of writing on the forums.
I'm not sure why you say Chess.com wouldn't do anything about a cheating subscriber, given adequate proof.
I think the thing that strikes me is all the incredibly easy tactics he missed in the first two games - like in the second game where, already losing, he blunders his rook. I already knew he was cheating before Qxe8+, but seeing as how I was already dead lost I thought I'd give him the opportunity to play it as the cherry on top.
But beyond all that, in the third game, every move from move 12 was an engine move. Playing the Nd8 was something you'd see from Kramnik. He put up an incredible defense.
In the last game, he didn't win immediately due to any blunder on my part - even though I am 400 points stronger, he won a war of attrition, blowing me completely off the board. Once the game was over I found that every single single move with only one of two exceptions was an engine move - either first choice or second choice. His average cp loss was better the GM level from move 12 on the third game (when facing the prospect of losing three in a row to me), and the final game.
I understand that there are a lot of poor sports who make excuses and accuse innocent people of cheating. But this is the real deal, and sadly, I don't think Chess.com will do anything about it, because he is a subscriber.
On the other hand, people tend to play better when winning, not when losing. If you are losing anyway, not blundering a rook is not such a high priority.
Nd8 is precisely the kind of move you'd also expect from a patzer. You attacked his pawn, he defended his pawn. Patzer's always like to defend pawns. The difference between Kramnik and a patzer might be, that Kramnik would see this defence several moves ago, whereas for a patzer it might be just a lucky coincidence that a defending move is available (but a 1200 patzer may plan some things ahead as well).
Qxe8+ tactics shouldn't be that hard to find. What's the point of always recommending tactics training if you don't expect people to find simple three-move tactics, in a daily game where you are even allowed to try things out on a chess board?
Also, it is much easier to see your own tactics than to avoid opponent's tactics.
Average cp loss and other statistics also depend a lot on the particular game and how the opponent plays. If the opponent makes soft moves, it is easier to find "engine moves". Sometimes many of them can be "forced".
I am not saying that your suspicions are unreasonable, these are just some things to keep in mind.
Why not? In the third game the 1600 player wasn't really doing anything and then blundered an exchange with 19. f4.
Again I'm not claiming anything, but the following comments show that it is quite plausible that a "patzer" can play a "perfect" game by just defending his pawns if the opponent is not really doing anything other than threatening pawns.

In the last game, click on 13. ... Rc8
Then click the engine button. On my machine it starts with Nxb6 then changes its calculation to Nbc3 for quite a time before going with Nxb6.
On the fork move I guess that depends on whether you can see that Q & R are both covering f6 but both can be shifted with QxR+
Nevermind that he had an online rating of ~1200 for well over 2000 games, I must sincerely commend my opponent on the rapid improvement - I'm flattered that I inspired that type of brilliance. And brilliance it must've been, to have won a war not of blunders, but of attrition, and blowing me completely off the board. I also commend his time consistency...he spent about 10 minutes, exactly, on every move...even simple continuations. It's hard to discipline oneself that way. As for the games, check out this improvement!
Another terrible loss for our hero:
HERE IS WHERE HE HAD HIS AWAKENING:
(Around move 12 or so - the patzer in his was destroyed, and he ascended to GM level!)
And after the somewhat dubious Nb5 (I mean, he doesn't want to "show off" too much!), he again regained his dominating form! I even played f6 at move 27 just to "test" if he really had improved, as I saw the tactic, but most 1200 players would not ...and he passed with flying colors! Remember those extremely easy tactics he missed in the first two games? Not anymore! Queen takes rook, baby!
This game has only one inaccuracy by white. In this game Kasparov's average centipawn loss was 10. Would you say Kasparov cheated with engine in this game?
You're comparing a 1300 rated player to Kasparov.
I will say this, I think it's terribly bad for chess that cheating accusations get thrown out so much. And much of it really is sour grapes - no one likes a poor sport, and to be honest, I am more interested in learning and getting better than I am in wins.
But I promise, this was different.
Maybe if you guys had actually played the games instead of me, it would be more obvious. It wasn't just that every move he played was the computer move, it was the fact that the opponent I played against in the first two and a half games was not the same opponent for the last game and a half - and the immediate difference was striking. It's like all of a sudden was alerted to every one of my tactics, and exploiting the smallest positional nuances for maximum effect.
Some people don't like losing every game against the same person - pride kicks in and they want to use an engine, because ya know, "that'll show 'em".
I figured there would be people in the comments defending this guy when I created the thread - the chess.com forums are notoriously pugnacious, where even the obvious goes unchallenged because people are more interested in leveling incisive jabs than in being considerate.
I challenge anyone to really look at the first two and a half games, and compare them with the last 34 moves in the match. I am honestly flabbergasted that people would actually play devil's advocate in such a clear cut, undeniable, unequivocal, obvious case of flat-out cheating.
And to those who suggested I report, I already did so before I created this thread.
The reason I created the thread is because nothing will happen. Chess.com, unlike lichess and other chess sites, require an extremely high burden of proof before leveling the banhammer. There are multiple instances talked about online and youtube where there was cheating - chess.com rarely does anything unless it's overly blatant and committed multiple times from the same user.
What you fail to mention in your post is that these are all Daily games with a time control of 1 move per 3 days. With Daily games, you are allowed to use opening books/databases. His Nb5 move was taken from this game (https://www.chess.com/games/view/931475) which he likely chose because white had a 100% win record with it (note: it is not surprising to see a 1200 make such a choice in a correspondence game for that exact reason). While he very well may be using unapproved assistance, it is not very likely given that he is rated ~1300 and 4 games is too small of a sample size to determine this.
I don't care where he got the move, considering it was the only move that wasn't a stockfish move.
Oh, but the first game you accuse him of cheating looked normal to me. Sometimes players whine that it's cheating when their opponent gets lucky and there's a very small 2 move tactic.
I just checked, and that game doesn't look like he was getting assistance as almost none of his moves match. But that last game I think he was cheating.
The third game is, I believe, the game to which you're referring. And it's true - the moves were normal for his level...until move 12 or so. That is when I believe that my opponent, facing the prospect of losing three straight, began consulting the engine. Every remaining move in that third game was an engine move up until I blundered. Punishing the blunder was straightforward enough, so even though he played the computer moves in punishing 19. f4, it doesn't prove anything in and of itself. But immediately after punishing the blunder, his final moves in that game tell the story. Let me explain:
25...a5 also wins him the d-file.
Well if what you guys suspect is true, and that it was the fourth game in which he cheated - perhaps he did so for this reason:
Which is what I wrote after losing in game 3.
I still think he cheated AFTER the first 12 moves of game 3, though.
Yeah, from the OP I had made the guess that you accused him of cheating during or after game 3, so he did it for real in game 4, looks like I wasn't so far off
Maybe he thought he'd teach a lesson to Mr. Bigmouth. And maybe Mr. Bigmouth deserved that lesson.
But still, it wasn't his lesson to teach. One can always just disable chat - that gets the point across.

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Nevermind that he had an online rating of ~1200 for well over 2000 games, I must sincerely commend my opponent on the rapid improvement - I'm flattered that I inspired that type of brilliance. And brilliance it must've been, to have won a war not of blunders, but of attrition, and blowing me completely off the board. I also commend his time consistency...he spent about 10 minutes, exactly, on every move...even simple continuations. It's hard to discipline oneself that way. As for the games, check out this improvement!
Another terrible loss for our hero:
HERE IS WHERE HE HAD HIS AWAKENING:
(Around move 12 or so - the patzer in his was destroyed, and he ascended to GM level!)
And after the somewhat dubious Nb5 (I mean, he doesn't want to "show off" too much!), he again regained his dominating form! I even played f6 at move 27 just to "test" if he really had improved, as I saw the tactic, but most 1200 players would not ...and he passed with flying colors! Remember those extremely easy tactics he missed in the first two games? Not anymore! Queen takes rook, baby!