Here is a position that illustrates the real problem facing Deep Blue, or any other computer hoping to beat the world champion. It's White to play. A good human player will think like this:

"Is there any reason I shouldn't take his knight? I know that a rook's pawn and wrong-coloured bishop can't win against a lone king, but what about two wrong bishops and two rook's pawns? (Pause for brief consideration to realise that the black king can never be dislodged from h8 by any number of white-squared bishops and h-pawns.) Well, I'd better avoid that one then."

Human therefore plays 1.Kh2 (or almost anything other than gxh5) and cautiously grinds out a victory. A computer, on the other hand, thinks like this:

1.gxh5 comes top of my list of attractive moves, since it leaves me with an advantage close to +8, which improves on the present figure of +5. So unless my endgame database includes the resulting position as something to avoid, that'll be the move I play."

The trouble is, as will be found by testing any chess computer, that even if the case of two white-squared bishops and two h-pawns is in its database, then you need only add another pawn on h2, or another bishop on a8, for the witless machine to blunder into the trap.

This position, of course, is a pathological freak, but the underlying problem is real: chess computers cannot generalise on the basis of past experience or existing knowledge. How do you program a machine to realise on its own a thought like "any number of white-squared bishops makes no difference"?

With their "I-go-here, he-goes-there" analysis, computers cannot move above it all to reach a level of higher understanding. And that is why Garry Kasparov will probably defeat Deeper Blue in New York over the next week.