I remember that incident as well; it was the next game after the random rook move and Kasparov was already unsettled about the computer's capabilities. By my memory, it went like this:
In a complicated midgame, Kasparov moved a pawn to a square under attack. He intended to sacrifice it for positional gain, opening up his attack lines and compromising the opponent's defensive structure. Kasparov expected that a computational chess engine would seize the calculable material gain and not see the deeper positional subtleties. (Deep Blue 'only' searched ahead about 10 to 15 moves, not nearly as deep as today's computers.) Deep Blue did in fact decline the pawn sacrifice, causing Kasparov to accuse IBM of intervention, that only a human grandmaster would see the response.
It was a little different from what you recall. 37. Be4 (instead of 37. Qb6) is the move that really made Garry suspect human intervention. Be4 is a much more positional move than Qb6.
In a complicated midgame, Kasparov moved a pawn to a square under attack. He intended to sacrifice it for positional gain, opening up his attack lines and compromising the opponent's defensive structure. Kasparov expected that a computational chess engine would seize the calculable material gain and not see the deeper positional subtleties. (Deep Blue 'only' searched ahead about 10 to 15 moves, not nearly as deep as today's computers.) Deep Blue did in fact decline the pawn sacrifice, causing Kasparov to accuse IBM of intervention, that only a human grandmaster would see the response.
This Wikipedia article mentions Kasparov setting a trap that the computer did not fall for, but it doesn't mention the details. http://en.wikipedia.org/wiki/Game_Over:_Kasparov_and_the_Mac...
It happened in game 2 of the 1997 match, the moves of which are recorded here. I haven't got the time at the moment to find the position in the game but perhaps someone can. http://en.wikipedia.org/wiki/Deep_Blue_versus_Garry_Kasparov