A knight's test!

THIS ONE IS REALLY AN AWESOME STUDY! 

(W)

White to play and win.

SOLUTION:

This position was sent as a message to me by a very strong Indian GM Lalith Babu. I was walking on the road and decided to solve it blindly as there were so few pieces. I tried and tried but really in vain. I soon forgot about this problem not finding the answer.
One fine day, IM Swapnil Dhopade messaged me this problem and this time I swore to myself to solve this position. However after some really hard thought and even moving the pieces, I wasnt able to solve it.
When Lalith Babu finally revealed the answer, I came to know that I was 70% close to the solution, but it really was a mindblowing exercise. I request the players who have not tried it,to give it a try. It will teach you a lot about the position.
Its always better to look at the answer after giving a sincere try. It just makes you understand that things werent as easy as the answer makes it look like!

THE METHOD:
How do we go about solving this position. The first thing to note is that black is threatening d3. So of course the first move is obvious. We have to play Ne1 to stop it.
Now before you start calculating, you must understand that this is a position which comes into the category of positions where you have to start from where you want to reach. That means you need the brilliant imagination to figure out a winning setup. For me this has really been a difficult task because many times I have tried hard to find a winning setup and when I do, the problem is that I cannot make it work with the moves. So instead of thinking of another setup, I tend to give up and just look at the solution.
So more than lacking imagination, I lack the perseverance and determination to repeat the same process again. If you too are in the same category then you really need to learn the art of not giving up.

So what is white looking for.
Of course white is looking for a simple thing and that is activation of his king!
If white king can get into the game, it will be all over.
So from where can the white king come into the game?
1. If white gets in Kc2, then he will most probably win this game!
2. If white gets in Kf3 then too he will win the game!

Of course the former seems easier but a close look at the position, reveals that Black has not 1, not 2 but in all 3 squares to prevent white king to come to c2. Black king will keep alternating between b3,b2 and c3 and Knight can at the most control only 2 squares.
So in short, its very difficult to manage to get in Kc2.

Now we start thinking about the other side. Whenever we try to reach Kf1 in order to go Kg2-f3, Black king will jump to the d2 square and keep alternating between d2 and d1.
Phew its really so complicated!! At this point, many people would give up trying to find the final winning position! But please don't give up! Because if you do, you really are not improving at the game of chess.
So you work harder and harder and finally come to a position whereby you see that the best place for the white knight can be f4. It not only prevents d3 but also protects e2 and thus freeing the white kings route to f3.
So let us try to setup that position.

What is happening in this position.?

Have a very hard look at this position and tell me whether its a draw or whether white is winning? When you think with a clear mind, you will realise, that this is a position of RECIPROCAL ZUGZWANG!!

Wow what a fancy word! What exactly does it mean? In simple language, it means that the side to move is the one who is at a disadvantage.

Lets imagine its black to play. Now if black moves his king away from the attack of the e2 pawn by lets say, Kc3 then white plays Kg2 Kd2 Kf3 and coming up next is Ke4 with a winning position. So in the diagram above, the only logical black move is to keep an eye on the e2 pawn and play Kd1. White will then play Kg2! threatening to win the game with Kf3. So the only move that black has is d3, but after ed3 e2 Ne2, we see that black king cannot take on d3, and white queens his pawn. Wow! What a discovery! If its black to move in this position then white wins!

But what if its white to play. First thing to note is that white cannot move is king. If he plays Kg2 then d3 draws on the spot, as after ed3 e2 Ne2 Kd3, the white pawn is lost.

So white king cannot move, but whats the big deal you may ask! White has a knight, definitely he can move here and there and bring the same above position in the diagram with black to play! This is where we come to a very important rule of the endgame:

KNIGHTS CANNOT LOSE A TEMPO!

What does the above statement mean? Let me explain it with a very simple position.

(B)

Black to play. Only 1 move draws. What is it?

Black needs to choose from Kc7 and Kc8. What would you play? A little bit of calculation will convince you that Kc8 is the right move! Now white plays Nf4 Kc7 Nd5 Kc8, If there existed a rule called pass in chess, then white would win now. But the fact of the matter is that the knight has to move again, thereby giving up the very crucial c7 square. thus after Ne7 Kc7, no matter what the white knight does, it will never be able to lose a move! This is a very important rule to remember in the endgame.

White to move can only draw this position as the knight can never lose a move!

We know now what we are aiming for.We are aiming for the above position but with black to move.

SO LETS GO BACK TO THE STARTING POSITION.

(W)

White begins with 1.Ne1 black plays 1...Kb2 not giving up c2 square.(1...Kb3 should also be fine) 2.Nd3 Kc3(forced)

This is the position which should be in your mind as this is the position that is reached by forcing play.

MEMORY MARKER POSITION.

(W)

This position can be used as a memory marker and we need not start from the initial position always as all the moves upto this point have been forced!

Now what are we to do. Let suppose white plays 3.Nf4 Kb3! (Kb2 now is an error that we shall soon find out) 4.Ke1 Kc2 5.Kf1 Kd2! We reach the same position of Reciprocal Zugzwang with white to move. Thus it is unfavourable for white.

Now instead of 4.Ke1 if white were to play 4.Nd5 the position will be interesting. Black king is on b3 and now has a choice to make. If he goes to 4...Kb2 then he will lose as we shall see in the main line of the study. But black can play the simple 4...Kc4 attacking the knight. Thus white king doesnt get the c2 square. After something like 5.Nf4 to control d3, Black plays 5...Kc3 and white has made no progress.

Now lets get back to the Memory Marker position and try to find a different route for the white knight.

If you are persevering, you will find 3.Nc1! taking away the b3 square. So black has to play 3...Kb2 (3...Kc4 loses to 4.Kc2!)  

(W)

Its time for you to find something different now!!

This is the key part of the study! White plays the very stunning move 4.Na2!!

(B)

This is not just a flashy move, it does a very important job of controlling the c3 square.

Of course you have already seen that the knight cannot be taken as after Ka2, Kc2 followed by Kd3 will simply end the game!

Now black has only 1 move to keep the balance. That move is 4...Kb1! (4...Kb3 would have been an error as after 5.Kc1! black has to lose the control of the c2 square, when white will win)

The problem with Kb1 is that, now the black king has lost a move. He has been pushed back. So white gets the much needed tempo to reach the crucial square on d5!

5.Nb4! Kb2 6.Nd5! (Nd3 would be a mistake as after Kc3 we would be back to where it all began.) 6...Kb3

(W)

White has made a very huge progress! We have seen the same position before in our analysis, but in this position it was black to play. When he would play Kc4. but here it is white's move! The reason is because black had to waste a tempo with Kb2-b1!

WHAT SHOULD WHITE PLAY NOW?

to tell you the truth, I was able to reach upto this point in my analysis but not any further. What should white play here? The answer to this question can be made easy by solving the below position.

(W)

How should white stop the b pawn?

The onus of stopping the b pawn is on the white knight as the white king is very far off. However in order to stop the pawn, white has only 1 move. Its obvious that we must bring the knight closer to the pawn, Hence moves like Na6 and Ne6 come to our mind. However both these moves lose! Infact the only move to draw in this position is Ne8! The knight will then come from d6 and will easily stop the pawn as you can easily verify.

This act of the knight which I like to call the "Bow principle" is very common in knight vs pawn endgames.

I call it the bow principle because the knight goes back in order to come forward with a greater speed, just like how we pull the bow in backward direction so that the arrow goes in the opposite direction!

USING THE BOW PRINCIPLE THE ROUTE FOR THE WHITE KNIGHT BECOMES SIMPLER IN OUR MAIN PROBLEM

(W)

White knight must go far away if it wants to win the battle!

The right move now is to play 7.Nc7!! The move makes use of the bow principle at the same time, its very logical as white knight wants to come to the b5 square in order to control c3 and d4. Black's move is forced as he cannot let the white king come to c2. Thus he must play 7...Kc3(Kc4 Kc2+- & Kb2 Nb5+-) 8.Nb5 Kc4 9.Nd6 Kc3 (Kd5 makes no sense as now the black king can no longer control the c2 square and after Nf7 white just wins with Kc2 next move)

(W)

How to finish off things accurately now?

White now plays 10.Ne4! When again for black he has only one move at his disposal and that is 10...Kb2! (10...Kc4? of course loses to Kc2 however the refutation to 10...Kb3 is subtle and very nice 11.Kc1! and black has to give up the control of the c2 square!)

White went 11 Nc5! Kc3 

(W)

What should be whites next item on the agenda?

Activation of the king of course! White now plays 12.Ke1! when the king has started his journey towards the f3 square. Black must remain near the d2 square as we already know the position of reciprocal zugzwang. 12...Kc2  Now white has to make an extremely accurate move 13.Nd3! Taking away the very important c1 square from the black king.

(13.Kf1 would be a huge and grave error and would spill water on all the previous efforts as black would reply 13...Kd2 Nd3 Kd1 Nf4 Kd2! and we have reached the position of reciprocal zugzwang with white to move and hence its a draw)

13...Kc3 14.Kf1 Kd2 15.Nf4!

BY HOOK OR BY CROOK WHITE HAS REACHED THE RECIPROCAL ZUGZWANG POSITION WITH BLACK TO PLAY AND HENCE HAS WON THE GAME!

The end is already mentioned above, but we will give the moves here anyway. After 15...Kd1 16.Kg2! Kd2(d3 ed3 e2 Ne2+-) 17.Kf3 +- its all over. The white king will come to e4 and pick up the d3 pawn.

What a Fantastic position!! You have to agree that in order to solve this position, you required not only a surgeon's precision but also a Ballerina's grace and nimble footedness!

So many things can be learnt from a single position! Rules like Knight cannot lose a tempo, or the bow principle or memory markers etc...

But one of the most important things to learn from this position is to ask yourself the question at the start :

HOW CAN WE SETUP A WINNING POSITION FOR WHITE? 

YOU MUST HAVE THIS QUALITY OF IMAGINING THE WINNING POSITION FROM THE START. ONLY THEN WILL YOU BE ABLE TO START OFF WITH YOUR CALCULATION. OTHERWISE, YOU WILL JUST BE RUNNING IN THE DARK AND COULD RUN INTO A DEAD END EVERY NOW AND THEN!

I hope you enjoyed this problem and learnt a lot!

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