Mastering the Endgame - Part Three

This post is Part Three of my journey through the systematic Endgame study book, Silman's Complete Endgame Course: From Beginner to Master.  Here's a link to this book on Amazon: https://www.amazon.com/Silmans-Complete-Endgame-Course-Beginner/dp/1890085103.  Go buy it!  It's fantastic and well worth your money!  All of the concepts and diagrams mentioned in this series come straight from the book, and are not my own (I've simply compiled them into a shortened blog format).  And any time I directly quote Jeremy Silman from the book, I'll put it in quote marks.
But before we begin this section, below are the answers to the test positions from Part Two.

PART TWO TEST - ANSWERS:










Position 1: White to move - "Does White have anything to worry about?"
Answer: No.  Remember that a Q vs. B endgame is an easy one to win for the player with the Q because the dark-square B can do nothing to affect the light squares.  There are multiple ways for White to force a checkmate in just a couple moves (all starting with various squares White can move his Q to with check), but perhaps the simplest one in accordance with the principle of keeping your Q on squares opposite the color of the enemy B in a Q vs. B endgame would be 1. Qg2+! Kb8 2. Qb7#.











Position 2: White to move - "Is Kf3 a good move?"
Answer: No.  Remember that when playing a Q vs. N endgame (if you're the one with the Q), in addition to making sure you don't accidentally stalemate the game you also have to watch out for forking (i.e. double attack) tricks that the enemy N can have.  If White plays 1. Kf3??, Black can reply with 1...Ne5+ forking the Q and K, and after White moves his K out of check (e.g. 2. Ke2) Black can play 2...Nxc6 capturing the Q and instantly drawing the game (since neither side has enough material to checkmate his opponent's K).











Position 3: Black to move - "Where should Black move his King?"
Answer: There's only one move Black has here that can force a draw, and that move is 1... Kd8! because it allows Black to maintain the opposition and therefore the control of the square directly in front of White's pawn.  The alternative move 1...Kc8?? instantly gives the opposition to the White K (and therefore control of the square directly in front of White's pawn) when White replies with 2. Kc6!, allowing White's pawn to promote with 2...Kd8 3. d7 Ke7 4. Kc7 Ke6 5. d8=Q.  And of course the alternative 1...Ke8?? allows the exact same thing: 2. Ke6! Kd8 3. d7 Kc7 4. Ke7 Kc6 5. d8=Q











Position 4: Black to move - "Which King move is correct?"
Answer: If this wasn't a rook-pawn, the only good move for the defending K would be to move directly back and stay on the same file as the pawn.  This would be the only move that wouldn't give the opposition to the enemy K, and thus allow the pawn to promote (just like in the previous test question).  However, because this is a rook-pawn, remember the rule for rook-pawns?  "If the defender's King gets in front of the pawn, the game will always be a draw!"  So because the Black K can get (and in fact already is) in front of the enemy rook-pawn, it actually doesn't matter where Black's K moves to now.  Regardless, the game will end in a draw.











Position 5: White to move - "Can White win?"
Answer: No.  Remember the chart from Part 2?  Two Knights and a King can't win against a lone King if the defender plays properly.  Feel free to experiment on your own in this position, but there's literally nothing White can do here to force a checkmate.  The only way White could possibly win here aside from black majorly blundering is if it was a timed game and white won by black running out of time.

Mastering the Endgame
Part Three: 1200 - 1399

Concepts included in this section:
BEYOND BASIC OPPOSITION
KING AND PAWN ENDGAMES
FOX IN THE CHICKEN COUP
THE DEEP FREEZE
MINOR PIECE VS. LONE PAWN
ROOK VS. LONE PAWN
____________________________________________

BEYOND BASIC OPPOSITION - We learned in Part Two that Opposition is where, "both Kings would like to advance and gain ground, and both Kings have moved into a position that prevents the other from doing so."  In its most basic form (see the same diagram below from Part Two), we learned that the principle of Opposition exists when there is only 1 square between the two Kings, and that whichever King has to move is the one that does not have the opposition.










But this principle of Opposition doesn't just exist when there's only 1 square between the two Kings.  It exists from a distance as well, regardless where the Kings are on the board.
All you need to remember is 2 simple rules of Opposition (the Rule of Distant Opposition, and the Rule of the Magic Rectangle), and then you'll know which King has the opposition no matter where they are in relation to one another:

Rule of Distant Opposition: "Whoever moves with an odd number of squares between the Kings does not have the Opposition."
This rule applies regardless if the Kings are connected with one another vertically, horizontally, or diagonally.  So in both of these side-by-side diagrams below, the Kings are connected with one another either vertically or diagonally and there are 6 squares between the Kings in both cases.  So whoever's turn it is to move, that King can advance one square closer to the enemy King along the same file or diagonal on which the Kings are connected, diminishing the number of squares between the Kings from 6 to 5.  And since 5 is an odd number of squares between the Kings, it means that the opposing King will not have the Opposition since it will be his turn to move.










But this begs another question: How does the principle of Opposition apply if the Kings aren't connected vertically, horizontally, or diagonally?
For example, notice how in the diagram below the Kings aren't along the same diagonal, file, or rank as each other.  Therefore, the Rule of Distant Opposition wouldn't make sense because the Kings aren't connected at all.  This is where the second rule of Opposition applies.

Rule of the Magic Rectangle: Whoever moves after an imaginary rectangle (or square) is made from one King to the other with all 4 corners the same color of squares does not have the Opposition.
With this rule in mind, let's go back to the example in the diagram below:
If it's white's turn to move, white's K can move to either a2, b2, or b1, but only one of them creates a magic rectangle from one K to the other with all 4 corners as the same color.  So the correct move here if it's white's turn is 1. Ka2, because if you draw an imaginary rectangle from that square to the square the black K occupies, all 4 corners are light squares.  This means that black will not have the Opposition because white created the magic rectangle and it's black's turn to move.
If it's black's turn to move, black's K can move to either d8, d7, e7, f7, or f8, but only one of them creates a magic rectangle from one K to the other with all 4 corners as the same color.  So the correct move here if it's black's turn is 1...Ke7, because if you draw an imaginary rectangle from that square to the square the white K occupies, all 4 corners are dark squares.  This means that white will not have the Opposition because black created the magic rectangle and it's white's turn to move.











KING AND PAWN ENDGAMES - In a King and Pawn vs. Lone King endgame, if the player with the pawn manages to get his K in front of the pawn, 3 questions will help determine if the player has a chance to win:
1. "Is the pawn a rook-pawn?"
Rule: Rook-pawns will always draw the game unless the defending K is so far away that the K with the rook-pawn can both (A) prevent the defending K from ever entering the file adjacent to the rook-pawn's file and (B) safely support the pawn all the way to promoting.

2. "Is the stronger side's King one square or two squares in front of its pawn?"
If you are the stronger side with the pawn, "move as far forward with your King as possible, while always making sure that your pawn is safe!"  In a King and Pawn vs. Lone King endgame, this "is the most important thing, with Opposition taking a back seat to this."
Rule: "When the stronger side's King manages to get two squares in front of its pawn (unless it's a rook-pawn, of course), the game is always a win [no matter who has the Opposition]."
So in the diagram below, because white's K is now 2 squares in front of his pawn, white will go on to win the game regardless whose turn it is to move.










3. "Who possesses the Opposition?"
Rule: "When the stronger side gets his King (on the 3rd, 4th, or 5th rank) directly in front of his pawn, the only question that matters is, "Who owns the Opposition?"  If the answer is the stronger side, the stronger side will win.  If the answer is the side with the Lone King, the game will result in a draw.
So in the diagram below, because white's K is now directly in front of his pawn on  the 3rd rank, all that matters is whose turn it is to move.  If it's white's turn to move, black has the Opposition and the game will result in a draw.  But if it's black's turn to move, white has the Opposition and will win the game.











FOX IN THE CHICKEN COUP - "Fox in the Chicken Coup refers to a situation where the stronger side's King (the "fox") rushes to the other side of the board to feast on helpless enemy pawns ("chickens") while the defending King is busy dealing with a pawn on the other wing.
For example, in the diagram below "white wins in a walk by pushing the black King back and then abandoning it for the unguarded "chickens" on the kingside."
So after 1. b5 Kb7 (since 1...Kc5 allows white to play 2. Ka5 and support his pawn all the way to promoting), the line continues with 2. Ka5 Ka7 3. b6+ Kb7 4. Kb5 Kb8 5. Kc6
And as Silman points out, "this position after 5. Kc6 is a basic draw if the kingside pawns didn't exist."  But they do.  So after 5...Kc8, white abandons his pawn with 6. Kd6!  This is because black's K is too busy spent capturing the b-pawn to defend against white's K snatching up black's kingside pawns.  So the line would continue with 6...Kb7 7. Ke6 Kxb6 8. Kxf6 Kc7 9. Kxg5, and white goes on to have an easy win in this endgame.











THE DEEP FREEZE - "In King and pawn endgames, it's very important to avoid having your pawn majority devalued by allowing a smaller force to freeze a larger one in its tracks."
For example, in the diagram below, "though black has a passed pawn, white's ability to create one of his own on the kingside ensures that the game will be drawn."
However, it is white's turn to move here, and if white isn't careful, he could make a serious blunder which allows black to create a "deep freeze" (i.e. completely freezing white's pawn majority) and thus win the game.

The blunder I'm referring to is 1. g4?? as shown in the diagram below.  Now black can play 1...g5! which simultaneously blocks white's g-pawn and prevents white from advancing his h-pawn to h4, because if white plays h4 black's pawn will capture it (causing black to be up a pawn) and promote before white's g-pawn can promote.  Then black can apply the Fox in the Chicken Coup principle and snatch both of white's before white's K can get over to defend them (since he has to first use up a move to capture black's b-pawn).
This Deep Freeze principle demonstrates that even if you have a pawn majority, you still have to be careful not to blunder by allowing your opponent's smaller force to "freeze" it.  So going back to the diagram above, white's correct move would have been 1. h4 because it prevents black's pawn from advancing to g5 and prepares for the follow up g3 and h5, safely creating a passed pawn and drawing the game.

MINOR PIECE VS. LONE PAWN - When one player has a minor piece (i.e. Bishop or Knight) and a King, v.s. the opponent's pawn and a King, the question which determines the outcome of the game is, "Can the Bishop or Knight stop the pawn from reaching its final destination?  If it can, then a draw results."  If it can't then the opponent will win since the pawn will become a Q or R.  The diagram below is a very simple example of this concept.  If it was black's turn in this position, he'd be able to promote his pawn to a Q on this turn and easily win the endgame.  But if it was white's turn in this position, white could place his B on f6, ready to snatch black's pawn the moment it advances to a1 and thus drawing the game.











BISHOP VS. LONE PAWN - The above diagram also demonstrates the simple fact that "a Bishop can stop a pawn even from a long distance," and is therefore quite useful in an open endgame position like this.  With this in mind, there are two rules regarding Bishop vs. lone pawn endgames:
Rule 1: A lone Bishop can always draw the game as long as it can control a diagonal that includes any square in front of the pawn.
Rule 2: "A lone Bishop can triumph over a lone pawn if that pawn is a rook-pawn and if its King is trapped in front of it.  Why?  Because, in certain extremely rare instances, the rook-pawn allows smother mates to occur."
An example scenario of the situation described in Rule 2 is the diagram below.  Notice how black's K is stuck on the a-file, preventing his pawn from being able to promote.  If it's black's turn to move in this position, he has 2 move options: 1...Ka2 and 1...a2.  If he chooses 1...Ka2, white can instantly draw the game via stalemate by responding with 2. Bd4.  But with rook-pawn situations in which the K is stuck like this, the player with the pawn has to be careful not to fall into a smothered mate.  If black chooses 1...a2, white instantly wins the game with 2. Bd4#!











KNIGHT VS. LONE PAWN - "The Knight does have the long distance powers of a Bishop, but it can usually stop an enemy pawn even without help from its King if it's close to the pawn and can maintain control over the square in front of the pawn."  With this in mind, there are two rules regarding Knight vs. lone pawn endgames:
Rule 1: "If the Knight can safely land on (or keep connected to) the square (or squares, if the pawn isn't on the 7th rank) in front of the pawn, the game will be drawn (a rook-pawn being the one case where exceptions might occur)."
The diagram below illustrates this rule.  Because white's N watches over c2 square, the game's outcome will be a draw regardless whose turn it is.
If it's white's move:
1. Nb4+ not only checks the enemy K, but also connects with the c2 square.  The only decent move black has here is 1...Kc4 (1...Kd2 accomplishes nothing after 2. Kg7 c2 3. Nxc2).  But then 2. Nc2 Kb3 3. Nd4+ (the exact mirror image of the first move in the line).  There's simply no way black can make any progress here, because white's N stays connected to the squares in front of black's pawn.
If it's black's move:
1...Kc4 cuts off the b4 and d4 squares that the white N would like to jump to (as we saw in the line if it was white's move first).  Note that black can't play the immediate 1...c2 because white instantly draws the game with 2. Nb4+ forking the K and pawn.  From here white has 2. Na5+ (Ne5+ would be an identical line but simply a mirror of it).  Black then has two main responses.  The first would be (2...Kb5 3. Nb3 Kb4 4. Nc1) which ends in an easy position for white to defend.  The second and arguable stronger line for black would be 2...Kb4 3. Nc6+ Kc5 4. Na5 c2 5. Nb3+ Kc4 6. Nc1.  From here white will permanently control the c1 square in front of the pawn.  There's nothing black can do to prevent a draw here, because white's N stays connected to the square in front of black's pawn. 

Now let's look at an example of a position with a rook-pawn to see why rook-pawns can be the exception to this rule of a Knight's ability to draw the game against a lone pawn.  In the diagram below, it is still true that if it's white's turn to move, the N can still force a draw with 1. Nb5, because black is forced to advance the pawn or lose it, and after 1...a2 2. Nc3 there's no way to stop white from taking it since black's K is in the way of the pawn's path.  However, if it's black's turn to move he can win starting with the simple pawn advance 1...a2!  From here, white has to play 2. Nc4 (because black can meet 2. Nb5 with 2...Kb2 which completely prevents the N from approaching).  And after 2...Kb1 3. Na3+ Kc1 black's pawn will successfully promote!  It's also worth noting here that if the white K started closer to black's pawn (say on b4 or d2 instead of on h7) the outcome would still be a draw even if it was black's turn to move.











Rule 2: "A lone Knight can only triumph over a lone pawn if that pawn is a rook-pawn and if its King is trapped in front of it.  Why?  Because, in certain rare instances, the rook-pawn allows smother mates to occur."
An example scenario of the situation described in Rule 2 is the diagram below.  Notice how white's K prevents black's K from being able to leave the a-file.  So if it's white's move here, white can play 1. Nb4! giving black only a single legal move that is 1...a2 which ends the game right away after 2. Nc2# smothered mate!











ROOK VS. LONE PAWN - "Unlike Bishop and King, which can't mate, Rook and King is a potent partnership.  In this case the Rook will win if the pawn can be stopped or won.  In this endgame, the side with the pawn can only hope to draw if the stronger side's King is too far from the action."
Below are three diagrams side-by-side to illustrate when a R can and can't stop a lone pawn on its own without its K assisting.
In the left diagram below, it doesn't matter whose turn it is, because white's pawn is already quite advanced on its path toward promotion and white's K is connected with it.  Therefore there's nothing black can do to prevent a draw.
In the middle diagram below, white's K isn't connected with its pawn, so if it's black's turn his R can cut off the white K from entering the 5th rank with 1...Rb5.  However, the fact that white's pawn is already on the 6th rank means that it can promote in only 2 moves.  This isn't enough time for the Rook to capture it and prevent white's K from coming up to support it.
In the right diagram below, white's K isn't connected with its pawn (just like in the middle diagram), so if it's black's turn his R can cut off the white K with 1...Rb4!.  But unlike in the middle diagram, in this position white's pawn is only on the 5th rank (not the 6th) and would need 3 moves to promote.  This leaves just enough time for the black R to both cut off white's K from advancing and prevent white's pawn from promoting.  This leads us to a rule regarding a Rook vs. a lone pawn and King.
Rule: "A pawn on the 5th rank and a King trapped on the 3rd rank by the enemy Rook is always a win for the side with the Rook."

And obviously it's far easier to stop the enemy pawn from promoting when the K is close enough to help.  In this final diagram below, white will win even if it's black's turn to move.  This is because in order for black to promote his pawn with support from his K, it will take 3 moves.  But white only needs to spend 2 moves to get his K connected with black's pawn, and already has his R connected with the pawn since the R is already on the d-file.














PART THREE TEST:












Position 1: White to move - "Is White winning?"













Position 2: White to move - "Is White in any danger?"













Position 3: "Is White winning?"













Position 4: "Is White winning?"













Position 5: Black to move - "Can White win?"













Position 6: White to move - "Is the King and pawn endgame after 1. Rf4 drawn?"













Position 7: White to move - "Is White lost?"