# How can I draw this KPPP-KR endgame?

I consider it one of the most amazing chess endgame puzzles.

``````[Title "White to play and draw"]
[fen "8/2k5/2r5/8/4PPP1/5K2/8/8 w - - 0 1"]
``````

Of course I tried to solve it myself... I tried different approaches. E.g., trying to promote the g pawn with the aid of my king. Unfortunately, I had little-to-no success.

So how must I act in order to draw the game (assuming black has perfect play, always makes best moves and does not accept my possible draw offer)? What is the proper analysis?

The underlying principle is that two connected passed pawns on the 6th rank are worth a rook (provided the opponent's king and rook are not too close). So, your aim is to to try and get close to that.

It's going to take several moves and meantime black is going to be getting closer so you have to try and keep black's king as far away from the pawns for as long as possible. The black king isn't allowed to move into check so the pawns can be used to keep the king at bay.

1.g5 looks tempting. Start moving the pawn which is furthest from the king and rook. The problem with this is that it doesn't do anything to restrict the black king.

How about 1.f5? The problem with this is that it creates a hole on e5 which sooner or later is going to be occupied by the black king. It is maybe the worst way of starting.

That leaves 1.e5. This stops the black king's best move 1... Kd6 getting closer to the pawns. It is the best first move.

Now let's think about something rather paradoxical. How is the black rook going to stop the pawns once they get far enough up the board to threaten to queen? The first principle of rook and pawn endgames is that the rook belongs behind the pawn. Ideally for black the rook is going to be on the first rank attacking the pawns from behind.

Here's the paradox. White does not want to move the king up with the pawns! White is going to want the king on the 2nd rank to control the black rook's attempts to attack the pawns from behind. If white doesn't do this then the black king is going to be able to stop the pawns going further while the black rook drives the white king away and the king and rook can start taking pawns.

If white stops the black rook from getting behind the pawns then the black king can stop the pawns making further progress but not start taking them because they are too far forward. If the rook tries to take the back pawn on g4 then the white king can step up to f3 to protect the pawn but must be prepared to allow black to take the g4 pawn.

This is the key position:

``````[fen "8/2k5/2r5/8/4PPP1/5K2/8/8 w - - 0 1"]
[Startply "9"]

1. e5 Rc3+ 2. Kf2! {not falling into the trap} Kd7 3. f5 {keep the black king away as long as possible} Ke7 4. e6 {almost there} Kf6 5. Kg2 {keep calm, don't panic} Ke7! {Draw} (5...Kg5 6. Kf2 Kxg4?? (6...Rc4 7. Kf3 Rf4+ 8. Ke3 Rxg4 (8...Kxg4 9. e7) 9. e7) 7. e7 {run baby, run!})
``````
• Thanks, @Brian Towers. It was really useful, and I managed to understand it almost perfectly. A small additional question though: I think if black plays perfectly then they won't take our pawns, but they will try to avoid threefold repetition by any means. So will the game still be a draw? (small doubt) Commented Oct 17, 2023 at 0:24
• @BrianTowers: Syzygy begs to differ - in the starting position, every move by White draws! Let's start with the silly 1.Kg2 Kd6, and now there is only one move that draws, which I'd play without thinking and you dismissed: 2.g5. You are spot on though with the central point, e.g.: 2...Ke6 3.g6 Kf6 4.f5 Rc1 5.Kf2!! (only move) - White must hinder the rook from attacking the pawns from behind. Commented Oct 17, 2023 at 7:04
• @Alexander: if White doesn't move any pawns and Black doesn't take them there are only a finite number of positions for the kings and rook, so after long enough you will have to repeat the position. In fact you will repeat much faster as most positions will cause one side to win Commented Oct 17, 2023 at 12:33