OK, that is not very helpful, except it does highlight the point that, as usual in chess, everything depends on the situation on the board.
Traditionally a rook is given the value of five pawns, and a queen the value of nine pawns, so two rooks, other things being equal, are a pawn better than a queen.
But database computer analysis by IM - now GM - Larry Kaufman found a queen is really worth, on average, 9.75 pawns.
In other words, a queen is more-or-less as valuable as two rooks, so everything really does depend on the game position.
Factors Favouring The Queen
1. Loose pawns. The queen is by far the most mobile chess piece. In effect it is a rook ranging horizontally and vertically, a bishop that can operate on either colour, and a king that attacks every adjacent square. Unprotected pawns are particularly vulnerable to a queen darting about.
2. Exposed enemy king. The player with two rooks is often in trouble if his king is not sheltered behind friendly pawns. This is because the queen can speed around the board even quicker than usual by checking the king to effectively gain a tempo. If all else fails, the player with the queen may be able to bail out to a draw via perpetual check.
3. Play on both sides of the board. The queen's mobility makes it easy to switch threats between wings.
4. Other pieces. The more other pieces there are on the board, the more this tends to favour the queen. This is partly because the queen is equally at home in a middlegame as in an ending, and partly because a queen normally needs a friendly piece to help create mating threats. In this context a knight can be particularly effective.
Factors Favouring The Rooks
1. Pawn chains. A pawn-chain only needs a rook protecting its base for the whole chain to be invulnerable to a queen.
2. Coordination. Rooks grow massively in strength if they are coordinated (another way of putting this is that rooks lose a lot of their combined strength if they are not in touch with each other).
3. Endings. Rooks operate best on open files, whereas in a middlegame a rook may not be worth much more, if anything, than a well-placed minor piece.
4. Bishops. A rook and bishop combine well because there is no redundancy - one operates on ranks and files, the other on diagonals. A queen can also be powerful in combination with a bishop - think of the two of them operating as a battery on a long diagonal - but there is some redundancy as they both run, at least partly, on diagonals.
Here is a game in which the rooks triumph, albeit with a major assist from the clock, despite many of the above factors favouring the queen. I will only lightly annotate the mistake-strewn early stages (before the diagram).
Spanton (164) - Adrian Waldock (142)
Sutton 1996
Sicilian Alapin
1.e4 c5 2.c3 d5 3.exd5 Qxd5 4.d4 Nf6 5.Nf3 Bg4 6.Nbd2!?
Normal is 6.Be2 but the text has been played by Shirov, Tiviakov, Adams and other strong grandmasters.
6...e6 7.Bc4 Qd7 8.Qb3 a6?
Better is 8...Nc6 or 8...cxd4.
9.Ne5 Qc7 10.a4?
10.Qa4+ Nc6 11.Bb5 Rc8 12.Bxc6+ bxc6 13.Nxg4 Nxg4 14.dxc5 Qe5+ 15.Qe4 Bxc5 was roughly level in Alessio Valsecchi (IM 2412) - Joan Fluvià Poyatos (IM 2491), Badalona (Spain) 2013, although White quickly blundered.
Stockfish10 and Komodo10 give 10.Nxg4 Nxg4 11.Ne4 (not 11.Bxe6?? fxe6 12.Qxe6+ Qe7) Be7 (if 11...cxd4, then 12.Bxe6! fxe6 13.Qxe6+ Be7 14.Qxg4 with a strong position) 12.Be2 h5 13.dxc5 with a large advantage for White.
10...Nc6?!
Black should probably preserve the light-square bishop, eg by 10...Bh5.
11.Nxg4 Nxg4 12.Qd1?!
This retreat leaves the bishop on c4 loose and vulnerable.
12...Nf6 13.Nf3?
Better is 13.dxc5 Bxc5 14.Nf3.
13...cxd4 14.0-0
Or 14.cxd4 Rd8 with advantage to Black.
14...Be7?
Black could safely remain a pawn up after 14...dxc3.
15.Qe2?
Correct is 15.Nxd4.
15...0-0?
Again ...dxc3 is safe and good.
16.cxd4 Rac8 17.Rd1 Nb4 18.b3 Nfd5 19.Bb2 Nf4 20.Qe4 Nfd5 21.Rac1 Qd8 22.h4 Nf6 23.Qe2 Nbd5
Black offered a draw.
24.Ne5 g6 25.Re1 Kg7 26.Rcd1 h5 27.Bc1!? Ng8
White is better after 27...Nc3 28.Qe3, but the engines' 27...b5!? seems to favour Black, eg 28.axb5 axb5 29.Bd3 Nc3 30.Qe3 Ng8.
28.Rd3 Bxh4!?
Having twice failed to take a safe pawn, Black now grabs a potentially hot one.
29.Rh3 Bg5 30.Bxg5 Qxg5 31.Rg3 Qh6
Black offered a draw.
32.Nxf7??
Missing how vulnerable the e1 rook is to a skewer.
32...Rxf7 33.Qxe6 Rxc4 34.bxc4 Re7 35.cxd5
Best, both objectively and from a practical view, but Black is completely winning.
35...Rxe6 36.dxe6 Qd2 37.Ree3 Qxd4??
This costs Black his knight. Any other reasonable move is winning.
38.e7 Nxe7 39.Rxe7+ Kf6
 |
| A pure two-rooks versus queen ending. |
40.Rge3
Possible is 40.Rxb7 as 40...Qxa4? 41.Rb6+ is good for White. But 40...Qd1+ 41.Kh2 Qd6 looks dead-drawn, and I presume, bearing in mind the relative grades, I wanted to try to avoid simplification.
40...Qd1+ 41.Re1
Not 41.Kh2?? Qd6+.
41...Qxa4 42.Rxb7 a5
Black offered a draw.
43.Rb6+ Kg5 44.Re5+ Kh6 45.Rbb5 Qd1+ 46.Kh2 a4 47.Ra5 Qg4 48.Re3 Qf4+ 49.Kg1 Qb4 50.Ra8 Qb1+ 51.Kh2 Qb4
Black offered a draw.
52.Ra6 Qb8+ 53.g3 h4!?
Stockfish10 reckons this keeps the draw in hand, but Komodo10 now has White slightly better.
54.Rxa4 hxg3+ 55.Rxg3 Qb6
Black offered a draw.
56.Rh4+ Kg7 57.Rg2
The active 57.Re3 poses more of a challenge to Black, but it seems he should be fine, eg 57...Qf6 58.Kg3 Qd6+ 59.Kg2 Qd5+ 60.Rhe4 Kf6.
57...Qd6+ 58.f4 Qe6 1-0
Black's flag fell as he made his 58th move.
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