Interesting analysis. Nothing more yet. (Hey I need this to be listed on my "forums I have posted in" right?)
Computer game analysis
Well, what would you like more? Looking at the insignificant differences of the non-maches (within one tenth of the value of a pawn), I would say that player B achieved almost a complete agreement with an engine, in a positional game. As far as I know, this has never been achieved before, in OTB or correspondence games.

costelus, did you let the chess.com staff know? They are always on the lookout for players who play like superGMs. You know, so they can... umm, promote them.

Gosh white played well too! This is why we need the cheat squad :)....alright I know no one liked that idea.
Player B is one of the top players here for some time. Chess.com claims that they periodically check their top players. Therefore, it is impossible that this player has not been checked. Maybe he does not play so well in other games, and that's why he is not suspected of cheating.
I have to add that B does not play like a super-GM. Any super-GM dreams to play like B in this game, but nobody achieved this so far.
White played reasonably well. In fact, this is how I picked the game. The large majority of B's opponents make tactical errors and they are swept away quite quickly. But White also did some mistakes, like 42.d6, just giving up the pawn for nothing. B on the other hand made absolutely no mistakes, he/she is always within +-0.10 of the optimal move. Amazing, isn't it?

Player B is one of the top players here for some time. Chess.com claims that they periodically check their top players. Therefore, it is impossible that this player has not been checked. Maybe he does not play so well in other games, and that's why he is not suspected of cheating.
I have to add that B does not play like a super-GM. Any super-GM dreams to play like B in this game, but nobody achieved this so far.
White played reasonably well. In fact, this is how I picked the game. The large majority of B's opponents make tactical errors and they are swept away quite quickly. But White also did some mistakes, like 42.d6, just giving up the pawn for nothing. B on the other hand made absolutely no mistakes, he/she is always within +-0.10 of the optimal move. Amazing, isn't it?
Yeah...wow. Was this live chess or correspondence? And is this level possible in correspondence? I heard someone beat Hydra in correspondence chess?

This looks like computer aided vs computer aided. At first look it looks like white make some mistakes, however they don't make white drop behind, simply becuase they ain't mistakes, they are made based on analysis of projected positions, thus seeing further ahead. Black do some of this too, but seemingly ain't as 'novelty'-seeking.
The fishy thing about the game is that after move 41 white shift from playing GM+ quality, to newbie quality, 4 out of the last 5 moves are grave mistakes.
This was correspondence. The point is that, apart from perfect openings, correspondence chess is not far from OTB level. The analytical skills are the same, if humans are involved. Here is a random game in which you will see the correspondence chess champion at that time making a huge blunder :
http://www.chessgames.com/perl/chessgame?gid=1293519
Keep in mind that such games took about an year to complete.
If someone beat Hydra in correspondence? Possible, using Fritz :) Or if Hydra was allowed to think let's say 5 seconds per move. Otherwise, definitely not.
To me white is clearly a strong human player. He makes good moves, but cannot make optimal moves. And he makes mistakes, not only on move 42.
"The fishy thing about the game is that after move 41 white shift from playing GM+ quality, to newbie quality, 4 out of the last 5 moves are grave mistakes."
Exactly this is how humans play!! Everybody, including Kasparov, makes mistakes! There was a dramatic ending of a decisive encounter between Karpov and Kasparov in 1986, when both of them made HUGE mistakes. Not in a complex position, but in a pawn endgame.

What methodology did you use when analyzing the game in question? I hope that it was not the built-in full game analysis feature that is standard fare in chess GUI's as this does not produce reliable data due to the fact that retrograde analysis is highly influenced by moves that are stored in the hash tables. Since this is a topic of some importance to you I'm hoping that you've read the highly regarded and well respected academic paper that outlines the best way for measuring fidelity to a chess engine. I'll refrain from posting a link as it might be counter-productive.
P.S.
GM Arno Nickel defeated Hydra in a CC style match several years ago. I'm not positive of the rules that were in place at the time so I can't comment on whether or not he was allowed to use engines to assist with his analysis but I suspect that he was not. He's a well known anti-computer player.
P.S.S.
The most unusual aspect of black's play to my eyes was the extremely aggressive use of the king. Granted, it was effective but most players I know would hesitate to activate the monarch so aggressively with so much firepower left in play.
The methodology is described here:
http://www.cse.buffalo.edu/~regan/chess/fidelity/
There you can find examples of cheating or not, as well as percentages of agreement with computer engines.
The analysis above was done using SCID with the engine Fruit (the best free engine I could find). I just simply went by hand through all the moves.

Of course I can't know for shure what happened, but there is a very clear shift in whites game, it is not a single blunder, it is 4 of them in a row, only separated by a move that anyone could have made. After 41 moves without a single one amongst them that I, using computer aid, can clearly identify as less than optimal, I cannot believe that this is by chance. Something happened to white player, and I believe the most likely explaination to be that the player stopped using computer aid.

Of course I can't know for shure what happened, but there is a very clear shift in whites game, it is not a single blunder, it is 4 of them in a row, only separated by a move that anyone could have made. After 41 moves without a single one amongst them that I, using computer aid, can clearly identify as less than optimal, I cannot believe that this is by chance. Something happened to white player, and I believe the most likely explaination to be that the player stopped using computer aid.
I strongly disagree! Just because white was able to perform well enough to keep the game close doesn't imply anything except he's a strong player. As the first player, if white had been cheating black wouldn't have achieved equality so easily and so early. If you're going to imply cheating at least offer some data so others can reproduce your results. i.e. engine, version, method etc.
White looks like a strong human player who played well but was getting slowly grinded down before blundering a pawn. After the blunder, white's position just collapsed. As for making a series of errors -- it's called tilt! That's what happens after you know you've blown it. From bad to worse....
A simple google search shows that Arno Nickel defeated Hydra while using a weaker program for assistance. I was wondering why I haven't heard of him until reading the post above :))

It is most likely the case that white was not using computer assistance, and that white missed that after d6 Bxd6 that Rxb6 was impossible because of Bc5+

The game didin't look computerized to me, the highly complex middlegame is typical of strong IM or standard GM games, both of the set ups adopted by the players are rarely used by computers if they have a choice and it's usually the case that after making one mistake you make more, it's what you call a "downward spiral" or a negative trend Happens to everybody.
Hello,
Following a discussion I had in another topic, I post here a game between two strong players at chess.com. I will not give their names and please refrain from searching/identifying the game.
What stroke me was player B's strength. I must mention that this player has been a top player at chess.com for a very long time. For sure he was investigated many times for cheating and things are very clear: B is definitely not a cheater. OK, then who is B? I claim that, judging after the game below, B plays much better than any chess player in the history. I strongly believe that a player with B's talent would become easily a super-gm, if he/she started to play OTB.
Do you think there is something wrong with the reasoning above? One can argue that this is just one game. I agree, I don't have the time to analyze in depth more games, but this one looks to me as being perfect.
Below is my analysis of this game, using the Fruit engine (last version, it is at least 2800). At the end there are my conclusions. Note that all the moves from 13... onwards which don't have a comment to the right are full matches with the engine.
delta is the difference between the best move the engine finds in the given position and the move chosen by the player.
1. d4 d5 2. c4 e6 3. Nc3 Nf6 4. Bg5 Be7 5. e3 O-O 6. Nf3 h6 7. Bh4 b6 8. Be2 Bb7 9. Bxf6 Bxf6 10. cxd5 exd5 11. b4 Qd6 12. Qb3 Rd8 13. O-O
13 ... a5 FULL MATCH.
Out of the database. The analysis starts with move 13 of Black.
14. b5 Nd7
15. Rfc1 Nf8
16. Na4 Ne6
17. Nb2 Re8
18. Qc2 Rac8
19. Nd3 c5 PARTIAL MATCH, delta = 0.02. 19...h5 is the best move.
20. bxc6 Rxc6
21. Qb2 Rec8
22. Rxc6 Qxc6
23. Rc1 Qd6
24. Rb1 Bd8
25. Nfe5 f6
26. Ng6 Kf7 NON MATCH, delta = 0.10, Best move: 26...Rc7
27. Bh5 Kg8
28. Bg4 Rc4
29. Ngf4 Nxf4
30. Nxf4 g5
31. Ne2 Qb4 PARTIAL MATCH, delta =0.02. Best move: 31...Qc7
32. Be6+ Kf8
33. e4 Qxb2
34. Rxb2 Ke7
35. exd5 Kd6
36. f4 gxf4 NON-MATCH, delta = 0.13. Best move: 36 ... Bc7.
37. Kf2 Bc7
38. Nxf4 Rxd4
39. Ke3 Ra4
40. g3 Ba6
41. Nh5 Ke5 NON-MATCH, delta = 0.14. Best move: 41...Ra3+.
42. d6 Bxd6
43. Bb3 Bc5+
44. Kd2 Rd4+
45. Kc1 Ba3
46. Nf4 0-1
Conclusions
Moves analized: 34
Full matches: 29
Partial matches: 2 (delta <=0.05)
Non - matches: 3.
Depth: 15 for all the moves, except for partial matches and non-matches, where it was at least 17.