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La lezione del GM Schwartzman I have to admit that I have used many of Karpov's games as examples in my Academy Lessons. In any case, it seems Karpov's moves impressed more than one of my students, and more than a few Academy members actually wrote me, wondering how come Karpov lost the supreme title to ex-world champion (still feels weird to be calling him an ex) Kasparov, with such a logical, almost-perfect play.
Well, I chose this puzzle as a perfect example of what happened in their lengthy matches. Apart from the occasional blunders that can occur even at their level, the main reason Kasparov won the battle was his incredible fantasy and the so-called moves out of the blue that were often not taken into consideration by Karpov, just because they were not the logical, straightforward moves he was used to, but they often proved decisive.
The puzzle you had to solve comes from the well known 16th game of their 1985 match, with Karpov playing with the white pieces. He is obviously a pawn up, but it doesn't take a world champion to see that black has more than enough compensation for it. The rooks on e8 and c8 have beautiful open files, the knight on d3 is stopping white from moving around, the bishop on f5 is on the great diagonal, and he even has more space. White's pieces, meanwhile, look totally uncoordinated. Neither knight can move, the rook on f1 is trapped inside, and the queen doesn't have one square to go to.
When I mentioned the fact that white just played 1.b3, it was for the reason. His intention is clearly to play Nb2 and trade the annoying black knight on d3, which would improve his position considerably. Another thing to remember in such positions with compensation, is that black's advantage is only temporary. If white defends carefully and trades some of the attacking pieces, and of course, doesn't lose the extra pawn in the process, his position in the endgame would be much better. Which means that black has to be extra careful not to let white get away. One of the easy ways to do that is to keep the white pieces strangled, like they are right now. But the question is, how do you stop Nb2?
One could spend a lot of time trying to find the answer to this question, with no apparent success. I mean there are ways to stop white from playing it immediately with moves such as 1...Bg3, 1...Ne4, etc but most of them either allow white to get some more breathing air, or are just plain bad. I would love to tell you the logical way Kasparov arrived to his extraordinary move, but it's not easy. It is the kind of move that Karpov would have probably never thought of, the kind of move that looks totally unrelated to the big question, but actually proves the exact contrary. And this move is 1...g5!!

So why is this move so hard to find? Because it runs against one of the first principles learned in chess: don't weaken your king with an open center. It is also not the kind of position where black thinks about an attack on the king side, which is usually what prompts a move such as g7-g5. Nor is there a white bishop on h4 annoying us with a pin. No, there is almost no reason g7-g5 should come to mind. Except one, maybe. Someone who will take the time to analyze the position very careful, will realize that white has one more very weak piece, which apparently isn't: the bishop on f3. This bishop looks like a very good bishop, with a safe square and the important job of defending the extra pawn, which is the only thing keeping white's position from immediate loss. But a more careful look reveals the weakness of this bishop: it has no other square on the h1-a8 diagonal, and the maneuver g2-g3 followed by Bg2 is not yet available because of the other bishop on g3.
I am pretty certain that this is the reason Kasparov thought about g7-g5, and as it so happens, in this position it is even stronger, because it indirectly stops 2.Nb2. Why? Because after 2.Nb2? Nb2 3.Qb2 g4 4.Be2 Rc2 black is winning the bishop.

What about all the weaknesses on the king side? Well, first of all, Kasparov is not the kind of player who worries too much about such things, and second of all, white's pieces can barely move, so how can they expect to pose any danger to the black king.
Of course, Karpov abandoned the Nb2 idea and played 2.Bd6 Qd6 3.g3 instead, but after a few more good moves by Kasparov, white's position became un-holdable and eventually black claimed victory in one of the key games of this important match.  Unfortunately for him, it seems like in the just ended match Garry was simply unable to bring his old self to the board...