How powerful is the Queen compared to 2 Rooks ?

[Chessqueen]

Chessqueen: A rook value of 4¾ is is my preferred value over 4½.

Pawn = 1.0
Knight = 3.0
Bishop = 3.25 (per Fischer)
Rook = 4.75
Queen = 9.5 ?
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King ~ 3.00 in the endgame.
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I agree more with Fischer valuation of the chess pieces, and I found out this in Wikipedia, but I disagree that the two Rooks are slightly more powerful in the endgame.

Changing valuations in the endgame
As already noted when the standard values were first formulated (Lolli 1763:255), the relative strength of the pieces changes as a game progresses to the endgame. The value of pawns, rooks and, to a lesser extent, bishops may increase. The knight tends to lose some power, and the strength of the Queen may be slightly lessened, as well. Some examples follow.

A queen versus two rooks
In the middlegame, they are equal
In the endgame, the two rooks are somewhat more powerful. With no other pieces on the board, two rooks are equal to a queen and a pawn
A rook versus two minor pieces
In the opening and middlegame, a rook and two pawns are weaker than two bishops; equal to or slightly weaker than a bishop and knight; and equal to two knights
In the endgame, a rook and one pawn are equal to two knights; and equal to or slightly weaker than a bishop and knight. A rook and two pawns are equal to two bishops (Alburt & Krogius 2005:402–3).
Bishops are often more powerful than rooks in the opening. Rooks are usually more powerful than bishops in the middlegame, and rooks dominate the minor pieces in the endgame (Seirawan 2003:ix).
As the tables in Berliner's system show, the values of pawns change dramatically in the endgame. In the opening and middlegame, pawns on the central files are more valuable. In the late middlegame and endgame the situation reverses, and pawns on the wings become more valuable due to their likelihood of becoming an outside passed pawn and threatening to promote. When there is about fourteen points of material on both sides, the value of pawns on any file is about equal. After that, wing pawns become more valuable (Berliner 1999:16–20).

[Nordlandia]

...I am convinced that a Queen is more powerful than two Rooks

From my observations over many years of watching engines playing, in general the queen has the edge.

What about three minor pieces vs two rooks?

[Graham Banks]

...I am convinced that a Queen is more powerful than two Rooks

From my observations over many years of watching engines playing, in general the queen has the edge.

What about three minor pieces vs two rooks?

Three pieces are generally more useful than two, but not much between these.
Two minors almost always do better v rook and extra pawn though.

[Nordlandia]

While two bishops + two pawns is stronger than rook and knight.

Example position: Stockfish is capable of beating Komodo as white here.

[d]5rk1/pp2npp1/7p/8/8/1B1PB1P1/PP2PP1P/6K1 b - - 0 1

[Chessqueen]

...I am convinced that a Queen is more powerful than two Rooks

From my observations over many years of watching engines playing, in general the queen has the edge.

What about three minor pieces vs two rooks?

Here is GM Karpov versus GM Boris Gulko, but I will also let SF10 play it out by itself = Program with same strength to see if Karpov held it because of his superior rating. In the game that I will show you SF10 vs SF10 it will also show you that a Knight and Bishop versus a single Rook is stronger with same amount of pawns 4 on each side.


[pgn][Event "Computer chess game"]
[Site "DESKTOP-OFQ3C0P"]
[Date "2019.01.28"]
[Round "?"]
[White "Stockfish_10_x64"]
[Black "Stockfish_10_x64"]
[Result "*"]
[BlackElo "?"]
[Time "08:07:09"]
[WhiteElo "?"]
[TimeControl "900"]
[SetUp "1"]
[FEN "3r4/k2N2pp/p7/3p4/B1r5/4P3/PP4PP/4BK2 w - - 4 1"]
[Termination "normal"]
[PlyCount "114"]
[WhiteType "program"]
[BlackType "program"]

1. Ba5 {(Be1-a5 Rd8-e8 Ba4-b3 Rc4-c1+ Kf1-f2 Re8-e7 Bb3-a4 Rc1-c4 b2-b4
Re7-f7+ Kf2-g3 h7-h5 Ba5-b6+ Ka7-b7 Bb6-d4 Rc4xb4 Nd7-c5+ Kb7-c8 Ba4-b3
Rf7-f5 Nc5xa6 Rb4-b7 Na6-c5 Rb7-e7 Nc5-d3 g7-g5 Nd3-b4 Re7-d7 h2-h3 Rd7-d6
a2-a4 Kc8-b7 Bb3-c2) +2.05/25 22} Re8 {(Rd8-e8 Ba4-b3 Rc4-c1+ Kf1-f2 Re8-e7
Bb3-a4 Rc1-c4 b2-b4 Re7-f7+ Kf2-g3 Rf7-e7 Ba5-b6+ Ka7-b7 Bb6-c5 Re7-e6
Bc5-d4 Re6-g6+ Kg3-f3 Rc4xb4 Nd7-c5+ Kb7-c7 Ba4-b3 Rb4-b5 a2-a4 Rb5-b4
Bb3xd5 Kc7-d6 Bd5-f7 Rb4xd4 Bf7xg6 Rd4-h4 Kf3-g3 Rh4-c4 Nc5-e4+ Kd6-e5
Ne4-d2 Rc4xa4 Bg6xh7 Ra4-a2 Nd2-f3+ Ke5-f6 Bh7-d3 a6-a5) -1.80/25 19} 2.
Bb3 {(Ba4-b3 Rc4-c1+ Kf1-f2 Re8-e7 Bb3-a4 Re7-e4 Ba5-b6+ Ka7-b7 Bb6-d4
Rc1-c4 Ba4-b3 Rc4xd4 e3xd4 Re4xd4 Kf2-e3 Rd4-b4 Nd7-c5+ Kb7-b6 Nc5-d3
Rb4-e4+ Ke3-f3 Kb6-c6 a2-a3 a6-a5 Bb3-c2 Re4-e7 b2-b4 Re7-a7 b4xa5 Ra7xa5
a3-a4 Kc6-d6 Kf3-e3) +2.15/24 7} Rc1+ {(Rc4-c1+ Kf1-f2 Re8-e7 Bb3-a4 Rc1-c4
b2-b4 Re7-f7+ Kf2-g3 Rf7-e7 Ba5-b6+ Ka7-b7 Bb6-c5 Re7-e6 Bc5-d4 Re6-g6+
Kg3-f2 Rc4xb4 a2-a3 Rb4xd4 e3xd4 Rg6-g4 Nd7-c5+ Kb7-b6 Nc5-e6 Rg4-e4 Ba4-d7
g7-g5 Ne6xg5) -1.85/22 4} 3. Kf2 {(Kf1-f2 Re8-e7 Bb3-a4 Re7-e4 Ba5-b6+
Ka7-b7 Bb6-d4 Rc1-c4 Ba4-b3 Rc4xd4 e3xd4 Re4xd4 Kf2-e3 Rd4-h4 h2-h3 Kb7-c6
Nd7-e5+ Kc6-d6 Ne5-f7+ Kd6-c5 Bb3-c2 Rh4-b4 Nf7-e5 Kc5-d6 Ne5-d3 Rb4-e4+
Ke3-d2 Re4-e8 Bc2-d1 a6-a5 Bd1-h5 Re8-c8 Bh5-f3 a5-a4 Nd3-b4 Rc8-c4 Nb4xd5
Rc4-d4+ Kd2-c3) +2.25/24 5} Re7 {(Re8-e7 Bb3-a4 Rc1-c4 b2-b4 Re7-f7+ Kf2-g3
Rf7-e7 Ba5-b6+ Ka7-b7 Bb6-c5 Re7-e6 Bc5-d4 Re6-g6+ Kg3-f3 Rc4xb4 Nd7-c5+
Kb7-c7 Ba4-b3 Kc7-d6 Nc5-d3 Rb4-b7 Bd4-e5+ Kd6-e6 Be5-g3 Ke6-e7 Nd3-f4
Rg6-h6 Nf4xd5+ Ke7-f8 e3-e4 Rh6-c6 h2-h3 Rb7-f7+ Kf3-e3 Rc6-c1 Ke3-d4)
-1.59/24 5} 4. Ba4 {(Bb3-a4 Re7-e4 Ba5-b6+ Ka7-b7 Bb6-d4 Rc1-c4 Ba4-b3
Rc4xd4 e3xd4 Re4xd4 Kf2-e3 Rd4-h4 h2-h3 Kb7-c6 Nd7-e5+ Kc6-d6 Ne5-f7+
Kd6-c5 Bb3-c2 Rh4-b4 Nf7-e5 Kc5-d6 Ne5-d3 Rb4-e4+ Ke3-d2 g7-g6 Bc2-d1 a6-a5
b2-b3 Re4-e8 Bd1-f3 Re8-c8 Nd3-f4) +2.32/22 6} Re4 {(Re7-e4 Ba5-b6+ Ka7-b7
Bb6-d4 Rc1-c4 Ba4-b3 Rc4xd4 e3xd4 Re4xd4 Kf2-e3 Rd4-e4+ Ke3-d3 Re4-f4
Nd7-e5 Kb7-c7 Ne5-f3 Kc7-d6 Bb3-d1 a6-a5 g2-g3 Rf4-f8 b2-b3 Rf8-c8 Nf3-d4
Rc8-c1 Bd1-e2 Rc1-a1 a2-a4 Ra1-h1 h2-h4 Kd6-c5 Nd4-f5 Kc5-b4) -1.67/26 23}
5. Bb6+ {(Ba5-b6+ Ka7-b7 Bb6-d4 Rc1-c4 Ba4-d1 Re4xd4 e3xd4 Rc4xd4 Bd1-e2
Kb7-c6 Nd7-e5+ Kc6-d6 Ne5-d3 a6-a5 Kf2-e3 Rd4-e4+ Ke3-d2 h7-h5 b2-b3 g7-g5
h2-h3 h5-h4 Nd3-f2 Re4-f4 Be2-f3 a5-a4 Nf2-d3 a4xb3 a2xb3 Rf4-f8 Kd2-c3
Rf8-c8+ Kc3-d4 Rc8-c2 Bf3xd5) +2.01/27 20} Kb7 {(Ka7-b7 Bb6-d4 Rc1-c4
Ba4-d1 Re4xd4 e3xd4 Rc4xd4 Bd1-e2 Kb7-c6 Nd7-e5+ Kc6-d6 Ne5-d3 a6-a5 Kf2-e3
Rd4-a4 a2-a3 Ra4-h4 h2-h3 Rh4-e4+ Ke3-d2 d5-d4 Nd3-e1 Re4-e3 Ne1-c2 Re3-b3
Nc2xd4 Rb3xb2+ Kd2-c3 Rb2-b6 g2-g4 Kd6-d5 h3-h4 g7-g6 Nd4-b3 a5-a4 Nb3-d4)
-1.79/25 4} 6. Bd4 {(Bb6-d4 Rc1-c4 Ba4-d1 Re4xd4 e3xd4 Rc4xd4 Bd1-e2 Kb7-c6
Nd7-e5+ Kc6-d6 Ne5-d3 a6-a5 Kf2-e3 Rd4-h4 h2-h3 Rh4-a4 a2-a3 Ra4-e4+ Ke3-d2
d5-d4 Be2-f3 Re4-e3 Nd3-f2 Kd6-c5 Nf2-e4+ Kc5-b6 Ne4-d6 Kb6-c5 Nd6-f5
Re3-b3 Kd2-c2 a5-a4 Nf5xg7 d4-d3+ Kc2-c1 Kc5-d4 Bf3-d1 d3-d2+ Kc1-c2)
+2.11/27 6} Rc4 {(Rc1-c4 Ba4-b3 Rc4xd4 e3xd4 Re4xd4 Kf2-e3 Rd4-e4+ Ke3-d3
Re4-f4 Nd7-e5 Kb7-c7 Ne5-f3 Kc7-d6 Bb3-d1 a6-a5 g2-g3 Rf4-f8 b2-b3 Rf8-c8
Kd3-d2 Rc8-f8 a2-a3 g7-g6 Kd2-d3 Kd6-c5 h2-h3 Rf8-e8 Nf3-d4 Re8-e7 Bd1-f3)
-1.69/29 12} 7. Bd1 {(Ba4-d1 Re4xd4 e3xd4 Rc4xd4 Bd1-e2 Kb7-c6 Nd7-e5+
Kc6-d6 Ne5-d3 h7-h5 Kf2-e3 Rd4-e4+ Ke3-d2 a6-a5 b2-b3 g7-g5 h2-h3 h5-h4
Be2-f3 Re4-e7 Nd3-b2 Kd6-c5 Kd2-c3 Re7-c7 Nb2-a4+ Kc5-b5+ Kc3-d4 Kb5-b4
Na4-b6 Rc7-c2 Nb6xd5+ Kb4-a3 Nd5-e3 Rc2-c8 Bf3-g4 Rc8-b8 Ne3-c4+ Ka3xa2)
+2.12/27 5} Rexd4 {(Re4xd4 e3xd4 Rc4xd4 Bd1-e2 Kb7-c6 Nd7-e5+ Kc6-d6 Ne5-d3
a6-a5 Kf2-e3 Rd4-a4 a2-a3 Ra4-h4 h2-h3 Rh4-e4+ Ke3-d2 g7-g6 b2-b3 Re4-e7
Nd3-e1 Re7-e8 Ne1-c2 Re8-b8 Kd2-c3 Rb8-c8+ Kc3-d3 Rc8-b8 Nc2-d4 Rb8-c8
g2-g3 h7-h5 Be2-f3 Kd6-e5) -1.65/26 3} 8. exd4 {(e3xd4 Rc4xd4 Bd1-e2 a6-a5
Nd7-c5+ Kb7-b6 Nc5-d3 Kb6-c7 h2-h3 Kc7-d6 Kf2-e3 Rd4-a4 a2-a3 Ra4-e4+
Ke3-d2 Re4-e8 Be2-h5 g7-g6 Bh5-d1 d5-d4 Kd2-c2 Re8-e3 Bd1-f3 Kd6-c7 Nd3-c5
Kc7-b6 Nc5-b3 a5-a4 Nb3xd4 Kb6-c5 Nd4-e2 Kc5-c4 Ne2-f4) +2.19/24 4} Rxd4
{(Rc4xd4 Bd1-e2 Kb7-c6 Nd7-e5+ Kc6-d6 Ne5-d3 a6-a5 Kf2-e3 Rd4-a4 a2-a3
Ra4-h4 h2-h3 Rh4-e4+ Ke3-d2 Re4-e7 b2-b3 g7-g6 Nd3-e1 Re7-e8 Kd2-d3 Kd6-e5
Be2-g4 Ke5-d6 Ne1-c2 Kd6-e5 Nc2-d4 Ke5-d6 Bg4-e2) -1.60/27 4} 9. Be2
{(Bd1-e2 Kb7-c6 Nd7-e5+ Kc6-d6 Ne5-d3 a6-a5 Kf2-e3 Rd4-h4 h2-h3 Rh4-a4
a2-a3 Ra4-e4+ Ke3-d2 Re4-e7 Be2-f3 Re7-e8 Nd3-f2 Re8-b8 Kd2-c3 g7-g6 Nf2-d3
Rb8-c8+ Kc3-d2 d5-d4 Bf3-g4 Rc8-b8 Kd2-c2 Kd6-d5 Bg4-f3+ Kd5-d6 h3-h4
Rb8-b5 b2-b3 g6-g5 h4-h5 Rb5-b8) +2.20/28 7} Kc6 {(Kb7-c6 Nd7-e5+ Kc6-d6
Ne5-d3 a6-a5 Kf2-e3 Rd4-a4 a2-a3 Ra4-h4 h2-h3 Rh4-e4+ Ke3-d2 Re4-e8 Be2-h5
g7-g6 Bh5-f3 Re8-e7 Nd3-f4 Re7-b7 Nf4xd5 Rb7xb2+ Kd2-c3 Rb2-a2 Kc3-b3
Ra2-d2 Nd5-c3 Kd6-c7 Bf3-e4 Rd2-f2 Kb3-c4 Kc7-b6 h3-h4 Rf2-f1 Be4-f3 Rf1-a1
Nc3-d5+ Kb6-a6) -1.81/29 11} 10. Ne5+ {(Nd7-e5+ Kc6-d6 Ne5-d3 a6-a5 Kf2-e3
Rd4-h4 h2-h3 Rh4-a4 a2-a3 Ra4-e4+ Ke3-d2 Re4-e7 Be2-f3 Re7-e8 Bf3-h5 Re8-c8
Bh5-e2 Rc8-b8 Be2-d1 Rb8-e8 Bd1-f3 Re8-e7 Nd3-f2 Kd6-c5 Kd2-c3 Re7-c7
Kc3-b3 Rc7-b7+ Kb3-c2 Kc5-d4 Nf2-d1 Rb7-d7 Nd1-c3 g7-g6 g2-g3 g6-g5)
+2.02/30 11} Kd6 {(Kc6-d6 Ne5-d3 a6-a5 Kf2-e3 Rd4-a4 a2-a3 Ra4-h4 h2-h3
Rh4-e4+ Ke3-d2 g7-g6 Be2-f3 Re4-e8 Bf3-g4 Re8-e4 Bg4-e2 Re4-e8 Be2-f3
Re8-e7 Nd3-f4 Re7-b7 Kd2-c3 Rb7-f7 Nf4xd5 Rf7xf3+ g2xf3 Kd6xd5 Kc3-b3
Kd5-c5 Kb3-a4 Kc5-b6 h3-h4 h7-h6 b2-b4 a5xb4) -1.74/29 3} 11. Nd3 {(Ne5-d3
a6-a5 Kf2-e3 Rd4-e4+ Ke3-d2 Re4-a4 a2-a3 Ra4-h4 h2-h3 Rh4-e4 Be2-d1 Re4-e8
Bd1-f3 Re8-b8 Kd2-e3 Rb8-c8 Bf3-d1 Rc8-e8+ Ke3-d4 Re8-e4+ Kd4-c3 Re4-c4+
Kc3-d2 Rc4-e4 Nd3-f2 Re4-d4+ Kd2-c3 Rd4-c4+ Kc3-d3 Rc4-c7 Kd3-d4 Rc7-c4+
Kd4-e3 h7-h5 Ke3-d2 h5-h4 b2-b3 Rc4-c7 Nf2-d3 d5-d4 Nd3-f2) +2.02/29 5} a5
{(a6-a5 Kf2-e3 Rd4-a4 a2-a3 Ra4-h4 h2-h3 Rh4-e4+ Ke3-d2 g7-g6 Nd3-f2 Re4-e8
Be2-f3 Re8-b8 Kd2-c3 Rb8-b7 Kc3-c2 Rb7-c7+ Kc2-d2 Rc7-b7 Kd2-c3 Rb7-b8
b2-b3 Rb8-c8+ Kc3-d3 Rc8-b8 Bf3-d1 Rb8-c8 Kd3-d4 Rc8-c1 Bd1-f3 Rc1-c2
Nf2-g4 a5-a4) -1.80/31 12} 12. Ke3 {(Kf2-e3 Rd4-e4+ Ke3-d2 Re4-a4 a2-a3
Ra4-h4 h2-h3 Rh4-e4 Be2-g4 Re4-e7 Bg4-h5 Re7-d7 Bh5-f3 Rd7-e7 Nd3-f2 Kd6-c5
Kd2-c3 Re7-c7 Nf2-d1 Rc7-e7 Kc3-c2 Kc5-c4 Nd1-c3 Re7-d7 h3-h4 g7-g6 g2-g3
Kc4-d4 a3-a4 Kd4-c4 Bf3xd5+ Rd7xd5) +2.10/29 5} Ra4 {(Rd4-a4 a2-a3 Ra4-h4
h2-h3 Rh4-e4+ Ke3-d2 g7-g6 Nd3-f2 Re4-e8 Be2-f3 Re8-b8 Kd2-c3 Rb8-b7 Nf2-d3
Rb7-c7+ Kc3-d2 Rc7-e7 Nd3-f4 Re7-f7 Kd2-e3 Rf7-b7 Nf4-d3 Rb7-c7 Bf3-d1
Rc7-e7+ Ke3-d4 Re7-e4+ Kd4-c3 Re4-c4+ Kc3-d2 Rc4-c7 b2-b3 Rc7-f7 Kd2-c3
Rf7-f1 Bd1-e2 Rf1-a1 Be2-f3 Ra1-a2 a3-a4) -1.84/32 6} 13. a3 {(a2-a3
Ra4-e4+ Ke3-d2 Re4-h4 h2-h3 Rh4-e4 Be2-f3 Re4-e8 Bf3-g4 Re8-e7 Bg4-d1
Re7-e8 Bd1-f3 Re8-b8 Kd2-e3 Rb8-c8 Nd3-f2 Kd6-c5 Ke3-d3 Rc8-e8 Kd3-c3
Re8-c8 Kc3-b3 Kc5-d4 Nf2-d1 Rc8-b8+ Kb3-c2 Rb8-c8+ Nd1-c3 Kd4-e5 Kc2-d3
Rc8-b8 Nc3xd5 Rb8xb2 Kd3-c3 Rb2-b5 Kc3-c4 Rb5-b1) +2.00/31 9} Rh4 {(Ra4-h4
h2-h3 Rh4-e4+ Ke3-d2 Re4-e7 Be2-d1 Re7-e4 b2-b3 Re4-e7 Kd2-c3 Re7-c7+
Kc3-d4 a5-a4 g2-g3 a4xb3 Bd1xb3 Rc7-a7 a3-a4 g7-g5 h3-h4 g5xh4 g3xh4 Ra7-a8
Nd3-c5 Ra8-c8 Nc5-b7+ Kd6-c7 Bb3xd5 Rc8-b8 Kd4-c5 Rb8xb7 Bd5xb7 Kc7xb7)
-1.90/30 14} 14. h3 {(h2-h3 Rh4-e4+ Ke3-d2 Re4-e8 Be2-g4 Re8-e7 Bg4-f3
Re7-e8 Nd3-f4 Re8-b8 Nf4xd5 Rb8xb2+ Kd2-c3 Rb2-f2 Nd5-e3 Kd6-c5 Ne3-c4
Kc5-b5 a3-a4+ Kb5-a6 Kc3-d3 Rf2-a2 Bf3-c6 g7-g5 Kd3-e3 Ka6-a7 Ke3-f3 h7-h5
Bc6-b5 h5-h4 Nc4xa5 Ka7-b6 Na5-c4+ Kb6-c5 Nc4-e3 Ra2-a1 Kf3-e4 Ra1-e1)
+2.12/31 11} Re4+ {(Rh4-e4+ Ke3-d2 Re4-e7 Be2-d1 Re7-f7 Bd1-f3 Rf7-b7
Kd2-e3 Rb7-c7 Nd3-f4 Rc7-c2 Nf4xd5 Rc2xb2 Ke3-d4 Kd6-c6 Nd5-c3+ Kc6-c7
Bf3-e4 Kc7-d6 Nc3-d5 Rb2-d2+ Kd4-c4 Rd2-a2 Nd5-c3 Ra2-b2 Be4-f3 Kd6-e5
Nc3-d5 g7-g5 Kc4-c5 Rb2-a2 Nd5-b6 Ke5-f4 a3-a4 Kf4-g3 Kc5-b5 Ra2xg2 Bf3xg2
Kg3xg2 Kb5xa5 h7-h5 Ka5-b5 Kg2xh3 a4-a5) -1.92/29 20} 15. Kd2 {(Ke3-d2
Re4-e7 Be2-f3 g7-g6 Nd3-f4 Re7-f7 Kd2-e3 Rf7-b7 Nf4-d3 Rb7-c7 Bf3-d1
Rc7-e7+ Ke3-d4 Re7-e4+ Kd4-c3 Re4-c4+ Kc3-d2 Rc4-e4 b2-b3 d5-d4 Nd3-b2
Kd6-c5 Nb2-c4 a5-a4 Kd2-d3 a4xb3 Kd3xe4 Kc5xc4 Bd1-e2+ Kc4-c3 Be2-d3 b3-b2
a3-a4 Kc3-b4 Ke4xd4 Kb4xa4 Kd4-c3 Ka4-a3 Bd3-b1 g6-g5 Kc3-c4 h7-h5 Kc4-c3)
+2.19/30 8} Re7 {(Re4-e7 Be2-d1 Re7-b7 Bd1-f3 Rb7-b8 Kd2-e3 Rb8-c8 Nd3-f4
Rc8-c2 Nf4xd5 Rc2xb2 Ke3-d4 Kd6-c6 Nd5-c3+ Kc6-c7 Kd4-c4 h7-h6 Nc3-d5+
Kc7-c6 Nd5-e3+ Kc6-b6 Kc4-c3 Rb2-b1 Ne3-c4+ Kb6-a6 Bf3-c6 Rb1-c1+ Kc3-b3
h6-h5 a3-a4 h5-h4 Bc6-b5+ Ka6-a7 Nc4xa5 Rc1-g1 Na5-c4) -1.83/30 6} 16. Bf3
{(Be2-f3 Re7-b7 Kd2-e3 Rb7-c7 Bf3-d1 g7-g5 Ke3-d2 Rc7-f7 Bd1-f3 Rf7-b7
Kd2-e3 Rb7-c7 Bf3-d1 Rc7-c8 Ke3-d2 Rc8-b8 Bd1-g4 Rb8-b3 Bg4-e2 Rb3-b7
Be2-f3 Rb7-b8 Bf3-d1 Rb8-e8 b2-b3 d5-d4 Nd3-b2 Kd6-c5 Nb2-a4+ Kc5-d6)
+2.18/27 6} Rb7 {(Re7-b7 Kd2-e3 Rb7-c7 Nd3-f4 Rc7-c2 Nf4xd5 Rc2xb2 Ke3-d4
Kd6-c6 Nd5-c3+ Kc6-c7 Bf3-e4 Kc7-d6 Kd4-c4 h7-h6 Be4-f3 Kd6-c7 Nc3-d5+
Kc7-b7 Nd5-e3+ Kb7-a6 Kc4-c3 Rb2-b1 Bf3-e2+ Ka6-a7 Ne3-c4 Rb1-c1+ Kc3-b2
Rc1-g1 Be2-f3 Ka7-a6 Kb2-b3 Rg1-c1 Bf3-e2 Rc1-e1 Be2-d3 Ka6-b5 a3-a4+
Kb5-c5 Nc4xa5 Re1-e3 Kb3-c3) -1.82/29 10} 17. Ke3 {(Kd2-e3 Rb7-c7 Nd3-f4
Rc7-c5 Ke3-d3 Rc5-b5 Nf4xd5 Rb5xb2 Kd3-c3 Rb2-b5 Kc3-c4 Rb5-c5+ Kc4-d4
Rc5-b5 Nd5-e3 Kd6-c7 Kd4-c3 Kc7-b6 Bf3-e4 g7-g6 Kc3-d4 Rb5-b3 Ne3-c4+
Kb6-a6 a3-a4 Rb3-b8 Be4-c6 Rb8-b1 Kd4-e5 Rb1-c1 Ke5-f6 Rc1-c2 h3-h4 Rc2-a2
Kf6-g7) +2.33/27 8} Rc7 {(Rb7-c7 Bf3-d1 Rc7-e7+ Ke3-d2 Re7-c7 Bd1-e2 Rc7-b7
Be2-f3 Rb7-b8 Bf3-d1 Rb8-b7 b2-b3 g7-g5 Nd3-e1 h7-h5 Ne1-f3 Rb7-f7 g2-g3
g5-g4 h3xg4 h5xg4 Nf3-d4 Kd6-c5 Kd2-c3 Rf7-e7 Kc3-d3 Re7-e1 Bd1xg4 Re1-g1
Nd4-f5 Rg1-a1 Kd3-c3 Ra1-c1+ Kc3-b2) -1.81/26 3} 18. Kd2 {(Ke3-d2 Rc7-f7
Kd2-e3 Rf7-c7 Nd3-f4 Rc7-c2 Nf4xd5 Rc2xb2 Ke3-d4 Kd6-c6 Nd5-c3+ Kc6-c7
Bf3-e4 Kc7-d6 Nc3-d5 Rb2-d2+ Kd4-c4 h7-h5 Be4-f3 h5-h4 Nd5-e3 Rd2-b2 Kc4-d4
Rb2-b3 Ne3-c4+ Kd6-c7 Bf3-e4 a5-a4 Be4-c2 Rb3-b5 Nc4-e3 Rb5-g5 Kd4-e4
Rg5-g3 Bc2xa4) +2.14/30 22} Rb7 {(Rc7-b7 Kd2-e3 Rb7-c7 Nd3-f4 Rc7-c2 Nf4xd5
Rc2xb2 Ke3-d4 Kd6-c6 Nd5-c3+ Kc6-c7 Kd4-c4 h7-h6 Nc3-d5+ Kc7-b7 Kc4-c3
Rb2-b1 Nd5-e3+ Kb7-a6 Bf3-e2+ Ka6-a7 Ne3-f5 Rb1-c1+ Kc3-b3 Rc1-c7 Nf5-d6
Rc7-c1 Kb3-a4 Rc1-c2 Be2-f3 Ka7-b6 Ka4-b3 Rc2-c1 Nd6-c4+ Kb6-b5 a3-a4+
Kb5-a6 Kb3-b2 Rc1-f1 Bf3-e4 Rf1-f2+ Kb2-b3 g7-g5) -1.75/29 5} 19. Bg4
{(Bf3-g4 Rb7-e7 Bg4-d1 Re7-c7 Bd1-e2 Rc7-b7 Be2-f3 Rb7-f7 Nd3-f2 Rf7-b7
Kd2-c3 Rb7-b8 Nf2-d3 Rb8-c8+ Kc3-d2 Rc8-b8 Kd2-e3 Rb8-c8 Nd3-f4 Rc8-c2
Nf4xd5 Rc2xb2 Ke3-d4 Kd6-c6 Nd5-c3+ Kc6-c7 Kd4-c4 h7-h6 Nc3-d5+ Kc7-c6
Nd5-e3+ Kc6-b6 Kc4-c3 Rb2-b1 Kc3-c2 Rb1-b5 a3-a4 Rb5-c5+ Kc2-b3 Rc5-c1
Ne3-c4+ Kb6-a6 Bf3-c6 Ka6-a7 Bc6-e4) +2.03/31 11} Rf7 {(Rb7-f7 Kd2-e3
Rf7-c7 Bg4-d1 Rc7-c8 Ke3-d2 Rc8-c7 Nd3-f2 Rc7-f7 Bd1-f3 Kd6-e5 Kd2-e3
Rf7-c7 Nf2-d3+ Ke5-d6 Nd3-f4 Rc7-c2 Nf4xd5 Rc2xb2 Ke3-d4 Kd6-c6 Nd5-c3+
Kc6-c7 Kd4-c4 h7-h6 Nc3-d5+ Kc7-b7 Kc4-c3 Rb2-b1 Nd5-e3+ Kb7-a6 Bf3-e2+
Ka6-a7 Ne3-f5 Rb1-c1+ Kc3-b3 Rc1-c7 Nf5-d6) -1.75/31 10} 20. Be2 {(Bg4-e2
Rf7-c7 Be2-d1 Rc7-b7 Bd1-f3 Rb7-b8 Kd2-e3 Rb8-c8 Nd3-f4 Rc8-c2 Nf4xd5
Rc2xb2 Ke3-d4 Kd6-c6 Nd5-c3+ Kc6-c7 Kd4-c5 Rb2-c2 Kc5-c4 h7-h6 Kc4-b3
Rc2-d2 Nc3-d5+ Kc7-d6 Kb3-c4 Kd6-c6 Nd5-e3+ Kc6-b6 Kc4-c3 Rd2-d8 Ne3-c4+
Kb6-a6 a3-a4 Rd8-c8 Kc3-d4 Rc8-c7 Bf3-d5 Rc7-c8 Kd4-e5) +2.12/31 7} Ra7
{(Rf7-a7 Be2-h5 Ra7-e7 Bh5-d1 Re7-c7 Nd3-f2 Kd6-e5 Kd2-e3 Rc7-c8 Nf2-g4+
Ke5-d6 Ke3-d4 Rc8-c4+ Kd4-d3 Rc4-c8 Ng4-f2 Rc8-b8 Kd3-c3 Rb8-c8+ Kc3-d4
Rc8-c4+ Kd4-d3 Rc4-c8 Bd1-f3 Rc8-b8 Kd3-c3 Rb8-b7 Kc3-c2 Rb7-c7+ Kc2-d3
Rc7-b7 Kd3-c3 Rb7-f7 Nf2-d1 Kd6-e5 Kc3-b3 d5-d4 Nd1-f2) -1.86/31 14} 21.
Bd1 {(Be2-d1 Ra7-c7 Nd3-f2 Rc7-b7 Kd2-c3 Rb7-c7+ Kc3-d4 Rc7-c4+ Kd4-d3
Rc4-c8 Bd1-f3 Rc8-b8 Nf2-d1 Kd6-e5 Kd3-c2 d5-d4 Nd1-f2 Ke5-f4 Nf2-e4
Rb8-c8+ Kc2-d3 Rc8-b8 Ne4-d2 Rb8xb2 Nd2-c4 Rb2-b5 Kd3xd4 h7-h5 Bf3-c6
Rb5-g5 a3-a4 h5-h4 Bc6-f3 Kf4-g3 Bf3-d5 Kg3-f4 Nc4xa5) +1.99/31 25} Re7
{(Ra7-e7 Bd1-e2 Re7-c7 Be2-h5 Rc7-a7 Bh5-g4 Ra7-f7 b2-b3 Rf7-b7 Bg4-d1
Rb7-c7 Bd1-f3 g7-g5 Nd3-f2 Rc7-b7 Kd2-c3 Rb7-c7+ Kc3-d3 Rc7-b7 Bf3-d1 h7-h5
Kd3-e3 Rb7-e7+ Ke3-d2 Re7-f7 Nf2-d3 Rf7-b7 Nd3-e1 h5-h4 Ne1-d3 Rb7-e7
Bd1-f3 Re7-c7 Bf3-g4 Rc7-b7 Kd2-c3) -1.75/32 6} 22. Kc3 {(Kd2-c3 Re7-c7+
Kc3-d2 Rc7-e7 Bd1-e2 Re7-f7 Be2-g4 Rf7-e7 Bg4-d1 Re7-c7 Nd3-f2 Rc7-b7
Kd2-c3 Rb7-c7+ Kc3-d4 Rc7-c4+ Kd4-d3 Rc4-c8 Bd1-f3 Rc8-b8 Nf2-d1 Kd6-e5
Kd3-c2 d5-d4 Nd1-f2 Ke5-f4 Nf2-e4 Rb8-c8+ Kc2-d3 Rc8-b8 Ne4-d2 Rb8xb2
Nd2-c4 Rb2-b5 Kd3xd4 h7-h5 Bf3-c6 Rb5-g5) +2.02/32 20} Rc7+ {(Re7-c7+
Kc3-d2 Rc7-e7 b2-b3 Re7-c7 Bd1-f3 g7-g5 Bf3-d1 Rc7-f7 Bd1-e2 Rf7-b7 Nd3-c1
Kd6-e5 Be2-f3 Rb7-b5 Kd2-e3 Rb5-b7 Bf3-d1 Rb7-c7 Ke3-d2 Ke5-d6 Bd1-g4
Rc7-f7 Bg4-f3 Rf7-b7 Kd2-d3 Kd6-e5 Kd3-c3 d5-d4+ Kc3-d2 Rb7-b8 Nc1-d3+
Ke5-d6 Bf3-d1) -1.68/28 5} 23. Kd2 {(Kc3-d2 Rc7-f7 b2-b3 Rf7-c7 Bd1-f3
Rc7-c8 Bf3-g4 Rc8-c6 Bg4-e2 Rc6-c7 Be2-d1 Rc7-e7 Bd1-f3 Re7-c7 h3-h4 Rc7-c8
h4-h5 Rc8-c7 Bf3-d1 Rc7-c8 Kd2-e3 g7-g6 h5-h6 Rc8-e8+ Ke3-d2 Re8-e4 Nd3-f2
Re4-h4 Nf2-g4 Rh4-h1 Bd1-f3 Kd6-c5 Kd2-d3 d5-d4 Ng4-f6 Rh1xh6 Nf6-e4+
Kc5-b5) +1.97/32 7} Re7 {(Rc7-e7 b2-b3 Re7-c7 Bd1-f3 g7-g5 Nd3-b2 Kd6-e5
Kd2-d3 Rc7-b7 Kd3-c3 Rb7-c7+ Kc3-d2 Ke5-d4 Nb2-d3 Rc7-c8 Nd3-c1 Kd4-e5
Bf3-g4 Rc8-c7 Nc1-d3+ Ke5-d4 Nd3-e1 Kd4-e4 Bg4-e2 Ke4-f4 Ne1-d3+ Kf4-e4
Be2-d1 Ke4-d4 Nd3-e1 Kd4-e4 Ne1-f3 h7-h6 Bd1-c2+ Ke4-f4 Nf3-d4) -1.71/28
10} 24. b3 {(b2-b3 Re7-c7 Bd1-f3 Rc7-c8 Bf3-g4 Rc8-c6 Bg4-e2 Rc6-c7 Nd3-b2
Rc7-b7 Be2-d1 h7-h5 Nb2-d3 h5-h4 Nd3-e1 Rb7-f7 Bd1-f3 Rf7-c7 Kd2-d3 Rc7-e7
Ne1-c2 Re7-b7 Nc2-d4 Rb7-f7 Nd4-b5+ Kd6-e5 Bf3-g4 Rf7-f4 Bg4-d1 Rf4-f1
Bd1-f3 Rf1-b1) +1.92/30 9} Rc7 {(Re7-c7 Bd1-f3 g7-g6 Bf3-d1 Rc7-c8 Bd1-g4
Rc8-c7 Bg4-f3 g6-g5 Nd3-b2 Kd6-e5 Kd2-d3 Rc7-b7 Kd3-c3 Rb7-c7+ Kc3-d2
Ke5-d4 Nb2-d3 Rc7-c8 Nd3-e1 Rc8-b8 Ne1-c2+ Kd4-e5 b3-b4 a5xb4 a3xb4 Rb8-b7
Kd2-d3 Rb7-a7 Bf3-d1 Ra7-f7 Nc2-d4 Rf7-c7 Bd1-b3 Rc7-b7 Nd4-f3+ Ke5-d6)
-1.71/28 16} 25. Bf3 {(Bd1-f3 Rc7-c8 Bf3-g4 Rc8-c6 Bg4-d1 Rc6-c7 Nd3-b2
Kd6-e5 Bd1-f3 Ke5-d4 Nb2-d3 Rc7-f7 Nd3-c1 Rf7-b7 Nc1-e2+ Kd4-e5 Kd2-c2
Rb7-c7+ Kc2-d3 Rc7-b7 Ne2-d4 Rb7-c7 g2-g3 g7-g6 Bf3-e2 Rc7-c1 h3-h4 Rc1-a1
a3-a4 Ke5-d6 Nd4-b5+ Kd6-c5) +1.98/28 5} g5 {(g7-g5 Nd3-b2 Kd6-e5 Bf3-g4
Ke5-d4 Nb2-d3 Rc7-b7 Nd3-c1 Kd4-e5 Bg4-f3 Rb7-b5 Bf3-d1 Rb5-b7 Bd1-g4
Ke5-d4 Bg4-f3 Rb7-b8 Nc1-e2+ Kd4-e5 Kd2-c3 Rb8-c8+ Kc3-d3 d5-d4 Bf3-h5
Rc8-b8 Bh5-f7 Rb8-f8 Bf7-c4 Rf8-f2) -1.69/28 16} 26. Nf2 {(Nd3-f2 Rc7-b7
Kd2-c3 Rb7-c7+ Kc3-d3 Rc7-b7 Bf3-d1 Kd6-e5 Kd3-e3 d5-d4+ Ke3-d2 Rb7-e7
Nf2-d3+ Ke5-d5 Bd1-f3+ Kd5-d6 Nd3-b2 Kd6-c5 Nb2-d1 Re7-e8 Kd2-c2 Re8-e1
Nd1-f2 Re1-e3 Nf2-e4+ Kc5-b5 Ne4-d6+ Kb5-c5 Nd6-f7 a5-a4 b3-b4+ Kc5-b6
Nf7xg5 Kb6-b5) +2.00/26 10} Rb7 {(Rc7-b7 Bf3-d1 h7-h5 Nf2-d3 h5-h4 Nd3-e1
Rb7-f7 Bd1-g4 Rf7-f1 Bg4-e2 Rf1-g1 Be2-f3 Rg1-f1 Ne1-c2 Rf1-f2+ Kd2-c3
g5-g4 Bf3xg4 Rf2xg2 Nc2-e3 Rg2-a2 Ne3-c2 Kd6-c5 b3-b4+ a5xb4+ a3xb4+ Kc5-d6
Nc2-e3 Kd6-e5) -1.54/24 3} 27. Kc3 {(Kd2-c3 Rb7-c7+ Kc3-b2 Rc7-f7 Nf2-g4
h7-h5 Ng4-f2 h5-h4 Kb2-c3 Rf7-c7+ Kc3-d3 Rc7-b7 Bf3-d1 Kd6-c5 Nf2-g4 Rb7-b6
Ng4-e3 Rb6-b5 Ne3-f5 Rb5-b6 Nf5-d4 Rb6-b7 Bd1-f3 Kc5-d6 Bf3-g4 Rb7-b8
Kd3-c3 Rb8-b7 Nd4-f3 Rb7-c7+ Kc3-b2 Rc7-f7 Nf3xg5) +2.09/25 10} Rc7+
{(Rb7-c7+ Kc3-b2 Kd6-e6 Nf2-g4 d5-d4 Ng4-f2 Ke6-e5 b3-b4 a5xb4 a3xb4 Rc7-c4
Nf2-d3+ Ke5-d6 Bf3-e4 Kd6-c7 Kb2-b3 Rc4-c3+ Kb3-a4 h7-h5 b4-b5 Kc7-b6
Ka4-b4 Rc3-c2 Be4-c6 g5-g4 h3xg4 h5xg4 Nd3-e5 g4-g3 Ne5-c4+ Kb6-a7 Bc6-d5
d4-d3 b5-b6+ Ka7-b8 Kb4-b3 Rc2-c1) -1.99/25 20} 28. Kb2 {(Kc3-b2 h7-h6
b3-b4 a5xb4 a3xb4 Kd6-e5 Nf2-d3+ Ke5-d4 Nd3-c5 Rc7-a7 Nc5-b3+ Kd4-e5 Bf3-e2
Ra7-c7 b4-b5 Ke5-d6 Kb2-a3 Rc7-c2 Be2-f3 Rc2-c7 Ka3-a4 Rc7-c3 Ka4-b4
Rc3-c4+ Kb4-a5 Rc4-c3 Nb3-d4 Kd6-c5 Nd4-e6+ Kc5-d6) +1.88/25 8} Rc8
{(Rc7-c8 b3-b4 a5xb4 a3xb4 Kd6-e5 Nf2-g4+ Ke5-d4 Ng4-f6 Kd4-c4 Nf6xd5
Rc8-h8 Kb2-c2 h7-h6 Kc2-d2 h6-h5 Nd5-f6 g5-g4 h3xg4 h5xg4 Nf6xg4 Kc4xb4
Kd2-d3 Kb4-c5 Ng4-e3 Kc5-d6 Kd3-e4 Rh8-e8+ Ke4-f4 Re8-f8+ Ne3-f5+ Kd6-e6
g2-g4 Ke6-f6 Bf3-e4 Kf6-g6) -1.75/26 12} 29. Nd3 {(Nf2-d3 Rc8-c7 b3-b4
a5xb4 a3xb4 Rc7-c4 Kb2-b3 h7-h6 Nd3-c5 Rc4-c1 Nc5-a4 d5-d4 Na4-c5 Rc1-c3+
Kb3-a4 Rc3-c2 Bf3-e4 Rc2-c3 Nc5-d3 Rc3-c4 Nd3-f2 Rc4-c3 b4-b5 Kd6-c5
Nf2-d3+ Kc5-b6 Ka4-b4 Rc3-c2 Be4-f3 Rc2-d2 Kb4-c4 Rd2-c2+ Kc4xd4 Kb6xb5
Nd3-e5 Rc2-c1) +2.02/28 12} Rc7 {(Rc8-c7 b3-b4 a5xb4 a3xb4 Rc7-c4 Kb2-b3
h7-h6 Nd3-b2 Rc4-c1 Nb2-a4 d5-d4 b4-b5 d4-d3 b5-b6 d3-d2 Na4-c3 Kd6-d7
Kb3-c4 Rc1-c2 Kc4-d3 Rc2-b2 b6-b7 Kd7-c7 Nc3-d1 Rb2-a2 Bf3-d5 Ra2-a5 Bd5-e4
Ra5-a2 Nd1-e3 h6-h5 Be4-d5 Ra2-b2 Kd3-c3 Rb2-b1 Kc3xd2 Rb1-b5 Kd2-c3)
-2.40/30 46} 30. b4 {(b3-b4 a5xb4 a3xb4 Rc7-c4 Kb2-b3 h7-h6 b4-b5 Rc4-d4
Nd3-b2 Kd6-c5 Kb3-c3 Rd4-h4 Nb2-d3+ Kc5xb5 Bf3-g4 h6-h5 g2-g3 h5xg4 g3xh4
g4-g3 Nd3-e1 g5xh4 Kc3-d4 Kb5-c6 Ne1-g2 Kc6-d6 Ng2xh4 Kd6-e6 Nh4-g2 Ke6-f6
Ng2-e3 Kf6-g5 Kd4-e5 d5-d4) +2.26/28 4} axb4 {(a5xb4 a3xb4 Rc7-c8 Nd3-c5
Rc8-e8 Nc5-a4 h7-h5 Na4-c3 d5-d4 Nc3-e4+ Kd6-e5 Ne4xg5 Ke5-f4 Ng5-f7 Re8-b8
Kb2-b3 d4-d3 Kb3-c3 d3-d2 Bf3xh5 Kf4-e3 Nf7-d6 Ke3-f2 Nd6-e4+ Kf2xg2 Bh5-g4
d2-d1Q Bg4xd1 Kg2xh3 Ne4-c5) -2.39/28 11} 31. axb4 {(a3xb4 Rc7-c4 Kb2-b3
h7-h6 b4-b5 Rc4-c8 Nd3-b4 Kd6-c5 Kb3-a4 Rc8-a8+ Nb4-a6+ Kc5-b6 Bf3xd5
Ra8-f8 Bd5-c6 g5-g4 h3xg4 Rf8-f4+ Ka4-a3 Rf4xg4 Na6-b8 Rg4-g3+ Ka3-b4
Rg3-g4+ Kb4-c3 Rg4-g3+ Kc3-c4 Rg3-g4+ Kc4-d5 Rg4-g5+ Kd5-e6 Rg5-g6+ Ke6-f7
Rg6-g5 Nb8-d7+ Kb6-c7 Kf7-f6 Kc7-d6 Nd7-b6 Rg5-g3 Nb6-a4 Kd6-c7) +2.51/27
6} Rc4 {(Rc7-c4 Kb2-b3 h7-h6 Nd3-b2 Rc4-c1 Nb2-a4 Rc1-b1+ Kb3-c3 Rb1-e1
Na4-b2 Re1-c1+ Kc3-b3 Rc1-a1 Nb2-d3 Ra1-a7 Kb3-b2 Ra7-b7 Kb2-c2 Rb7-c7+
Nd3-c5 Rc7-a7 Kc2-b2 Kd6-e5 b4-b5 Ra7-a5 Bf3-e2 h6-h5 Kb2-c3 h5-h4 Kc3-b4
Ra5-a1) -2.37/28 11} 32. Kb3 {(Kb2-b3 h7-h6 b4-b5 Rc4-c8 Nd3-b4 Kd6-c5
Kb3-a4 Rc8-a8+ Nb4-a6+ Kc5-b6 Bf3xd5 Ra8-f8 Bd5-c6 g5-g4 h3xg4 Rf8-f4+
Ka4-b3 Rf4xg4 Na6-b8 Rg4-g3+ Kb3-c4 h6-h5 Nb8-d7+ Kb6-c7 Nd7-f6 h5-h4
Kc4-c5 Rg3-c3+ Kc5-d4 Rc3-g3 Nf6-d5+ Kc7-d6 Nd5-c3 Kd6-c7 Kd4-c4 Kc7-b6
Nc3-a4+ Kb6-c7 Kc4-c5 h4-h3) +2.66/26 6} Rc8 {(Rc4-c8 Nd3-b2 Rc8-c1 Nb2-a4
Rc1-b1+ Kb3-c3 Kd6-e5 Na4-c5 Rb1-c1+ Kc3-b2 Rc1-c4 Kb2-b3 Rc4-d4 Nc5-d7+
Ke5-d6 Nd7-b6 h7-h5 Bf3xh5 Kd6-c6 Nb6-a4 Rd4-d3+ Kb3-c2 Rd3-a3 Kc2-b2
Ra3-e3 Bh5-f3 Kc6-b5 Na4-c3+ Kb5-c4 Nc3xd5 Re3-e1 Nd5-f6 Kc4xb4 Nf6-e4
Kb4-c4) -2.65/28 13} 33. Nc5 {(Nd3-c5 Rc8-e8 Kb3-c3 Kd6-c6 Kc3-d4 Kc6-b5
Nc5-d3 Re8-f8 Bf3xd5 Rf8-c8 Bd5-e4 Rc8-c4+ Kd4-d5 h7-h6 Kd5-e5 Kb5-b6
Be4-d5 Rc4-c3 Ke5-d4 Rc3-c2 Nd3-e5 Kb6-b5 Ne5-f7 h6-h5 Nf7xg5 h5-h4 Bd5-f3
Kb5xb4 Kd4-e5 Kb4-c3 Ke5-f5) +2.83/26 4} Re8 {(Rc8-e8 Kb3-c3 Kd6-c6 Nc5-d3
Re8-c8 Kc3-d4 Kc6-b5 Kd4xd5 Rc8-e8 Bf3-e4 h7-h6 Kd5-d4 Re8-c8 Be4-f3 Rc8-c7
Bf3-d5 Rc7-c2 Kd4-e5 Rc2-d2 Bd5-e4 Kb5-c4 Ke5-f5 Rd2-a2 Nd3-e5+ Kc4xb4
Ne5-g4 Kb4-c3 Ng4xh6 Ra2-a5+ Kf5-g6) -2.59/24 3} 34. Kc3 {(Kb3-c3 Re8-a8
Kc3-d4 Ra8-b8 Nc5-d3 Rb8-b5 g2-g3 Kd6-e6 Bf3-g4+ Ke6-d6 Bg4-f5 Rb5-b8
Bf5xh7 Kd6-e6 Bh7-g6 Rb8-h8 Nd3-c5+ Ke6-d6 Bg6-f7 Rh8xh3 Bf7xd5 Kd6-c7
Nc5-e4 Kc7-b6 Kd4-c4 Rh3-h1 Ne4xg5 Rh1-c1+ Kc4-b3 Kb6-b5 Bd5-e4 Rc1-g1
Be4-d3+ Kb5-b6) +2.87/27 8} Rh8 {(Re8-h8 Kc3-d4 Rh8-b8 Nc5-d3 Rb8-b5 Bf3-d1
Rb5-b8 Bd1-b3 Rb8-b5 g2-g3 h7-h5 Bb3-d1 h5-h4 g3xh4 g5xh4 Bd1-b3 Rb5-b8
Bb3xd5 Rb8-b5 Bd5-f3 Rb5-b8 Bf3-e4 Rb8-g8 b4-b5 Rg8-b8 Kd4-c4 Rb8-e8 Be4-c6
Re8-e3 Nd3-b4 Re3xh3 b5-b6 Rh3-a3 Kc4-b5 h4-h3 b6-b7 Kd6-c7) -2.45/29 28}
35. Kd4 {(Kc3-d4 Rh8-b8 Nc5-d3 Rb8-b5 g2-g3 Kd6-c6 Bf3-g4 Rb5-b7 Bg4-e6
Kc6-b5 Be6xd5 Rb7-c7 Nd3-c5 Rc7-a7 Kd4-c3 Ra7-a1 Nc5-e4 Ra1-c1+ Kc3-d4
Rc1-g1 Kd4-e5 h7-h6 Ke5-f6 Kb5xb4 Kf6-g6 Rg1-h1 Bd5-e6 Rh1-e1 Be6-f5 Re1-f1
g3-g4 Rf1-f3 Kg6xh6 Rf3xh3+ Kh6xg5 Rh3-h1 Kg5-f4) +2.59/29 18} Rb8 {(Rh8-b8
Nc5-d3 Rb8-b5 Bf3-d1 Rb5-b8 Bd1-b3 Rb8-b5 g2-g3 h7-h5 Bb3-d1 h5-h4 g3xh4
g5xh4 Bd1-b3 Rb5-b8 Bb3xd5 Rb8-b5 Bd5-h1 Rb5-g5 Bh1-f3 Rg5-g3 Bf3-g4 Kd6-c6
Kd4-c4 Rg3-g1 Bg4-f3+ Kc6-c7 Bf3-e4 Rg1-g3 Nd3-f4 Kc7-d6 Kc4-d4 Rg3-g8
b4-b5 Rg8-g3 b5-b6 Rg3-b3 b6-b7 Kd6-c7 Kd4-c5 Rb3-c3+ Kc5-b4) -2.73/32 5}
36. Nd3 {(Nc5-d3 Rb8-b5 Bf3-d1 Rb5-b8 Bd1-b3 Rb8-b5 g2-g3 h7-h5 h3-h4 g5xh4
g3xh4 Rb5-b8 Bb3xd5 Rb8-b5 Bd5-f3 Rb5-b8 Bf3-e4 Rb8-g8 Nd3-e5 Rg8-b8
Ne5-c4+ Kd6-d7 Kd4-c5 Rb8-c8+ Kc5-d5 Rc8-f8 b4-b5 Rf8-f4 b5-b6 Rf4xh4
Nc4-d6 Rh4-h2 Kd5-c5 Rh2-b2 Nd6-c4) +3.12/25 2} Rb5 {(Rb8-b5 Bf3-d1 Rb5-b8
Bd1-b3 Rb8-b5 g2-g3 h7-h5 Bb3-d1 h5-h4 g3xh4 g5xh4 Bd1-b3 Rb5-b8 Bb3xd5
Rb8-b5 Bd5-e4 Rb5-g5 Be4-f3 Rg5-g3 Bf3-g4 Kd6-c6 Nd3-f4 Rg3-g1 Bg4-f3+
Kc6-d6 Nf4-e2 Rg1-b1 Kd4-c4 Rb1-f1 Bf3-e4 Rf1-e1 Ne2-c3 Re1-e3 Be4-f5
Re3-f3 Nc3-b5+ Kd6-e5 Bf5-g4 Rf3-f1) -2.48/33 5} 37. Bd1 {(Bf3-d1 Rb5-b8
Bd1-b3 Rb8-b5 g2-g3 h7-h5 h3-h4 g5xh4 g3xh4 Rb5-b7 Bb3xd5 Rb7-b8 Bd5-e4
Kd6-c7 Be4-g6 Kc7-d6 Kd4-e4 Rb8-h8 Ke4-f5 Kd6-d5 Nd3-f4+ Kd5-d4 Bg6xh5
Rh8-b8 Bh5-f7 Rb8xb4 h4-h5 Rb4-b5+ Bf7-d5 Rb5-b2 Kf5-g5 Rb2-h2 Bd5-f3
Kd4-e3 Bf3-g4 Ke3-f2) +3.23/30 7} Rb8 {(Rb5-b8 Bd1-g4 Rb8-b6 Bg4-f3 Rb6-b5
Bf3-e2 Rb5-b6 Be2-g4 Rb6-b8 Bg4-d1 Rb8-b6 Bd1-b3 Rb6-b5 g2-g3 h7-h5 Bb3-d1
h5-h4 g3xh4 g5xh4 Bd1-b3 Rb5-b8 Bb3xd5 Rb8-b5 Bd5-f3 Rb5-b8 Bf3-g4 Rb8-b7
Kd4-c4 Rb7-c7+ Nd3-c5 Rc7-f7 Kc4-b5 Rf7-f8 Nc5-e6 Rf8-b8+ Kb5-c4 Rb8-c8+
Kc4-b3 Rc8-e8 Ne6-g7 Re8-e3+ Kb3-c4) -2.38/31 6} 38. Bb3 {(Bd1-b3 Rb8-b5
g2-g3 h7-h5 h3-h4 g5xh4 g3xh4 Rb5-b7 Bb3xd5 Rb7-b6 Bd5-c4 Rb6-b8 b4-b5
Rb8-f8 Bc4-d5 Rf8-f5 Bd5-c6 Kd6-c7 Nd3-e5 Kc7-b6 Ne5-c4+ Kb6-c7 Bc6-d5
Rf5-f4+ Kd4-c5 Rf4xh4 b5-b6+ Kc7-c8 Kc5-d6 Rh4-d4 Nc4-e5 Rd4-b4 Kd6-c6
h5-h4 Bd5-e6+ Kc8-d8) +3.37/26 3} Rb5 {(Rb8-b5 g2-g3 h7-h5 Bb3-d1 Rb5-b8
Bd1-f3 Rb8-f8 Bf3xd5 Rf8-f1 b4-b5 Rf1-b1 Bd5-c6 Rb1-b3 Kd4-c4 Rb3-a3 Nd3-c5
Kd6-c7 Nc5-e4 h5-h4 g3xh4 g5xh4 Ne4-c3 Ra3-a1 Bc6-d5 Ra1-g1 Bd5-e4 Rg1-g3
Nc3-a4 Rg3xh3 b5-b6+ Kc7-d6 b6-b7 Kd6-c7 Na4-c5 Rh3-a3 Kc4-b5) -2.84/32 25}
39. Bd1 {(Bb3-d1 Rb5-b8 Bd1-b3 Rb8-b5 g2-g3 h7-h5 h3-h4 g5xh4 g3xh4 Rb5-b7
Bb3xd5 Rb7-b5 Bd5-f3 Rb5-b8 Bf3-e4 Rb8-h8 b4-b5 Rh8-b8 Kd4-c4 Rb8-c8+
Kc4-b4 Rc8-e8 Nd3-f2 Re8-f8 Nf2-h3 Kd6-c7 Kb4-c5 Kc7-b8 b5-b6 Rf8-f1 Kc5-b5
Rf1-e1 Nh3-g5 Re1-e2 Be4-d5 Re2-b2+ Kb5-c5 Rb2-h2 Ng5-e4 Rh2xh4 Ne4-f6)
+3.32/31 18} Rb6 {(Rb5-b6 Bd1-b3 Rb6-b5 g2-g3 h7-h5 Bb3-d1 Rb5-b8 Bd1-f3
Rb8-f8 Bf3xd5 Rf8-f1 b4-b5 Rf1-b1 Bd5-c6 Rb1-b3 Kd4-c4 Rb3-a3 Nd3-c5 Kd6-c7
Nc5-e4 h5-h4 g3xh4 g5xh4 Ne4-c3 Ra3-a1 Bc6-f3 Ra1-c1 Kc4-b4 Rc1-f1 Bf3-e4
Rf1-e1 Kb4-c4 Kc7-b6 Nc3-d5+ Kb6-b7 Be4-d3 Re1-c1+ Nd5-c3) -2.81/31 8} 40.
Bb3 {(Bd1-b3 Rb6-b5 g2-g3 h7-h5 h3-h4 g5xh4 g3xh4 Rb5-b7 Bb3xd5 Rb7-b5
Bd5-f3 Rb5-b8 Bf3-e4 Rb8-h8 b4-b5 Rh8-b8 Kd4-c4 Rb8-e8 Nd3-f2 Re8-f8 Nf2-h3
Kd6-c7 Kc4-c5 Rf8-f1 b5-b6+ Kc7-c8 Kc5-b5 Rf1-f6 Be4-d5 Rf6-f1 Nh3-g5
Rf1-b1+ Kb5-c6 Rb1-c1+ Kc6-d6 Rc1-b1 b6-b7+ Kc8-b8 Ng5-e4 Rb1-b6+ Bd5-c6
Rb6-b1 Ne4-c5) +3.37/29 3} Rb5 {(Rb6-b5 g2-g3 h7-h5 Bb3-d1 Rb5-b7 Bd1xh5
Rb7-h7 Bh5-g4 Rh7-f7 Bg4-e2 Rf7-c7 Nd3-c5 Rc7-f7 Be2-d1 Rf7-f1 Bd1-b3
Rf1-b1 Bb3xd5 Rb1xb4+ Bd5-c4 Kd6-e7 Nc5-e4 g5-g4 h3-h4 Ke7-f8 Ne4-d6 Kf8-g7
Kd4-e5 Rb4-b6 Bc4-e6 Kg7-g6 Be6xg4) -3.24/28 10} 41. g3 {(g2-g3 h7-h5 h3-h4
g5xh4 g3xh4 Rb5-b7 Bb3xd5 Rb7-b8 Bd5-e4 Rb8-h8 b4-b5 Rh8-b8 Kd4-c4 Rb8-e8
Nd3-f2 Re8-f8 Nf2-h3 Rf8-c8+ Kc4-b4 Kd6-c7 Nh3-f4 Rc8-g8 Nf4-d5+ Kc7-d6
Nd5-e3 Kd6-e5 Be4-c6 Ke5-d4 Ne3-f5+ Kd4-e5 Nf5-h6 Rg8-g1 b5-b6) +3.61/27 3}
h5 {(h7-h5 Bb3-d1 Rb5-b7 Bd1-f3 Rb7-f7 Bf3xd5 Rf7-f1 b4-b5 Rf1-b1 Bd5-c6
Rb1-b3 Kd4-c4 Rb3-a3 Nd3-c5 Kd6-c7 Nc5-e4 h5-h4 g3xh4 g5xh4 Ne4-c3 Ra3-a1
Kc4-c5 Ra1-c1 b5-b6+ Kc7-b8 Kc5-b4 Rc1-c2 Bc6-d5 Rc2-d2 Bd5-e4 Rd2-b2+
Kb4-a5 Kb8-c8) -3.28/28 9} 42. h4 {(h3-h4 g5xh4 g3xh4 Rb5-b7 Bb3xd5 Rb7-b6
Bd5-c4 Rb6-b8 b4-b5 Rb8-f8 Bc4-d5 Rf8-b8 Bd5-c6 Rb8-f8 Bc6-e4 Rf8-b8 Kd4-c4
Rb8-e8 Nd3-f2 Re8-f8 Nf2-h3 Rf8-c8+ Kc4-b4 Kd6-c7 Kb4-a5 Kc7-b8 b5-b6
Rc8-c3 Nh3-g5 Rc3-c5+ Ka5-b4 Rc5-e5 Kb4-c4 Kb8-c8 Be4-d5 Re5-e1 Kc4-c5
Re1-c1+ Kc5-d6 Rc1-b1 b6-b7+ Kc8-b8) +3.76/29 4} gxh4 {(g5xh4 g3xh4 Rb5-b8
Bb3xd5 Rb8-f8 Bd5-e4 Rf8-b8 Be4-f3 Rb8-f8 Bf3-d5 Rf8-f1 Bd5-e4 Rf1-a1
Nd3-b2 Ra1-f1 Kd4-e3 Kd6-c7 Nb2-c4 Rf1-c1 Ke3-d4 Rc1-g1 b4-b5 Rg1-g4 b5-b6+
Kc7-c8 Nc4-d6+ Kc8-b8 Nd6-f5 Rg4-g6 b6-b7 Rg6-g8 Kd4-e5 Rg8-g4 Be4-d5
Rg4-a4 Bd5-f3) -2.87/23 1} 43. gxh4 {(g3xh4 Rb5-b7 Bb3xd5 Rb7-b6 Bd5-c4
Rb6-b8 b4-b5 Rb8-f8 Bc4-d5 Rf8-b8 Bd5-c6 Rb8-f8 Bc6-e4 Rf8-b8 Kd4-c4 Rb8-e8
Nd3-f2 Re8-f8 Nf2-h3 Rf8-c8+ Kc4-b4 Kd6-c7 Nh3-f4 Rc8-e8 Nf4-d5+ Kc7-c8
Be4-f3 Re8-e1 Nd5-b6+ Kc8-d8 Bf3-c6 Re1-c1 Nb6-c4 Rc1-f1 b5-b6 Rf1-f4
Kb4-c5 Rf4xh4 Nc4-e5 Rh4-h2) +3.86/29 3} Rb8 {(Rb5-b8 Bb3xd5 Rb8-b6 Bd5-f3
Rb6-b5 Kd4-c4 Rb5-f5 Bf3-e4 Rf5-f1 b4-b5 Rf1-b1 Nd3-b4 Rb1-e1 Kc4-d4 Kd6-c7
Nb4-d5+ Kc7-b8 Nd5-f4 Kb8-c7 Nf4xh5 Re1-f1 Kd4-e5 Kc7-b6 Nh5-f4 Rf1-c1
Be4-c6) -3.26/26 6} 44. Bxd5 {(Bb3xd5 Rb8-b5 Bd5-f3 Rb5-b8 Bf3-e4 Rb8-g8
b4-b5 Rg8-b8 Kd4-c4 Rb8-e8 Nd3-f2 Re8-f8 Nf2-h3 Rf8-c8+ Kc4-b4 Rc8-b8
Nh3-g5 Rb8-f8 b5-b6 Rf8-f2 Kb4-b3 Rf2-f6 Kb3-c4 Rf6-f2 Be4-d5 Rf2-c2+
Kc4-b3 Rc2-c1 Bd5-e4 Rc1-e1 Kb3-b4 Kd6-d7 Kb4-b5 Kd7-c8 Be4-d5 Re1-b1+
Kb5-c6 Rb1-c1+ Kc6-d6 Rc1-b1 b6-b7+ Kc8-b8 Ng5-e4) +4.06/30 7} Rb6 {(Rb8-b6
Bd5-f3 Rb6-b8 Bf3-e4 Rb8-g8 b4-b5 Rg8-b8 Kd4-c4 Rb8-e8 Nd3-f2 Re8-f8 Nf2-h3
Kd6-c7 Kc4-c5 Rf8-f1 b5-b6+ Kc7-b8 Kc5-b5 Rf1-d1 Kb5-c4 Rd1-c1+ Kc4-b4
Rc1-f1 Kb4-c5 Rf1-c1+ Kc5-d6 Rc1-d1+ Kd6-e5 Rd1-a1 Nh3-g5) -3.21/28 5} 45.
Bc4 {(Bd5-c4 Rb6-b8 b4-b5 Rb8-e8 Bc4-d5 Re8-b8 Bd5-c6 Rb8-f8 Bc6-e4 Rf8-b8
Kd4-c4 Rb8-e8 Nd3-f2 Re8-f8 Nf2-h3 Rf8-c8+ Kc4-b4 Rc8-c1 b5-b6 Rc1-e1
Nh3-g5 Re1-e2 Kb4-c3 Re2-e3+ Kc3-c4 Re3-e2 b6-b7 Re2-b2 Be4-d5 Rb2-b1
Ng5-e4+ Kd6-c7 Ne4-c5 Rb1-a1 Nc5-d7 Ra1-b1 b7-b8Q+ Rb1xb8 Nd7xb8 Kc7xb8
Kc4-d4 Kb8-c7 Kd4-e5 Kc7-d8) +4.36/32 12} Rb8 {(Rb6-b8 Bc4-d5 Rb8-b6 Bd5-f3
Rb6-b8 Bf3-e4 Rb8-g8 b4-b5 Rg8-b8 Kd4-c4 Rb8-e8 Nd3-f2 Re8-f8 Nf2-h3 Rf8-f1
b5-b6 Rf1-c1+ Kc4-b4 Rc1-e1 Nh3-g5 Re1-e2 Kb4-b3 Re2-e3+ Kb3-c4 Re3-e2
Be4-d5 Re2-c2+ Kc4-b3 Rc2-c1 Bd5-e4 Rc1-e1 Ng5-f7+ Kd6-d7 Nf7-e5+ Kd7-d6
b6-b7 Re1-e3+ Kb3-c2 Kd6-c7 Ne5-d7) -4.02/31 15} 46. b5 {(b4-b5 Rb8-e8
Bc4-d5 Re8-b8 Bd5-c6 Rb8-f8 Bc6-e4 Rf8-b8 Kd4-c4 Rb8-e8 Nd3-f2 Re8-f8
Nf2-h3 Rf8-c8+ Kc4-b4 Rc8-c1 b5-b6 Rc1-e1 Nh3-g5 Re1-e2 Kb4-c3 Re2-e3+
Kc3-c4 Re3-e2 b6-b7 Re2-b2 Be4-d5 Rb2-b1 Ng5-e4+ Kd6-c7 Ne4-c5 Rb1-a1
Nc5-d7 Ra1-b1 b7-b8Q+ Rb1xb8 Nd7xb8 Kc7xb8 Kc4-d4 Kb8-c7 Kd4-e5 Kc7-d8
Ke5-f6 Kd8-e8 Kf6-f5 Ke8-f8 Kf5-g6 Kf8-e7 Bd5-f7 Ke7-f8) +4.39/30 2} Rf8
{(Rb8-f8 Bc4-d5 Rf8-f5 Bd5-c6 Rf5-f8 Bc6-e4 Rf8-b8 Kd4-c4 Rb8-e8 Nd3-f2
Re8-f8 Nf2-h3 Rf8-f1 b5-b6 Rf1-c1+ Kc4-b4 Rc1-f1 Nh3-g5 Rf1-f8 b6-b7 Rf8-e8
Kb4-c4 Kd6-c7 Kc4-c5 Kc7-b8 Kc5-d6 Re8-d8+ Kd6-e5 Rd8-d2 Ng5-e6) -4.16/26
2} 47. Bd5 {(Bc4-d5 Rf8-f5 Bd5-c6 Rf5-f8 Bc6-e4 Rf8-b8 Kd4-c4 Rb8-e8 Nd3-f2
Re8-f8 Nf2-h3 Kd6-c7 Kc4-c5 Rf8-f1 b5-b6+ Kc7-b8 Kc5-b5 Rf1-d1 Nh3-g5
Rd1-d4 Kb5-c5 Rd4-a4 b6-b7 Ra4-a6 Be4-c6 Ra6-a2 Ng5-e6 Ra2-d2 Bc6-d5 Kb8-a7
Kc5-c6 Rd2xd5 Kc6xd5 Ka7xb7 Ne6-c5+ Kb7-c7 Nc5-e4 Kc7-d8 Kd5-d6) +4.62/30
4} Rb8 {(Rf8-b8 Bd5-c6 Rb8-f8 Bc6-e4 Rf8-b8 Kd4-c4 Rb8-e8 Nd3-f2 Re8-f8
Nf2-h3 Rf8-b8 Nh3-g5 Rb8-f8 b5-b6 Rf8-f2 Kc4-c3 Rf2-f8 b6-b7 Rf8-e8 Kc3-c4
Kd6-c7 Kc4-c5 Re8-e7 Be4-d5 Kc7-b8 Kc5-d6 Re7xb7 Bd5xb7 Kb8xb7 Ng5-e6
Kb7-c8 Ne6-f4 Kc8-d8 Nf4xh5 Kd8-e8 Kd6-e5 Ke8-f7 Ke5-f5 Kf7-f8) -4.56/29 6}
48. Bc6 {(Bd5-c6 Rb8-f8 Bc6-e4 Rf8-b8 Kd4-c4 Rb8-e8 Nd3-f2 Re8-f8 Nf2-h3
Kd6-e5 Nh3-g5 Ke5-d6 b5-b6 Rf8-f2 b6-b7 Rf2-b2 Be4-d5 Rb2-b1 Ng5-e4+ Kd6-c7
Ne4-c5 Rb1-a1 Bd5-e4 Ra1-a2 Nc5-e6+ Kc7-b8 Kc4-c5 Ra2-e2 Kc5-d4 Re2-h2
Ne6-c5 Kb8-a7 Nc5-a6 Rh2-b2 b7-b8Q+ Rb2xb8 Na6xb8 Ka7xb8 Be4-d5) +4.72/29
2} Rf8 {(Rb8-f8 Bc6-e4 Rf8-b8 Kd4-c4 Rb8-e8 Nd3-f2 Re8-f8 Nf2-h3 Rf8-b8
Nh3-g5 Rb8-f8 b5-b6 Rf8-f2 Kc4-c3 Rf2-f8 b6-b7 Rf8-e8 Kc3-b4 Kd6-c7 Kb4-c5
Re8-e7 Be4-d5 Re7-d7 Kc5-d4 Rd7-d6 Kd4-e5 Rd6-b6 Ng5-e6+ Kc7-b8 Ne6-c5
Kb8-c7 b7-b8Q+ Kc7xb8 Nc5-d7+ Kb8-a7 Nd7xb6 Ka7xb6 Bd5-f3 Kb6-a5 Bf3xh5)
-4.61/31 5} 49. Be4 {(Bc6-e4 Rf8-b8 Kd4-c4 Rb8-e8 Nd3-f2 Re8-f8 Nf2-h3
Rf8-f1 b5-b6 Rf1-c1+ Kc4-b4 Rc1-e1 Nh3-g5 Re1-e2 Kb4-c3 Re2-e3+ Kc3-c4
Re3-e2 b6-b7 Re2-b2 Be4-d5 Rb2-b1 Ng5-e4+ Kd6-c7 Ne4-c5 Kc7-b8 Kc4-d4
Kb8-a7 Kd4-e5 Rb1-b6 Nc5-d7 Rb6xb7 Bd5xb7 Ka7xb7 Nd7-f6 Kb7-c6 Nf6xh5
Kc6-d7 Ke5-f5 Kd7-e7 Nh5-f6) +5.00/29 4} Rb8 {(Rf8-b8 Kd4-c4 Rb8-e8 Nd3-f2
Re8-f8 Nf2-h3 Rf8-b8 Nh3-g5 Rb8-f8 b5-b6 Rf8-f2 Kc4-c3 Rf2-f6 b6-b7 Kd6-c7
Kc3-d4 Rf6-b6 Kd4-e5 Rb6-b5+ Be4-d5 Rb5-a5 Ng5-e6+ Kc7-b8 Ke5-d6 Ra5xd5+
Kd6xd5 Kb8xb7 Kd5-c5 Kb7-b8 Kc5-c6 Kb8-a7 Ne6-f4 Ka7-a6 Kc6-c5 Ka6-b7
Nf4xh5 Kb7-c7 Nh5-f6) -4.68/31 2} 50. Kc4 {(Kd4-c4 Rb8-c8+ Kc4-b4 Rc8-e8
Nd3-f2 Re8-f8 Nf2-h3 Kd6-c7 Kb4-c5 Rf8-f1 b5-b6+ Kc7-b8 Kc5-b5 Rf1-d1
Nh3-g5 Rd1-d4 Kb5-c5 Rd4-a4 b6-b7 Ra4-a6 Be4-c6 Ra6-a2 Kc5-d6 Ra2-h2 Bc6-d5
Rh2-b2 Ng5-e6 Rb2-b6+ Bd5-c6 Rb6-b1 Ne6-c5) +5.34/29 6} Re8 {(Rb8-e8 Nd3-f2
Re8-f8 Nf2-h3 Rf8-b8 Nh3-g5 Rb8-f8 b5-b6 Rf8-f2 Kc4-c3 Rf2-f6 b6-b7 Rf6-f8
Kc3-c4 Rf8-e8 Be4-d5 Kd6-c7 Kc4-d4 Kc7-b6 Ng5-e6 Kb6-a7 Kd4-e5 Re8-h8
Ne6-c5 Rh8-d8 Bd5-e4 Rd8-e8+ Ke5-d6 Re8xe4 Nc5xe4 Ka7xb7 Ne4-f6 Kb7-b6
Nf6xh5 Kb6-a6 Nh5-f4 Ka6-a5) -4.78/30 3} 51. Bh1 {(Be4-h1 Re8-g8 b5-b6
Rg8-g4+ Kc4-b5 Rg4xh4 Bh1-d5 Rh4-h2 Nd3-b4 Rh2-b2 Kb5-c4 Rb2-f2 b6-b7
Rf2-f4+ Kc4-b5 Rf4-f8 Bd5-c6 Kd6-e6 Nb4-a6 h5-h4 b7-b8Q Rf8xb8+ Na6xb8
Ke6-e5 Nb8-d7+ Ke5-f4 Nd7-c5 h4-h3 Nc5-e6+ Kf4-e5 Ne6-g5 Ke5-f5 Ng5-f3
Kf5-f4 Bc6-d5 Kf4-f5 Nf3-d4+ Kf5-e5 Kb5-c4) +7.85/28 5} Rc8+ {(Re8-c8+
Kc4-b4 Rc8-g8 b5-b6 Rg8-g4+ Kb4-b5 Rg4xh4 Bh1-d5 Rh4-h2 Nd3-b4 Rh2-f2 b6-b7
Rf2-f8 Bd5-c6 h5-h4 Nb4-a6 Kd6-e7 b7-b8Q Rf8xb8+ Na6xb8 h4-h3 Nb8-d7 Ke7-e6
Nd7-c5+ Ke6-f6 Bc6-e4 Kf6-g5 Nc5-d3 Kg5-g4 Be4-c6 Kg4-h4 Kb5-c4 Kh4-g5
Bc6-e4 h3-h2 Kc4-b3 Kg5-g4 Be4-h1 Kg4-g3 Nd3-e5) -7.62/28 10} 52. Kb4
{(Kc4-b4 Rc8-g8 b5-b6 Rg8-g4+ Kb4-b5 Rg4xh4 Bh1-d5 Rh4-h2 Nd3-b4 Rh2-b2
Kb5-c4 Rb2-f2 b6-b7 Rf2-f4+ Kc4-b5 Rf4-f8 Bd5-c6 Kd6-e6 Nb4-a6 h5-h4 b7-b8Q
Rf8xb8+ Na6xb8 Ke6-e5 Nb8-d7+ Ke5-f4 Nd7-c5 h4-h3 Nc5-e6+ Kf4-g4 Ne6-d4
Kg4-f4 Bc6-f3 h3-h2 Bf3-h1 Kf4-g3 Nd4-f3 Kg3-f2 Kb5-c6 Kf2-g3 Kc6-b6)
+7.87/28 2} Ke6 {(Kd6-e6 b5-b6 Ke6-f5 b6-b7 Rc8-b8 Nd3-c5 Kf5-g4 Nc5-d7
Rb8-h8 b7-b8Q Rh8xb8+ Nd7xb8 Kg4xh4 Nb8-c6 Kh4-g5 Bh1-d5 Kg5-f5 Kb4-b5
Kf5-f6 Nc6-b4 Kf6-g7 Nb4-a6 Kg7-f6 Na6-c5 h5-h4 Nc5-a6 h4-h3 Na6-c5 h3-h2
Nc5-b3) -7.62/26 1} 53. Be4 {(Bh1-e4 Ke6-d6 b5-b6 Rc8-c2 Be4-d5 Rc2-c8
Bd5-h1 Rc8-g8 Kb4-b5 Kd6-e6 Bh1-e4 Rg8-e8 Kb5-c5 Re8-c8+ Kc5-b4 Ke6-f6
b6-b7 Rc8-b8 Kb4-b5 Rb8-g8 Nd3-c5 Kf6-e5 Be4-c6 Rg8-b8 Nc5-d7+ Ke5-d6
Nd7xb8) +9.67/26 4} Rb8 {(Rc8-b8 Nd3-c5+) -11.73/27 15} 54. Ka5 {(Kb4-a5
Rb8-f8 b5-b6 Ke6-f6 b6-b7 Rf8-e8 Ka5-b6 Kf6-g7 Kb6-a7 Re8-e7 Ka7-a8 Re7xe4
b7-b8Q Re4-e7 Qb8-g3+ Kg7-h7 Qg3-g5 Re7-g7 Qg5xh5+ Kh7-g8 Nd3-e5 Rg7-g2
Qh5-f7+ Kg8-h8) +11.19/22 2} Kd6 {(Ke6-d6 b5-b6 Rb8-e8 Be4-h1 Kd6-e6 Bh1-c6
Re8-f8 Bc6-e4 Ke6-d6 Ka5-b5 Rf8-e8 Nd3-c5 Kd6-e5 Be4-c6 Re8-h8 b6-b7 Ke5-f4
Nc5-a6 Rh8-d8 Bc6-d7 Rd8xd7 b7-b8Q+ Kf4-f3 Qb8-e5 Rd7-d3 Qe5xh5+ Kf3-f4
Qh5-f7+ Kf4-e3 Qf7-g6 Rd3-d2 Qg6-g5+ Ke3-d3 Qg5-e5) -11.81/21 1} 55. b6
{(b5-b6 Rb8-e8 Be4-h1 Kd6-e6 Bh1-c6 Re8-d8 Bc6-e4 Rd8-h8 b6-b7 Rh8-e8
Ka5-b6 Ke6-f7 Nd3-c5 Kf7-e7 Be4-f3 Re8-f8 Kb6-c7 Rf8xf3 b7-b8Q Rf3-f8
Qb8-b7 Rf8-f7 Kc7-b6+ Ke7-f8) +12.59/21 2} Re8 {(Rb8-e8 Be4-h1 Kd6-e6
Bh1-c6 Re8-b8 Bc6-e4 Rb8-g8 Ka5-b4 Ke6-d6 Kb4-b5 Rg8-e8 Nd3-c5 Kd6-e5
Be4-c6 Re8-h8 b6-b7 Ke5-f4 Nc5-a6 Rh8-d8 Kb5-c5 Kf4-g3 Bc6-d5 Kg3xh4 Bd5-e6
Kh4-g3 Be6-c8 Kg3-f3 b7-b8Q Rd8-d2 Kc5-b5 h5-h4 Na6-b4 Kf3-e4 Qb8-b7+
Ke4-d4 Qb7-g7+ Kd4-e4 Qg7-g4+ Ke4-e5) -14.56/25 8} 56. Bh1 {(Be4-h1 Kd6-e6
Bh1-c6 Re8-d8 Bc6-e4 Rd8-e8 b6-b7 Ke6-f6 Ka5-b5 Re8-h8 Kb5-b6 Rh8-e8 Kb6-a7
Re8-e7 Be4-c6 Kf6-f5 Bc6-f3 Re7-d7 Bf3-e4+ Kf5-f6 Ka7-b6 Rd7-d6+ Kb6-c7
Rd6-d4 b7-b8Q Rd4-c4+ Be4-c6 Rc4xh4 Qb8-d8+ Kf6-g7 Qd8-g5+ Kg7-f7 Qg5xh4)
+20.11/25 16} Ke6 {(Kd6-e6 Bh1-c6 Re8-b8 Bc6-e4 Ke6-d6 b6-b7 Rb8-e8 Be4-h1
Kd6-e6 Bh1-c6 Re8-b8 Bc6-e4 Ke6-f7 Ka5-b6 Kf7-f8 Nd3-c5 Kf8-f7 Kb6-b5
Rb8-h8 Nc5-d7 Kf7-e6 b7-b8Q Rh8xb8+ Nd7xb8 Ke6-e5 Be4-f3 Ke5-f4 Bf3xh5
Kf4-g3 Kb5-c5) -49.08/25 44} 57. Bc6 {(Bh1-c6 Re8-b8 Bc6-e4 Rb8-h8 b6-b7
Rh8-e8 Ka5-b5 Ke6-f6 Kb5-b6 Kf6-g7 Nd3-c5 Kg7-h6 Kb6-b5 Re8-f8 Nc5-a6
Rf8-f2 b7-b8Q Rf2-b2+ Kb5-c4 Rb2xb8 Na6xb8 Kh6-g7 Be4-d5 Kg7-f6 Kc4-b5)
+43.60/23 7} Rg8 {(Re8-g8 Bc6-e4 Ke6-d6 b6-b7 Kd6-c7 Nd3-c5 Kc7-d6 Nc5-a6
Kd6-e5 Be4-f3 Ke5-f4 Bf3xh5 Kf4-g3 b7-b8Q+ Rg8xb8 Na6xb8 Kg3xh4 Bh5-e2
Kh4-g3 Ka5-b5 Kg3-f4 Be2-d3 Kf4-g5 Kb5-c4 Kg5-h6 Kc4-d5 Kh6-g7 Kd5-e5
Kg7-h8 Ke5-f6 Kh8-g8 Bd3-e2 Kg8-h8 Nb8-c6 Kh8-g8 Be2-f3) -49.23/27 17 Black
resigns} *[\pgn][/pgn]

[lkaufman]

With no minor pieces on the board and an average number of pawns (five per side), two rooks are nearly a pawn better than the queen. But on a full board the queen is indeed better than two rooks, as GM Roman Dzindzichashvilli taught me before computers were strong enough to answer the question. On average thruout the game the queen is a bit weaker.

[Nordlandia]

With no minor pieces on the board and an average number of pawns (five per side), two rooks are nearly a pawn better than the queen. But on a full board the queen is indeed better than two rooks, as GM Roman Dzindzichashvilli taught me before computers were strong enough to answer the question. On average thruout the game the queen is a bit weaker.

Maybe "reinfeld values" need to be renewed for engine play. Reinfeld values is still good enough for human play i suppose.

[Dann Corbit]

One problem in this thread is data.
You can't prove a point based on a single game.
You can't prove a point based on a hundred games.
You have a bit of probability in your favor after a thousand games.

Here is what Stockfish says about the value of chessmen (note that pawns are not 100) during the midgame and during the endgame:

Code: Select all

    PawnValueMg   = 136,   PawnValueEg   = 208,
    KnightValueMg = 782,   KnightValueEg = 865,
    BishopValueMg = 830,   BishopValueEg = 918,
    RookValueMg   = 1289,  RookValueEg   = 1378,
    QueenValueMg  = 2529,  QueenValueEg  = 2687,

Note that two rooks are 2578 so a bit better than the queen in midgame. But it's close enough where it doesn't matter much.
Note that two rooks are 2756 so significantly better than the queen in the endgame.
It appears that Stockfish's lips are sealed about the value in the opening.

The point totals here are based on careful experiments with lots of games.

I guess that Larry has done a careful calculation too. He did, after all, write the book on imbalances. Literally.

In addition, chessmen can change their values based on special conditions.
Edge pawns are wimps in the opening and tigers in the endgame.
If there is a giant row of locked pawns, I once heard a king moan, "Half my kingdom for a knight!"
So all the generalities have exceptions anyway.

[Nordlandia]

Ceteris paribus, shouldn't the idea about major piece redundancy nullify the two rook advantage in material. After all neither Rook does anything that the other one can't do. Maybe the minus effect is not so apparent for the rooks as compared to two knights and particularly two queens.

[Dann Corbit]

Two rooks have a certain synergy together.
E.g.
One rook on the 7th is good. Two rooks on the 7th rank is savage. Utter devastation is just around the corner.
E.g.
Endgame KRRvk compared to KRvk
Both times the side with rook(s) win, but you can win much faster if the weaker king starts in the center of the board with 2 rooks than with 1.
They are also great for battery (e.g. Alekhine's gun variants).
If you have to have a duplicate of something then a queen would be wanted because of her power.
But if you could not have a queen, I would pick a rook, unless there was a driving reason to pick something else (e.g. one of those kinky knight underpromotion only mates).