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 7man 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 Rc5c1, 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 hfile with his rook.
This is a new discovery in the theory of rook endgames!

(1) Smagin,Sergey  Bronstein,David
Moscowch (5), 1982
1.e4
e5
2.Nf3
Nc6
3.Bc4
Nf6
4.d3
h6
5.c3
d6
6.00
Be7
7.Nbd2
00
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 7man 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 hfile, 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 afile; 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] 1/21/2

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