Passed pawn races in rook endgames

The endgame of rook and two pawns against rook and one pawn occurs frequenly in practice, making this probably the most important type of endgame to be solved by the 7-man tablebase.

All chess players need to know how to manage such positions as these where there is a race between passed pawns on opposing wings, and they can be very hard to judge, especially as it is often necessary to calculate the consequences far ahead, when taking decisions on how to simplify more complicated positions.

I consulted a standard textbook on rook and pawn endings by GM Averbakh and his colleague N. Kopayev seeking examples of R+2 v R+1. The first few did not contain any errors.

Eventually until I found this one where the Probe tablebase at chessok.com came to different conclusions from those of the authors. White (Sergey Smagin) has just played 71 Rc5-c1, getting ready to sacrifice his rook at the right time and win with two pawns against rook. For example, if Black plays 71...b2? he loses quickly as the analysis below demonstrates. So instead Black played 71...Rh8 to hold up the pawns' advance. The game continued 72 Kg3? whereas 72 Rb1 (suggested by Averbakh and Kopayev) was correct and would win.

The second diagram shows the start of the variation proposed by Averbakh with 73 Rh1 instead of 73 Rb1? which Smagin actually played.

The authors believed that Rb1 threw away the win but the talebase shows that GM Bronstein's 72...b2! was a unique saving move.

After 73 Rh1, analysis in the book continues 73...Kb3? leading to a win for White. However the tablebase shows that Black had a way to draw this position by waiting on the h-file with his rook.

This is a new discovery in the theory of rook endgames!

(1) Smagin,Sergey - Bronstein,David
Moscow-ch (5), 1982

1.e4 e5 2.Nf3 Nc6 3.Bc4 Nf6 4.d3 h6 5.c3 d6 6.0-0 Be7 7.Nbd2 0-0 8.Bb3 Nh7 9.Nc4 Bf6 10.Ne3 Ne7 11.h3 Kh8 12.d4 Qe8 13.Ba4 b5 14.Bc2 Bb7 15.Re1 Ng6 16.Ng4 Qe7 17.a4 a6 18.Bd3 c6 19.Ne3 Qc7 20.Nf5 Rad8 21.Qc2 Rfe8 22.Be3 Nhf8 23.axb5 axb5 24.Ra7 Ne6 25.g3 Ne7 26.Nxd6 Qxd6 27.dxe5 Bxe5 28.Nxe5 Qxe5 29.Rxb7 Nc5 30.Bxc5 Qxc5 31.Bf1 Kg8 32.e5 Qd5 33.e6 fxe6 34.c4 Qf5 35.Qxf5 Nxf5 36.cxb5 Nd6 37.Rb6 Nxb5 38.Bxb5 cxb5 39.Rbxe6 Rxe6 40.Rxe6 Rd2 41.b3 Rb2 42.Re8+ Kf7 43.Re3 Kf6 44.Kg2 g5 45.g4 Kg6 46.Rd3 b4 47.Kg3 Rc2 48.f4 Rc3 49.Rf3 Rc1 50.fxg5 hxg5 51.Kf2 Rb1 52.Re3 Kf6 53.Kf3 Rd1 54.Ke4 Ke6 55.Rd3 Re1+ 56.Kd4 Rc1 57.Rf3 Rc2 58.Re3+ Kf6 59.Kd5 Rc3 60.Ke4 Rc8 61.Rd3 Ke6 62.Rd4 Rf8 63.Ke3 Rb8 64.Rc4 Kd5 65.Kf3 Ke5 66.Rc5+ Kd4 67.Rxg5 Kc3 68.h4 Kxb3 69.Rc5 Ka4 70.h5 b3 71.Rc1 Averbakh & Kopayev, Rook Endings #661 on p249 of 1987 Pergamon edition, saying: "The following examples show some of the curious tactical subtleties which can arise in this ending" [of R+2 v R+1 all pawns passed. But they don't show all the twists found by the 7-man Lomonosov tablebase. It says White mates in 34. Let us see how it refutes the defence shown in the book. 71...Rh8 ! from A&K: "Black tries for the moment to halt the advance of the pawns." [71...b2 72.Rb1 Kb3 73.g5 Kc2 74.Rxb2+ Kxb2 75.g6+- ] 72.Kg3? [72.Rb1!+- More logical say A&K correctly, "following the same method and forcing the black king to go to a2." This is one of three moves that win according to the tablebase; the others are 72 Ra1+ (which transposes after 72...Kb4 73 Rb1) and 72 Rc6. A&K imply it is only 73 Rb1 that costs the win but the tablebase shows that Kg3 is already a big error.] 72...b2! Unique saving move 73.Rb1? Loses time and throws away the win, they say. But the win has already gone. [A&K give 73.Rh1! Kb3? But this is a mistake that A&K did not notice. Instead the tablebase shows that Black could wait with the R on the h-file, showing both 73...Rh6 and 73...Rh7 as drawing, everything else losing. (73...Rh7! 74.Kf4! How else to make progress? (74.h6 Rxh6= because the black king is still on the a-file; 74.g5 Rxh5 ) 74...Rh8! 75.Kf5 Kb3 Tablebase shows both Rf8+ and Ka3 also draw 76.Kf6 Rc8 Threat ...Rc1. Several other moves also hold 77.Re1 White will have to give up his R one way or another; Rb1 and Rd1 also draw. 77...Ra8 (WHY NOT 77...Rc1 ) 78.h6 Ra1 As in game but Ra6+ also holds. 79.h7[] Rxe1 80.h8Q b1Q 81.Qb8+ followed by Q exchange and draw with P v R) 74.h6!+- /\Rxh6? 75.Rxh6 b1Q 76.Rb6+ A&K] 73...Kb3 A&K say that "Now Black manages to save the game by an original rook manoeuvre." Black goes via a1 to get the R to h1, its best position behind the pawns. It worked in practice anyway. [RR73...Ka3 also draws according to the tablebase. 74.h6 (74.g5 ; 74.Kh4 ) 74...Rxh6 75.g5 ] 74.Kh4 According to the tablebase, several moves draw (even g5 or h5) but there is no win for White. 74...Ra8! 74.. .Rc8 also draws (similar idea heading to h1 via c1) 75.g5 Ra1[] 76.Rxb2+ Kxb2 77.Kg4 [77.g6 Rg1= ; 77.h6 Rh1+ 78.Kg4 Kc3 79.Kf5 Kd4 80.Kg6 Ke5 81.Kh7 Rg1 82.g6 Kf6 83.g7 Kf7= RR84.Kh8 Rg6 85.h7 (85.Kh7 Rg1 86.Kh8 Rg6 repetition) 85...Rxg7 stalemate] 77...Kc3 [77...Rh1! (A&K) transposes to the game next move] 78.g6 Rh1[] 79.Kg5 Kd4[] 80.g7 [80.h6 Ke5 81.h7 (81.g7? Rg1+ 82.Kh5 Kf6-+ ) 81...Rg1+ 82.Kh4 (82.Kh5? Kf5 83.h8Q Rh1# ) 82...Rh1+ 83.Kg5 (83.Kg4? Kf6 ) 83...Rg1+ draws] 80...Ke5[] 81.Kg6 Rg1+[] 82.Kf7 Rf1+[] 83.Ke7 [83.Ke8 Rg1 84.h6 Kf6 85.Kf8 Ra1 also with a draw (A&K)] 83...Rg1[] 84.h6 Rg6[] After five successive only moves for Black, the draw is clear. 85.Kf7 Rf6+ 86.Ke8 Re6+ 87.Kd8 Rd6+ 88.Kc8 Rc6+ [88...Rc6+ Drawn, though A&K point out that after 89.Kb7? (89.Kd8= ; 89.Kd8 ; 89.Kd7 ) 89...Rg6 White could even have lost] 1/2-1/2