Rook vs. Three Connected Passed Pawns

This position arose in a game that I played Wednesday morning online. It is a technical draw, but my opponent erred along the way.

White to move

Several moves earlier, I could have reached a favorable ending with the same material, except that my  understanding of rook vs. three connected passed pawns was deficient. 

Black to move

In haste to eliminate the passed b-pawn, I played 54...Rb1

54...Rd3 is better, as it prepares to get behind the b-pawn while also protecting the h-pawn with a threat on the f-pawn. 

55.Kxh3

Black to move

Tablebases reveal that Black has two winning moves here, but they do not explain the reasoning. I've spent a bit of time playing through tablebase lines in search of understanding.

I started looking through the 65 endgame books on my shelf. Few books are helpful. Reuben Fine, Basic Chess Endings has three pages on rook vs. three pawns, but these have limited application to the position before me. Ilya Rabinovich, The Russian Endgame Handbook has a page and a half with some of the same illustrative positions found in Fine. I have this book both in a print version and in the Forward Chess app.

Some useful analysis appears in Sam Shankland, Theoretical Rook Endgames.

In the game, I played 55...Rxb4?? 56.Kg3 Kg7 to reach the diagram at the top of the page. After several more moves, we reached this position.

White to move

My opponent's move here was the decisive error, but it took me quite a few more moves to find the winning idea.

65.Ke4??

Either 65.Kf2 or 65.Kg2 holds the draw.

Shankland has this position.

Black to move

Shankland points out that the king needs to step back and shuffle the king between g7 and h7. The h-pawn is secure because otherwise Black's other two pawns became a serious threat, although White can hold the draw. Shankland does not analyze this line in detail, stating only, "White is lucky not to be lost" after snatching the h-pawn (373). When I played the White side against two students on Thursday, I failed to hold the draw after snatching the pawn.

Shankland's position differs from that in my game, but the idea of shuffling the king back and forth on the second rank could have been known to my opponent from Theoretical Rook Endgames.

How Could I Win?

Back to the position after 55.Kxh3. My haste to eliminate the b-pawn was an error. Instead, there were two winning moves that I could have played. Lines following from either move require me to centralize my king.

a) 55...Kg7!

The best move, according to Stockfish.

After 56.Kg3, only one move wins.

Black to move

56...Kf6! 57.h4 Ke5!

Again, there was only one winning move.

58.f4+ Ke4!

Another only move.

White to move

After 59.b5, 59...Rg1+ is the shortest distance to mate.

59.g5 is the longest distance to mate, and now Black has 59...Kf5.

b) 55...Rg1 was also winning.

56.b5 Kg7! 57.b6 Kf6 58.f4

Black to move

58...Ke6!

The only winning move.

59.b7 Rb1

At this point, not earlier, it is necessary to stop the passed b-pawn. Afterwards, Black's king will move to d5 and then e4. For example, 60.Kg3 Rxb7 61.Kh3 Rb3+ 62.Kg2 Kd5 63.h3 Ke4 64.f5

Black to move

The pawn chain is vulnerable because of the placement of Black's pieces. Shankland's defensive idea fails here because the pawns all need to advance one square further.

In two games this week, I prevailed with a rook against three pawns. Analysis of these games showed that there is much that I can learn about these endings, which can often lead to interesting positions demanding precise play. 22 years ago, I chose to exchange my last rook for one of my opponent's rooks, reaching a ending where I had three connected passed pawns against a rook. I drew that game, but only because my opponent missed the right idea in a critical position. That is the subject of tomorrow's post.