02 September 2013

Rook vs. Bishop

In pawnless endings, rook vs. bishop is a theoretical draw that should offer few difficulties for the weaker player when the stronger wants to press. Rook vs. bishop with pawns on the board is another matter entirely.

Chess Informant 113/10 presents such an endgame without commentary. Tablebases clarify that the moves by the stronger player did not extend the length of the game by more than a few moves, nor did poor play by the defender shorten the game to any significant extent. While neither player was perfect from a computer's point of view, both were quite close. Their play was as optimal as should be expected from humans.

The game is Vitiugov -- Morozevich, Reggio Emilia 2011. Nikita Vitiugov annotated the game for Informant. After 46...Bd3, White had a double attack that provoked Black to swap off the dark-squared bishops.

White to move

The game continued 47.Ra4 Be5 (Vitiugov mentions 47...Bf2 as an alternative that leads to a pawnless ending that is won for White). 48.Bxe5 Kxe5 49.Kg3 Be2

White to move

White's pawn cannot be touched, but neither can it advance without a sacrifice. The problem for White is that after the rook captures Black's pawn, leading to exchange of rook for bishop and pawn, White's king will be on f3, but the Black king will be able to move to f5--a drawn pawn ending.

White must drive the Black king back to the eighth rank. That requires rook and king in coordination. Occasionally, targeting Black's bishop helps force matters. Once the Black king has been driven back, the rook must confine it there while White's king returns to g4 or f4.

While looking through this game in Informant, I did not perceive that White could force matters. After going through the moves several times, however, and checking the play with tablebases, I began to see that White's play is relatively straightforward.

50.Kg4 Kf6

At first glance, this move appeared cooperative with White's plans. However, after 50...Bd1 51.Rb4, the effort to shuffle the bishop between e2 and d1 will alow White's rook to seize the e-file after the White king occupies g5. The consequence of Black's king being driven to the d-file will be that White's king can return to g4, the rook will snatch the pawn, and in the pawn ending the White king will outflank Black. (Readers not familiar will opposition and outflanking can watch my video, "Pawn Endings: First Steps.")

51.Kf4 Bd1 52.Ra6+ Kf7 53.Ke5 Be2 54.Rf6+

Black to move


54...Ke7 is slightly more stubborn, but White has several methods to continue at his disposal, including 55.Rf4 Bd1 56.Rc4 and the Black king will be driven back.

55.Kf5 Bd3+ 56.Kg5 Be2 57.Rf4 Kg8

If 57...Bd1, 58.Rd4.

58.Kh6 Bd1

58...Kh8 59.Rf8#

White to move

The king has been driven to the eighth rank, now the second phase begins: confinement.

59.Rd4 Be2 60.Rd7 Kf8

And now the third phase: White's king returns to f4.

61.Kg5 Ke8 62.Ra7 Kf8 63.Kf4 Kg8

White to move

White is now able to seize the pawn because the Black king is too far back to reach a drawn pawn ending.

64.Ra3 Kf7 65.Rxf3 Bxf3 66.Kxf3

Black to move

White has the distant opposition, and so wins.

66...Kf6 67.Kf4 1-0

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