17

I know the basics of opposition, but I am struggling to evaluate positions for drawishness in King + Pawn VS King endgame. A lot of times it is useful to know whether you should make an exchange. For example, in this position:

[Title "Black to move"]
[FEN "k7/8/8/8/1PR4r/2K5/8/8 w - - 0 1"]

Black can simply exchange the rook and then move to b8 knowing that he has a draw. But in order to do so, he should know that position after exchange is drawish.

The problem is, that looking at positions like this

[Title "White to move"]
[FEN "8/4k3/8/8/8/2P5/2K5/8 w - - 0 1"]

this

[Title "Black to move"]
[FEN "k7/8/8/8/1PR4r/2K5/8/8 w - - 0 1"]

or this

[Title "White to move"]
[FEN "4k3/8/8/8/8/2P5/8/6K1 w - - 0 1"]

I can not quickly determine whether it is drawish or not. I end up thinking for 5 minutes and in the end I can be wrong (so to me it looks like I am simply guessing).

So is there an easy way to determine win/draw in King + Pawn vs King endgame (I am not asking how to secure a draw/win. I hope that I will be able to find it, knowing the evaluation in advance).

  • The third board (same position as first, but white to move) is tough to call? Looks like a decisive win for white to me with 1. RxR. Am I missing something? If the answer is yes, please let me know so I can open a proper question on it. – Esoteric Screen Name Aug 11 '14 at 12:28
  • 1
    @EsotericScreenName: 3rd board with white to move is obviously a win, OP probably meant yet another example – Nikana Reklawyks Aug 11 '14 at 12:49
18

There is a very easy way to detect whether King and Pawn endgames are drawn or not.

This method I use is a very easy to understand one from Karsten Mueller and Frank Lamprecht's excellent book Secrets of Pawn Endings

It concerns key squares and opposition

The rule states that if pawn has not reached or crossed the central line (5th rank for White and 4th rank for Black) then there are 3 key squares 2 squares in front of it.

For example this starting position, the key squares are b5, c5 and d5. If white's king can occupy any of these key squares then the game will be a win for white no matter what.

  [Event "?"]
[Site "?"]
[Date "????.??.??"]
[Round "?"]
[White "White to Move"]
[Black ""]
[Result "1/2-1/2"]
[SetUp "1"]
[FEN "4k3/8/8/8/8/2P5/8/6K1 w - - 0 1"]
[PlyCount "27"]

1. Kf2 {The Key squares in this position are b5, c5 and d5. If white's king
can occupy any of these key squares then the game will be a win for white no
matter what.} Kd7 2. Ke3 Kc6 3. Kd3 (3. Kd4 Kd6 $11 {Opposition}) 3... Kd5 {
Unfortunately black has occupied the key squares mentioned, there is no way
for white's king to enter the key squares, therefore, the game is a draw.
Analysis will be continued to prove this} 4. c4+ Kc5 5. Kc3 Kc6 6. Kd4 Kd6 7.
c5+ Kc6 8. Kc4 Kc7 9. Kd5 Kd7 10. c6+ Kc7 11. Kc5 Kc8 12. Kb6 Kb8 13. c7+ Kc8
14. Kc6 $11 (14. Kb5 Kxc7) 1/2-1/2

It turns out white could not occupy the key squares in time, therefore the game is a draw.

The second rule is that if a pawn is on the 5th rank (or 4th for black) or beyond, there are 3 key squares in front of it.

In this position the key squares for white's king are f6, g6 and h6

White is able to occupy one of these squares with his king and the win is secured. The variation shown shows if white had chosen a different route, black would then be able to secure the opposition and the key squares and the game would be a draw.

[Event "?"]
[Site "?"]
[Date "????.??.??"]
[Round ""]
[White "White to Move"]
[Black ""]
[Result "1-0"]
[SetUp "1"]
[FEN "4k3/8/8/6P1/6K1/8/8/8 w - - 0 1"]
[PlyCount "9"]

1. Kh5 (1. Kf5 Kf7 2. g6+ Kg7 3. Kg5 Kg8 4. Kf6 Kf8 5. g7+ Kg8 $11) 1... Kf7 2.
Kh6 Kf8 3. g6 Kg8 4. g7 Kf7 5. Kh7 1-0

One last key squares example, with a position you gave.

This is a win because White can occupy the key squares of the pawn b5, c5 and d5 (3 squares since the pawn is on the 3rd rank) without any problems

However the variations I gave are to show if white had chosen the wrong route to get to the squares, 1.Kd3 would be a heartbreaking failure as black can secure distant opposition with 1...Kd7 and can therefore control the key squares.

The second variation 2.Kc4 would also be met by brutal opposition 2...Kc6 and control of the key squares for Black.

The text moves show white occupying the key squares, sidestepping any tricks black has (and there are plenty as shown) and securing the win.

[Event "?"]
[Site "?"]
[Date "????.??.??"]
[Round "?"]
[White "White to Move"]
[Black ""]
[Result ""]
[SetUp "1"]
[FEN "8/4k3/8/8/8/2P5/2K5/8 w - - 0 1"]
[PlyCount "5"]

1. Kb3 (1. Kd3 Kd7 2. Kc4 Kc6) 1... Kd7 2. Kb4 (2. Kc4 Kc6) 2... Kd6 3. Kb5 1-0

One final position, I hope you know this one!

OK, Black has the opposition, isn't he safely drawing the game then? Well, there are exceptions to every rule, and this happens to be one. Opposition in King and Pawn endgames always works, except when the pawn is on the 5th rank and your king is also in front of it. This is an important pattern to know!

This position is a good one to emphasize the fact that King and Pawn endgames are very concrete and are based on calculation, judgement can be used with opposition and key squares but in the end stone cold analysis is the ultimate weapon; although it is best equipped with the knowledge of opposition and key squares! :)

[Event "?"]
[Site "?"]
[Date ""]
[Round "?"]
[White "White to Move"]
[Black ""]
[Result "1-0"]
[SetUp "1"]
[FEN "6k1/8/6K1/6P1/8/8/8/8 w - - 0 1"]
[PlyCount "7"]

1. Kf6 Kf8 2. g6 Kg8 3. g7 Kh7 4. Kf7 1-0
  • Last board : Opposition always works, except when the pawn is on the 5th rank ... and the pawn is not in between kings (or it's back to first board). Great answer, +1 – Nikana Reklawyks Aug 11 '14 at 12:55
  • The Kg4, g5 vs. Kd8 example is excellent, as it shows that the straightest way doesn't always yield the result: someone who has not seen that example would probably try the 1.Kf5 variation and deduce that White cannot reach a key square. – JiK Aug 11 '14 at 13:25
  • For completeness, you could also include positions with an a or an h pawn. With the a pawn, White wins if his king can reach b7 (of course without giving up the pawn like King b7, pawn a2 vs. King c2), and Black draws if his king can reach a8, b8 or c8. – JiK Aug 11 '14 at 13:27
  • Thanks for pointing out my mistake Nikana, it has been edited. – sco-ish Aug 11 '14 at 13:34
  • Also, positions like Ke5 Pg6 vs. Ke7 may also be tricky to evaluate: 1.Kf5 Kf8 2.Kf6 wins, but black can try 1..Ke8!? when 2.Kf6? Kf8 draws, but 1.Kf5 Ke8 2.Kg5! Kf8 3.Kh6 wins after all. – JiK Aug 11 '14 at 13:36
0

For the sake of a quick evaluation, the fastest and safest method in my opinion is the rule of the two plusses.

First, let's get rid of the cases where it doesn't apply. White has the pawn.

  • If the bK is not in the square of the pawn, White wins.

  • If the bK can take the pawn, it is a draw.

  • Pawns on the edge of the board (the a- and h- files) have their own rules (less often a win, race to the key squares f7-g7-f8-g8).

Ok, now we have a pawn not on the edge and both kings "close enough" to prevent immediate promotion or capture. Then White tries to bring his king as much as possible in front of the pawn and Black's king comes to oppose that.

When both kings are on the nearby files (for an e-pawn, that means files d-e-f) you can evaluate the position with the "two plusses rule".

  • If the wK is one square in front of the pawn, count one plus. If it is two squares in front of the pawn, two plusses, etc.

  • If White has the opposition, count one plus.

  • If wK is on the 6th rank, count one plus.

Sum up.

White wins if and only if he has at least two plusses.

Examples:

Here white has only one plus: king in front of the pawn. Black draws.

[Event "?"]
[Site "?"]
[Date ""]
[Round "?"]
[White "White to Move"]
[Black ""]
[Result "1-0"]
[SetUp "1"]
[FEN "8/6k1/8/6K1/6P1/8/8/8 w - - 0 1"]
[PlyCount "11"]

1. Kf5 Kf7 2. g5 Kg7 3. g6 Kg8! 4. Kf6 Kf8 5. g7 Kg8 6. Kg6 1/2

Here White has two plusses: his king is two ranks in front of the pawn. White wins.

[Event "?"]
[Site "?"]
[Date ""]
[Round "?"]
[White "White to Move"]
[Black ""]
[Result "1-0"]
[SetUp "1"]
[FEN "8/6k1/8/6K1/8/5P2/8/8 w - - 0 1"]
[PlyCount "11"]

1. f4 Kf7 2.Kf5! Kg7 3.Ke6 1 0

Here, with Black on move, White has two plusses: king in front of the pawn and the opposition. He wins.

[Event "?"]
[Site "?"]
[Date ""]
[Round "?"]
[White "Black to Move"]
[Black ""]
[Result "1-0"]
[SetUp "1"]
[FEN "8/6k1/8/6K1/6P1/8/8/8 b - - 0 1"]
[PlyCount "15"]

1... Kf7 2. Kh6 Kg8 3. Kg6 Kh8 4. g5 Kg8 5. Kh6 Kh8 6. g6 Kg8 7. g7 Kf7 8. Kh7 1-0

Here, one rank higher on the board, White, on move, has two plusses: king one square in front of the pawn and king on the 6th rank. He wins.

[Event "?"]
[Site "?"]
[Date ""]
[Round "?"]
[White "White to Move"]
[Black ""]
[Result "1-0"]
[SetUp "1"]
[FEN "6k1/8/6K1/6P1/8/8/8/8 w - - 0 1"]
[PlyCount "7"]

1. Kf6 Kf8 2. g6 Kg8 3. g7 Kh7 4. Kf7 1-0

Your positions:

[Title "White to move"]
[FEN "8/4k3/8/8/8/2P5/2K5/8 w - - 0 1"]

After 1.Kb3 Kd6 2.Kb4! Kc6 3.Kc4! White has two plusses (one square in front + opposition) White wins.

[Title "Black to move"]
[FEN "k7/8/8/8/1PR4r/2K5/8/8 w - - 0 1"]

After 1...Rxc4! (the simplest, but the rook ending is a dead draw too) 2.Kxc4 Kb8! 3.Kc5 Kc7! or 3.Kb5 Kb7! White has only one plus (king in front of the pawn) : Draw

[Title "White to move"]
[FEN "4k3/8/8/8/8/2P5/8/6K1 w - - 0 1"]

After 1.Kf2 Kd7 2.Ke3 Kc6 3.Kd4 Kd6! White has only one plus (king in front of the pawn) : Draw

Thanks to this method, the variations are much shorter: you only need to calculate until the kings are near the pawn, and then you count the plusses.

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.