During these lectures we will call the king with the pawn the "offensive" king.
The first case we will consider is where the offensive king cannot help
his pawn. This is exemplified in the following position:
In all positions like this, there are two evaluations, one with White to move, and one with Black to move. First consider White to move.
The key is whether the defensive king can get within the promotion "square".
Note: Some call the square a "triangle" but that does the same thing - I like a square.
With White to move, before you draw the square first move the pawn 1.h4.
Then draw a line to the promotion square. Then complete the square by making
all sides equal toward the defensive king:
Now to see if it is a win, see if the defensive king can move "inside" the square. In this case it cannot, so it cannot stop the pawn from promoting, e.g.
1...Kc4 2.h5 Kd5 3.h6 Ke6 4.h7 Kf7 5.h8=Q and White wins.
On the other hand, if the original diagram is with Black to move, then Black first plays 1...Kc4 and then will be able to move within the square:
1...Kc4 2.h4 and now Black can move within the square, so it is a draw: 2...Kd5 3.h5 Ke6 4.h6 Kf7 5.h7 Kg7 6.h8=Q Kxh8
So that case was easy! - Now let's consider cases where the offensive king can help. For the moment we will ignore cases with an a-pawn or h-pawn. Those are actually easier.
A typical case where the offensive king is behind the pawn might be:
As always, there are two evaluations, one with each player to move. What are they?
If you said White to move draws and Black to move loses...You are wrong! :)
With proper play it is a draw no matter who moves first.
Can Black lose if he plays it wrong? Of course! You might say that in any position where the opponent has mating material if you play wrong you can lose!
But when studying you want to know what would happen if both players play correctly! Here the defensive king needs to follow just two rules to draw:
1) Do not let the offensive king in front of the pawn, and
2) When the offensive pawn reaches its "6th" rank the king should move straight back and forth on the file in front of the pawn until the offensive king goes to the 6th rank and then move onto the same file as the offensive king.
So with White to play (play is very similar with Black to play), sample play might be:
1. Ke1 Kc4 Just to show it does not matter much where Black's king plays - only 1...Kc2?? 2.d4 loses. 2.Ke2 Kd4 Black should prevent White's king from getting in front of the pawn. 3.d3 Else White cannot make progress. 3...Kd5 Black may as well practice going straight back in any case - it doesn't hurt! 4.Ke3 Ke5 5.d4+ Kd5 6.Kd3 Kd6 7.Ke4 Ke6 8.d5+ Kd6 9.Kd4 Kd7 10.Ke5 Ke7 11.d6+ Kd7 12.Kd5 Now is when it really matters what the defensive king does! Straight back! 12... Kd8 13.Kc6 Kc8 The defensive king must "oppose" the other king when it comes up. 14.d7+ In a futile attempt to make progress, but Kd5 is met by Kd7, repeating position 14...Kd8 And now White must either stalemate Black with Kd6 or lose the pawn. 15.Kd6 stalemate
Now suppose Black had played it wrong and gone back diagonal: 13...Kc8?? - Throwing away the whole game in one move - that is why you need to play lots of slow games to improve and give yourself time to think about the endgame! 14. Kc6 White now opposes Black who must play 14...Kd8 15.d7 Zugzwang! Black does not wish to vacate d8, but must. 15...Ke7 16.Kc7 and White wins by queening the pawn next move.
So by observing those two rules Black draws easily no matter who is to move. This applies to all non rook-pawn positions where the offensive king is not in front.
Therefore, most interesting are the positions where the offensive king
IS in front.
In this position what are the two evaluations?
This time if you said White to move draws and Black to move loses you are right!
This is the famous "Whoever has the opposition position." What is the
"opposition"? Before I define it, it is better to give an example!:
In this position, the kings are having a "race" to the 4th rank. Who should win?
The answer is, whichever King does NOT move first has the advantage, e.g.
1. Ke3 Kc4
And the Black king "wins the race" to the 4th rank. Back to our primary
In this type of position, if the offensive side has the opposition it can win, and if the defensive side has the opposition it can draw.
So what is a good definition of "opposition"? Without getting too technical, it describes positions where there are no pawns on the same rank or the ranks between the kings and, if the kings are on the same file or rank, the king who is NOT to move when there is an odd number of squares between the kings has the opposition.
Here there are no pawns on the 3rd, 4th, or 5th ranks, where the kings are, there is 1 empty square between the two kings, on d4, and "1" is an odd number so the side that has the opposition is whoever is NOT to move.
Here it is White to move, so Black has the opposition and draws. For example:
1. Ke3 Ke5
Black keeps his king opposing the White king (odd number of square, etc.)
Now already White has nothing constructive to do because:
1) If he goes back to the second rank 2.Ke2 then Black will not let him in front of the pawn with 2...Kd4 and we have the kind of position we examined before which is a draw.
2) If White continues sideways 2.Kf3 then Black will also force the White king to no longer be in front of the pawn 2...Kd4 3.Ke2 and again we have the drawn position where the king is no longer in front. Finally,
3) If White tries to go back 2.Kd3 Kd5 This repeats the position and White has made no progress. If this happens one more time, then Black can claim a draw by three-fold repetition of position.
If in the starting position Black is to move, then White has the opposition and can win!
In order to win, White should best use the following rules:
1) Move the king first! Never use the pawn unless the king cannot make progress. To use an analogy from US football: Think of the king as a pulling guard and the pawn as a running back. Gotta block first!
2) Only push the pawn if the king cannot make progress or if 100% sure it can queen. Never push the pawn to the same rank as the king until queening is trivial.
3) Keep the opposition with the king - but "make progress" wherever possible.
With these rules, the rest is easy. Let's try it:
1...Ke5 Black must give way, so 2.Kc4 White must make progress. No credit for the "blindly oppositional" 2.Ke3? 2...Kd6 There are other moves, but nothing can save Black! 3.Kd4 Of course! White re-establishes the opposition one file up. Just keep doing this! 3...Kc6 4.Ke5 Still making progress toward further ranks. 4...Kc5 Black tries to vary an confuse White. Otherwise the same pattern continues. 5.d4+ Moving the pawn is OK here since otherwise progress is stopped. Besides, the pawn is still on a rank behind the White king, so that is OK. 5...Kc6 6.Ke6 Kc7 7.d5 Not 7.Ke7 when 7...Kc6 forces the repetition with 8.Ke6. 7...Kd8 The best defense, else White plays Ke7 next move and then d6-d7-d8Q. Now what should White play? 8.Kd6! - The king always comes first - let us look what would happen after 8.d6? Ke8 Look familiar? The king is behind the pawn as in the earlier examples and this is a draw!: 9.d7+ Kd8 10.Kd6= So 8.Kd6 was the right move - remember this idea! After 8.Kd6 White keeps the opposition and wins easily after 8...Ke8 9.Kc7 followed by 10.d6-11.d7-12.d8Q and wins.
Now suppose we move the starting position one rank up the board:
Does this make any difference in the two evaluations?
If you read the Novice Nook "Techniques" at www.chesscafe.com you know! The answer is no! - Black to play loses, White to play draws.
How about up another rank?:
Any different now?
No, still White to move draws, Black to move loses. Finally, one more rank up:
Does either evaluation change here?
If you said "No, still Black to play loses and White to play draws," you are wrong! In fact, in this position NO MATTER WHO IS TO PLAY WHITE WINS! So this is not a position where the opposition matters!
Even with White to move, Black can do no better than: 1.Ke6 Ke8 2.d6 Kd8 3.d7 Kc7 4.Ke7 And White wins!
I call the general rule the Tic-Tac-Toe Rule. It works this way:
Create a Tic-Tac-Toe board on the chessboard in the following way:
Find the pawn's promotion square,
in this case d8. Come back to the square before promotion. Make this the
center of a 3x3 Tic-Tac-Toe board:
Now the rule is, if the following all hold:
1) The offensive king is anywhere
inside the Tic-Tac-Toe board, and
2) The pawn is on any rank behind the king, and
3) The defensive king cannot win the pawn, then
WHITE ALWAYS WINS WITH BEST PLAY NO MATTER WHO IS TO MOVE!
How can you use this rule? Many ways. Consider the following problem.
This is Black to play and draw!
The obvious 1...Ke7 does not work!: 1...Ke7 2.d5 Now Black's king will be "elbowed out": 2...Ke8 Black tries the "diagonal opposition". 3.Kf6 Kd7 Nothing really works. 4.Kf7 Kd8 5.Ke6 Kc7 6.Ke7 This is a good maneuver to remember! 6...Kc8 Black goes for the opposition. 7.Kxd6 Kd8 and White wins as the opposition does not matter: This is a Tic-Tac-Toe win!
So that is not the solution to this problem! What should Black do instead? 1...d5! Black avoids Tic-Tac-Toe and gives up the pawn on a non Tic-Tac-Toe square. 2.Kf6 Ke8 What square does Black need to go to when White captures the pawn? d7! And there is no way for White to prevent this, so it is a draw! 3.Ke6 Kd8 4.Kd6 This does not help White, but he is trying! 4...Ke8 5.Kxd5 Kd7 and Black has the opposition and draws.
Let's consider positions where the White king starts further in front of the pawn. What are the two evaluations here (White to move and Black to move)?
If you said White wins either way you are correct! The reason is easy: With Black to move White has the opposition and wins as before. With White to move he plays 1.d3! and gets the opposition and wins anyway!
One special case worth noting is where the offensive king is far enough to one side of the pawn that the other king cannot catch it "sideways":
Here the "obvious" 1.Kc2 Kd6 2.Kc3 Kc5 draws as above. But White's king is further "left" of Black's king, so the right way is:
1.Kb2! Kd6 2.Ka3! and now either 2...Kc6 or 2...Kc5 loses to 3.Ka4.
Let's quickly consider rook pawns - The only way the offensive King can win is if it can occupy the b or g-file 7th or 8th rank and not lose the pawn. An example:
This is White to play and win. I once saw someone play this wrong: 1.h5? The right move was "king first!" with 1.Kg7! and then the pawn queens, but after the incorrect 1.h5? Kf8 Whoops! Now if 2.h6 Kg8 draws easily with the defensive king in the corner. 2.Kh7 The only way to keep the Black king out of the corner, but 2...Kf7 Now the White king is stuck. And if he tries to get out with 3.Kh6 Kg8 and Black draws, but if White instead pushes the pawn 3. h6 Kf8 4.Kh8 Kf7 5.h7 Kf8 and it is stalemate - Draw anyway! So from the original position 1.Kg7! wins and h5? only drew.
Finally, a "distant opposition" problem. White to play:
Distant opposition can roughly be defined as "Putting your king on a square which creates a rectangle with the other king with all four corners of the rectangle the same colored square (such as a light square)."
For kings on the same file, this is just an odd number of squares between kings!
In the above position, Black's King will be inside the square after 1.b4? Kf8 so running doesn't work. It looks like White should play Kg2 (to get the opposition!) and have 5 (odd #) squares between the kings:
1. Kg2 And Black has nothing better than 1...Kf7 2.Kf3 Keeping the opposition with 3 squares in between and the opponent to move. 2...Ke7! - Coming up with Ke6 and allowing Ke4 is not as good - you will see why soon! 3.Ke3 and not 3.Ke4? Ke6! and Black grabs the opposition and draws. 3...Kd7 Black keeps his distance and waits for a chance. 4.Kd3 Kc7 5.Kc3 Now what can Black play?:
* Going back to the 8th rank loses to 6.Kb4 and the White King will
get two squares in front of the pawn.
* Going 5...Kd7? loses to 6.Kb4 when Black cannot get the opposition.
* Going to the 6th rank loses to White opposing on the 4th, e.g. 5...Kc6 6.Kc4 with the opposition! Or 5...Kb6
6. Kb4 and again White has the opposition and wins, but...
5...Kb7! What can White do now? He wants to go to b3 to maintain the distant opposition but his pawn is there. That is why I defined opposition as not being in effect if pawns are on the same ranks (or in between) the kings!
So in this problem White never really had the distant opposition, even if it looked so. Suppose White tries:
* 6.Kb4 Kb6 Black has the opposition and draws.
* 6.Kd3 Kc7 ! We have been here before - White is making no progress. Finally:
* 6.Kb2 Kb6 7.Ka3 Kb5 and White cannot get in front of the pawn! Draw!
This problem teaches you a lot about king and pawn endgames.
The reason you need to study king and pawn endgames first is that you need to know when to trade down from more complex endgames, like king & 2 pawns vs. king and pawn or king and rook and pawn versus king and rook!
No matter on the offensive or defensive, you need to know which trades lead to wins.
Study the above and you will be ready for more difficult endgames.
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