Say the game is world champion vs Deep Blue. The book opening is over, the position is even.
Would the human do better with time control of one hour/40 moves or at three hours/40 moves... or more.?
Deep Blue versus the Would Champion? You want to go back 20 years and figure out if Kasparov could have won somehow?
Human, no doubt.
The number of moves the engine sees ahead is logarithmic with time, because the number of positions it considers increases exponentially with number of moves. More time gives the engine diminishing returns much faster than it gives the human.
A (strong) human, on the other hand, often can come to a conclusion as to what the best move is in most positions with a good amount of time, because of the different thinking process.
That's what I was thinking, but even given, say, an hour a move it seems like the human would come to a wall that he just couldn't see past.
Kasparov boasted, “In the end, that may have been my biggest advantage: I could figure out its priorities and adjust my play. It couldn't do the same to me. So although I think I did see some signs of intelligence, it's a weird kind, an inefficient, inflexible kind that makes me think I have a few years left.”
He didnt.. the computer came back stronger and Kasparov was never the same. He even accused IBM of cheating!!! In fact it was later discovered the moves that baffled Kaspy was a computer glitch.. so given the circumstances of the humans win or loss, advantage human. They will suffer thru it and the computer will not. 
He didnt.. the computer came back stronger and Kasparov was never the same.
This is an interesting observation. How was he not the same? Didn't he remain world #1 and world champion for a long time after the Deep Blue match, or have I got my timeline messed up?
the interesting observation is:
They will suffer thru it and the computer will not. 
i was in agreement about humans benefiting more, until i read this
he was stripped of his FIDE title in 1993 for playing short outside of FIDE. So he wasnt the recognized world champ while being #1. Deep Blue was 1996 and 1997. Anand and Kasparov was PCA in 1995 when they played for the world chess title of which at the time were 3 of them. PCA lost its sponser INTEL in 1996 when Gary decided to play Deep Blue. Then comes The Classical World Chess Championship which he lost in 2000 to Kramnik. in 2006 PCA was absorbed back into FIDE with the Kramnik -Topalov. Wasnt that pottygate ?
He wasnt the same after Deep Blue and you make me put my finger on exactly why and I cant. He was changed after all that time he spent bashin his brain against the computers.
Say the game is world champion vs Deep Blue. The book opening is over, the position is even.
Would the human do better with time control of one hour/40 moves or at three hours/40 moves... or more.?