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La lezione del GM Schwartzman After a little excitement, I was looking for a nice quiet puzzle to wrap up the month of June, and I don't think I could have found any better position than the one you have been contemplating.  It comes from a fairly well known game between the late Polugaevsky and the former Brazilian wunderkind Mecking, and it perfectly illustrates the point that I want to make with this Lesson.
Let me start by saying that this was definitely not a welcome puzzle for those who like combinations and other exciting fireworks during the game.   As a matter of fact, you did not have to calculate a single move  to arrive to the solution.  All you had to do is comprehend the situation on the board very well and make your decision accordingly.
The fact that this is an endgame, makes the above much easier to do.  Why?  Because in the middle game we often have situations where certain moves would be recommended from a strategic point of view, or would be great preparatory moves for an endgame that could ensue, but we can not make them, because we are still in the middle game, and they are not as good with so many pieces around.
This is the advantage of already being in an endgame.   With the exception of pawn promotions, we can be fairly sure that no other new pieces will appear on the board, so we can make our decisions based only on the pieces that are present right now, and since there aren't so many, it should be easier.   However, it is also important to try to foresee what other pieces could disappear.   For instance, do you think that the knights might be traded, the bishops, or both?   Which trade is better for us?  And can we better prepare for one of the ensuing endgames?
Chess is a dynamic game with a lot of interaction between the pieces of the two sides, which is why questions such as these have to be asked, as we can not always avoid certain trades.  In this particular position, it seems rather obvious that we, as white, have a slightly superior position, thanks to our better pieces and slightly better pawn structure.  Both the knight on d4 and bishop on d3 are better than their  counterparts and as you know, in endgames, such a factor could be decisive.  But here comes a very important question:  can we preserve this superiority?
The answer is not as good as we might have hoped.  While our bishop seems in control and there is no clear cut way for the black bishop to reach a trade, the knights situations is not as rosy.  Our superiority is due to having a knight on d4, but who can stop black from moving his knight to e6 and proposing a trade?   And if we refuse it, we will have to leave our dear home, while black's knight will get the jump to c5 and then become just as active... 
There is a well known strategy in chess that involves trading enough pieces to reach a position where all our pieces are better than the opponent's.   In this position, such a strategy would consist of accepting the knight trade and keeping only the bishops.  If our bishop is indeed better, then we should have some winning chances.  This doesn't mean that we have to run after the black knight in order to trade it. No, in this case, our better knight means that black will be the one running after us, and all we have to do is accept the trade when offered.
So, why I did I then waste so much time talking about something that we don't even have to do?  Very simple: preparation!  Just letting things happen is not the way to go in chess.  We have to MAKE things happen.   You see, everything I said up to now was based on the fact that our bishop is better than black's.  And while this seems very obvious just looking at the two bishops, the fact is that we should never take something like this for granted.  We have to actually explore the reason why the bishop is better, and if this will stay so forever.
So, why is our bishop better?  Well, it looks like it is more active, and controls more important squares.  But it is not such a beautiful bishop - it is actually the black bishop that is really weak.  And the question why is answered with one word: pawns.  It is black's pawn on d5 that takes away a lot of potential diagonals and that's not all.  As basic endgame theory indicates, the more of one's own pawns lie on the squares of the color of the bishop, the weaker the bishop is.  Currently, black leads in the number of misplaced pawns. 
So, have you been able to guess the move after these hints?   It is the beautiful 1.a5!

I know it is not a queen sacrifice or a checkmate, but if you truly understand this move, you too should realize its beauty.  You see, 1.a5 basically does just one thing: fix black's queen side pawns in their current configuration.   But if you expand on this idea, you will quickly see how many other things it does!
First of all, it keeps the weak b7 pawn where it is.  A weak pawn is rarely weak if it can move. Why? Because just like in football, where if the quarterback can scramble out of the pocket, the blitzing defensive line will end up empty handed, in chess too you can not do a very good job of attacking an objective, if that objective can change its position.  So if we ever want a shot at capturing b7, we should make sure it stays there.
Secondly, it keeps both b7 and a6 where they are, and that's on light squares.  This means that in the current endgame, and especially in the upcoming bishop endgame, black's bishop will always have to stay nearby, to provide the much needed defense for the two pawns.  Which makes the bishop a defensive bishop, and thus definitely a less active one - exactly what we want to insure.
Finally, 1.a5 also moves our pawn from a light square to a dark square.   And since the 'b' pawn will soon follow to b4, it means both our queen side pawns get out of the light squares.  Significance?  Simple:  Black will have no attack objectives for his bishop, and our bishop will have no worries.  So, while our bishop will be able to put pressure on d5, b7, a6, and who knows what other pawns on the king side, black's bishop will be stuck defending all these weaknesses.
Now please do not misunderstand me.  This move, 1.a5, didn't win the game.  It took white another 32 (!) moves of precise play to claim victory against the tough defense that black put up.  But what this move did, was to secure the advantage that allowed GM Polugaevsky's quest for the victory.  Because if black would have had the opportunity to move his queen side pawns up, on safer squares, then it would have been practically impossible to even claim an advantage for white.  So, while 1.a5 didn't score the actual touchdown, it gained enough yards to set up the successful drive.  My sincere congratulation to all those who found this difficult move!