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La lezione del GM Schwartzman This being the last game of a rather powerful tournament a few years ago, you would expect Kasparov to play for the win.  However, if Kasparov wanted to win this game, he certainly didn't show it.   He played the symmetrical variation against the English, and allowed a line which forces a significant amount of trades, and is thus known to only give white some winning chances, but generally leads to draws.  So, did he want to win it? 
My educated guess is no!  As I found out, Kasparov was not feeling quite well, and the last few games showed it eloquently.  I am sure this caused him to choose the safe way out, which at least guaranteed him a shared first place.  In other words, he entered this game with the draw on his mind. 
You might wonder why I am wasting this much space on the background of the game.  Well, as you will see in a second, it has a lot to do with the right move.
So, after starting the game with the desire to draw it, and then successfully defending a slightly less comfortable situation, Kasparov reached this position.  Lautier had just made the last move, 20.Rc7 (the rook was on a7) and ... offered a draw.  Guess what Kasparov did?  He took it!  Why?
Well, it is purely psychological.  When you have a draw on your mind, a pretty drawish position on the board, and a draw offer from your opponent, it is hard, even for a player of Kasparov's stature, to even think about refusing it.  Is this a good idea?  Absolutely not, as this example nicely shows.
The fact is that Lautier's latest move, it too made with the idea of proposing a draw and thus considered less carefully, was a big mistake.  The idea itself didn't look bad: c6 is black's only weak pawn and there seems to be nothing wrong with attacking it.  Except that white forgot to take into account two of his biggest weaknesses: the king on the 1st rank without any breathing room and thus susceptible to a back rank checkmate, and the fact that both the bishop on b2 and pawn on b4 are undefended and happen to reside on the same file.
This interesting configuration is what would have allowed black to gain a nice, safe advantage with the cute 20...c5!

Please note that this is quite different from the pawn gain that would result after 20...Rb8.  In that case, white would have the option of playing 21.Rc6 Rb4 22.Rc2 and giving up the e4 pawn, which would lead to black having an extra pawn, but because of the pawn structure is an almost impossible to win game, especially when Grandmasters are playing it.
The right move, 20...c5, on the other, is different, because it allows black not only to win a pawn, but also preserve the most important asset he could imagine: a passed pawn on the queen side.  As to why this move wins a pawn, well, it is exactly the disadvantages I mentioned earlier.  For instance, the natural 21.bc5 is followed by 21...Rb8 and white suddenly finds himself losing a bishop because of the 1st rank checkmate problem.
Defending the pawn instead with a move such as 21.Bc3 doesn't help either, because now when black's rook comes in with 21...Rb8, it is white's pawn that is stuck because of the same checkmate threat, and will once again succumb. 
Finally, pushing the pawn with 21.b5 doesn't save it either, this time for the simple reason that after the same 21...Rb8, white has absolutely no reasonable way of defending the pawn which is now on a light square, and thus out of the reach of the bishop.
As you can thus see, all the lines after 20...c5! would have lead to black winning a pawn and gaining a significant advantage thanks to the passed queen side pawn.    There is little doubt that Kasparov would have been able to convert the advantage into a victory, and this in turn, into a clear first place in the tournament.   So, why didn't it happen?  Psychology!  Having a draw on your mind is not always a bad thing, but as you can see, keeping an open mind is even better!