Thing is that computers have to evaluate the position, too, at every ply. If programmers would still consider only material in that evaluation (as they did in the early days), the programs would still be bad. Nowadays, the engines also evaluate the positions with respect to the so called "general principles" (like e.g. expounded in Soltis' "The wisest things ever said about chess"). So they may find that a position is better for White even if White's down, say, the exchange. But I find it not surprising at all that the programs are yet not perfect in this as it is probably extremely difficult to program positional understanding. Now, as they have to evaluate positions in a rapidly expanding search tree at every ply, it is practically certain that they make positional mistakes "down the line"- at least as long as the lines are not yet tactics-heavy. But as the very opportunity for tactics eventually flows from the better position (as Fisher said), I find it totally believable that they may still be inferior in correspondence chess as long as the masters manage to avoid tactical blunders.
Humans v Houdini chess engine (Elo 3300)

Seems like there are two conversations going on here.
Nobody disputes that human+computer > computer (given more or less equal hardware+software). Arno Nickel beat Hydra with the help of a computer so it is no wonder he won that match.
What is disputed is whether a GM without the aid of a computer beats today's engines like Houdini. Common sense tells me this: Kasparov lost >15 years ago his match against Deepl Blue 2. Deep Blue 2 would be thrashed by today's engines. Ergo: GM's don't stand much of a chance against today's engines.
pfren comments that Kramnik would win hands down in such a match therefore sounds strange to me unless I'm missing something.
You are missing that what is being discussed in correspondence vs classic time controls.
No one doubts computer dominance in classic (or blitz of course).
But the fact is that there is dimishing returns that set in for computers due to the way they calculate.
The fact that computer + human > computer is telling.
I don't know if the difference is enough for a GM to overcome a computer in CC, but I suspect it is. 3 day time control, my money is on Kramnik vsHoudini. But I would not bet a large sum on it.

It's weird the way they always win though . . .
When? To my poor knowledge, the last time a strong corr. player met a computer, the human won 2-0, but this is some five years ago.
The reasons that such matches are not held is rather simple: The programmers are well aware of the limitations of their engines, and won't put up such a challenge before improving on them.
ELO points mean nothing for that matter- their statistical model was tuned for different sorts of events. On ICCF championships, the highest ELO currently is 2729, which is way below your 3300 dream. But this is the highest a super modern engine under skillfull human aid has achieved.
How well Kramnik, or any other strong GM can play without computer aid at long time controls? Logic says more than that, factly they would beat the machine without too much effort. Chess is not a bunch of zeroes and ones which should be counted as fast as possible, this is the truth- whether you like it, or not.
But of course, the first thing the silicon lovers will think when the GM beats their beloved Dumbini is that the GM had computer aid...
I don't really get what you're saying Pfren... what matches are you referring to? Currently, correspondence chess (outside of chess.com) is centaur chess -- it's computer + human ... so "strong correspondence players" are, at this point, basically people who knows how to get top performance out of a chess engine. This was demonstrated if memory serves (last year? year before?) when a team of ~1800 elo level players with Rybka and fast systems beat some GMs with Rybka and slower systems.

I'm not sure that a strong GM would win "hands down" against a strong engine, but I would guess that it would win given long enough time controls. Like I said before, a computer doesn't benefit as much as a human with the extra time.
If a Kramnik vs Houdini 2.0c x64 correspondence match was played, Kramnik would get crushed hands down.
The only way a human can beat a computer nowadays is if the human is also aided by a computer. Please note that the machines are MUCH stronger today than they were in 2005 (When Adams lost 5.0 - 0.5). The notion that an elite player like Kramnik alone would win hands down in a 2012 correspondence match against Houdini is absurd. Perhaps a tie, but certainly not a win.
When Arno Nickel beat Hydra 2-0:
- It was 7 years ago - chess engines have improved
- One of the games lasted 5 months
- He could use engines to help him
It was a good achievement but it's not what I think of as a chess game.
The original question was about whether a human (not human + computer) had beaten a Houdini-like chess engine when the engine's grade was well over 3000 (as they currently are) .
There are several examples where human GMs have lost under these circumstances. Are there any games they have won?

I think i favour computers over GMs slightly but saying they are over 3000 ELO is baseless. If the number isnt derived from actually playing the worlds top 50 or top 10 its just a meaningless estimation(ie people that own the program want to sell the program)
Again, I don't think it is. If, when X and Y are combined, they end up being stronger than X alone, that does not entail that X and Y are of comparable strength. It's possible that GMs can correct for tiny faults in engines in some positions while still being far weaker than engines at playing an entire game of chess.

Kasparov's style versus Deep Blue weren't the greatest match.
I'd like to see Karpov, Carlsen, Capablanca, Lasker or Petrosian take
a shot.
Apart from the 2 games that Nickel won which were not OTB, has any GM beaten any super-engine recently in any game OTB at all?
I can't find any evidence they have. There are only draws and losses.

Kasparov's style versus Deep Blue weren't the greatest match.
I'd like to see Karpov, Carlsen, Capablanca, Lasker or Petrosian take
a shot.
Three of those dudes are dead and one of them just about retired.
I suspect you are out of your depth.

Again, I don't think it is. If, when X and Y are combined, they end up being stronger than X alone, that does not entail that X and Y are of comparable strength. It's possible that GMs can correct for tiny faults in engines in some positions while still being far weaker than engines at playing an entire game of chess.
Its also possible its the other way around, the GM makes the basic plans and uses the engine for tactical error checking.
The point is that if the combination is stronger than just the engine, then humans are able to add something to the equation, making it unclear.
I dont foresee an actual match because it is impossible to prevent cheating (from either side!) in a CC game.

Okay. Then, surely, being able to see 64 moves ahead in all lines with 100% accuracy, plus having some positional understanding, is superior to being able to see a handful of moves ahead in some lines with reasonable accuracy, and having some position understanding.
It seems to me that strategy is simply long-term tactics, and engines are wonderful at tactics, whether in the short term or the long term.
Well, as BQ said above me, engines don't see that far ahead, and have far from perfect accuracy (notice they lose to eachother all the time).
Fair point.

If we're talking about unaided human vs computer in correspondence, I think the numbers speak for themselves. What is the match-up rate for old CC WC games? It's not over 70% or so right? (help me out here cheater forum people).
So it would be hard to believe the lattest modle of computer could lose.

While I still firmly positively believe that the best engines will outplay a human and only EVIDENCE will sway me from that view,... I do think it is worth mentioning that there are a few people here who believe that engines see every possible move tree with perfect clarity. This is far from the truth.
The math on it is astounding. Assuming 35 move possibilities for every half-move, do some math on, say, 10 moves (20 half-moves):
35*35*35*35*35*35*35*35*35*35*35*35*35*35*35*35*35*35*35*35 equals what?!
7,609,583,501,588,058,567,047,119,140,625 or thereabouts?!
How many positions per second can your engine do? Even at 10 million per second, it would take millenia for a computer to look at every possible variation.
Sorry, but no engine looks at everything. Algorithms and human judgement both eliminate plenty of lines to be able to make a good move.
I need evidence the other way!
But yes, you bothered to do some of the math, the ability to keep adding ply starts to choke off, which means adding lots of time (CC chess) doesnt help the computer much after a certain point.
The more time you have, the better the human is relative to the computer. The question is, is CC chess enough extra time to bridge the gap?

They aren't fooling me its really the turk in disguise!
I would be afraid to stick my hand under that little clamp, though. Especially after making a good move...

Well, Kramnik drew this blitz game anyway... don't know the software though.
And to those that say computers understand positional chess so well, my houdini still thinks white is clearly winning in the final drawn position.

A couple of questions:
When did the rules of correspondence chess change to allow use of computers? (I have been assuming the human in a correspondence chess game against a computer would be unaided.)
What is the greatest depth that a computer can look (or has looked) when moves are forced? If you count the use by computers of endgame tablebases, the maximum depth is potentially larger than 64.

http://en.wikipedia.org/wiki/Solving_chess is a brief intro to the debate about whether or not PCs will ever be able to solve chess
You mean the one referred to on Arno Nickels wiki page?
"In a correspondence match lasting many months, he won two games and drew a third against Hydra, the most powerful chess supercomputer in the world at that time (2005). Nickel, who achieved his grandmaster title in the era before GM-level chess computers, was allowed to use weaker personal computer chess engines to help him decide on his moves in this match. Hydra also received limited assistance from human chess experts and programmers, especially in choosing its opening book moves.""
Not exactly a clean example from either side
Edit:beaten to the punch by the above poster. Fast!