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
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
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!
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!
How else to make progress? (74.h6
because the black king is still on the a-file; 74.g5
Tablebase shows both Rf8+ and Ka3 also draw 76.Kf6
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
As in game but Ra6+ also holds. 79.h7
followed by Q exchange and draw with P v R) 74.h6!+-
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
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
(A&K) transposes to the game next move] 78.g6
also with a draw (A&K)] 83...Rg1
After five successive only moves for Black, the draw is clear. 85.Kf7
Drawn, though A&K point out that after 89.Kb7?
White could even have lost] 1/2-1/2
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