Material Imbalances - Queen vs. Two Rooks Part One

Sun, 2015-02-22 16:59 -- IM Max Illingworth

One of the most misunderstood elements of chess is that of the material imbalance – this is where each side has different pieces on the board. Of course, we don’t have to concern ourselves with the gigantic material imbalance of being a queen up for nothing, but many players avoid the opportunity to enter positions with a (on the pawn = 1, knight = 3.25, bishop = 3.5, rook = 5, queen = 9.75 material values) near-equal material imbalance. This can mainly be attributed to fear of the unknown (as there aren’t so many articles or books on this subject).

In this first part of my Material Imbalances series, I will address the material imbalance of queen vs. two rooks. I’ll focus on positions with just the queen vs. two rooks to minimise other, possibly extraneous factors, though I will deal with how the addition of other pieces influence the queen vs. two rooks imbalance at the end of the post.
The first point to note is that, while the two rooks are, materially speaking, better than the queen (10 points vs. 9.75), in many cases the rooks are not properly coordinated on reaching the queen vs. two rooks position and that often allows the queen to wreak havoc right away:

[Event "England sim"]
[Site "England"]
[Date "1822.??.??"]
[Round "?"]
[White "Cochrane, John"]
[Black "NN"]
[Result "1-0"]
[ECO "C53"]
[Annotator "Illingworth,Max"]
[PlyCount "59"]
[EventDate "1822.??.??"]
[EventRounds "1"]
[EventCountry "ENG"]
[Source "ChessBase"]
[SourceDate "1998.11.10"]

1. e4 e5 2. Nf3 Nc6 3. Bc4 Bc5 4. c3 Qe7 5. O-O d6 6. Kh1 Nf6 7. d4 Bb6 8. Bg5
Bg4 9. h3 Bxf3 10. Qxf3 exd4 11. Bd5 Ne5 12. Bxf6 gxf6 13. Qf5 c6 14. Bb3 Nd3
15. Nd2 dxc3 16. bxc3 Nc5 17. Nc4 Nxb3 18. axb3 Bc7 19. f4 Qe6 20. Qh5 Kd7 21.
e5 d5 22. f5 Qe8 23. e6+ fxe6 24. fxe6+ Qxe6 25. Rae1 Be5 26. Nxe5+ fxe5 27.
Rxe5 Raf8 28. Rxe6 Rxf1+ 29. Kh2 Kxe6 {Black is losing as White can win one of
the rooks right away with} 30. Qe2+ {.} 1-0 

The next game is also fairly simplistic but shows my point about the rooks often needing time to coordinate at first, and how fatal it can be for the side with the queen when they do:

[Event "USA-01.Kongress"]
[Site "New York"]
[Date "1857.10.09"]
[Round "1.4"]
[White "Raphael, Benjamin"]
[Black "Kennicott, Hiram"]
[Result "0-1"]
[ECO "C33"]
[Annotator "Illingworth,Max"]
[PlyCount "85"]
[EventDate "1857.10.05"]
[EventRounds "4"]
[EventCountry "USA"]
[Source "ChessBase"]
[SourceDate "2001.11.25"]

1. e4 e5 2. f4 exf4 3. Bc4 Qh4+ 4. Kf1 g5 5. Nc3 Bg7 6. g3 fxg3 7. Kg2 Qh6 8.
hxg3 Qg6 9. d4 d6 10. Nf3 h6 11. Nd5 Kd8 12. Re1 c6 13. Nc3 Bg4 14. e5 Bxf3+
15. Qxf3 d5 16. Bd3 Qe6 17. Bf5 Qe7 18. Na4 Na6 19. Bd2 b5 20. Nc5 Nxc5 21. Bb4
Bf8 22. Bxc5 Qe8 23. Bd6 Ne7 24. Bh3 Bg7 25. Qa3 a5 26. Qc5 Nc8 27. e6 fxe6 28.
Rxe6 Qd7 29. Rae1 Ra6 30. Re8+ Qxe8 31. Rxe8+ Rxe8 {In this position, with two
sets of minor pieces on the board, White is better despite being material down
as the bishop pair are very strong and Black's pieces are very passive.
However, once the minor pieces are exchanged, it is Black who obtains the
advantage.} 32. Bxc8 $2 (32. Be5 $1 {would be quite strong as White can
continue keeping the a6-rook out of play and generate threats against Black's
king and pawns, e.g.} Bf8 (32... Bxe5 33. dxe5 {gives White the threat of Qf2!,
and} h5 34. Bf5 Kc7 35. Qe3 {is no picnic for Black, who will lose the
kingside pawns and still has his useless knight on c8.}) 33. Qc3 Nd6 34. Qf3
Ra7 35. Qh5 $1 Nc4 36. Qg6 Nxe5 37. dxe5 {and Black is still under a lot of
pressure. You might notice how in these lines, the queen and minor piece
coordinate a lot better than the two rooks and minor piece.}) 32... Kxc8 33.
Be5 $2 {Now things are definitely bad for White as Black will be able to
safeguard his king and get his a6-rook into the game.} ({The unlikely} 33. Be7
$1 Bxd4 34. Qd6 $1 {would still keep the balance.} Rxe7 $5 35. Qxe7 Bxb2 {
might then lead to another material imablance, of queen vs. rook and minor
piece! We'll save that for another time but I'll just point out that} 36. Qe6+
Kb7 37. Qxh6 Ra8 38. Qxg5 Re8 {is not worse for Black, who can construct a
fortress by putting a rook on the 7th rank, a bishop on c3 and a pawn on b4,
for example.}) 33... Bxe5 34. dxe5 Kb7 $1 {Black threatens to take on e5, and
if White does nothing Black will coordinate his rooks with ...Raa8, ...Re6 and
...Rae8, destroying the e5-pawn.} 35. Qd6 Kb6 36. Qxh6 $2 {This move gives
Black time to get his a6-rook into play, which could have been very pricey.} (
36. Qd7 $1 Raa8 37. e6 {still leaves Black with some problems coordinating his
rooks, and should hold the draw.}) 36... Rxe5 $2 {In this position, the
material is less important than piece coordination:} (36... Ra7 $1 37. Qxg5
Rae7 38. Qe3+ Kb7 39. g4 Rxe5 40. Qc5 {and the White queen is powerless
against the rooks now that the position is fixed and Black's rooks are solidly
placed:} Rg8 41. Kf3 Re4 {and the passed pawn is destroyed, just like that.
After this the win will be a matter of technique as Black will be effectively
two pawns ahead (the two rooks are way, way better than the queen when the
remaining pawns are on one side of the board, with no minor pieces).}) 37. Kf3
$2 {A complete waste of a move.} (37. Qf6 $1 Re2+ 38. Kf1 Rxc2 39. Qd8+ {would
end in a draw by perpetual check. Trying to avoid it with} Kc5 40. Qe7+ Kc4 $6
{would lose the rook to} 41. Qb7 {, though incredibly Black can still draw with
} g4 $3 42. Qxa6 Kd3 $1 {when there's no way to avoid the ...Rc1-c2 perpetual
checking net.}) 37... Ra7 $1 {Now with an extra pawn as well, the win is a
piece of cake.} 38. Qd6 Rae7 (38... Re8 {first was better, avoiding checks
from the back.}) 39. c3 (39. Qb8+ Kc5 40. Kg4 {was a more tenacious defence.})
39... a4 (39... Re4 $1) 40. Qd8+ Kc5 {In fact the king is very safe on c5,
shielded by the pawns and rooks.} 41. b3 axb3 42. axb3 Re4 43. Qh8 {White
resigned rather than count the moves to mate with 43...g4.} 0-1 

What about when both sides have passed pawns? Are the rooks or queen stronger then? The correct answer is that it depends on the position – mainly how secure the rooks are (not to mention whether the king can avoid perpetual check from the queen). The following example shows that even two rooks and a pawn may not be as good as a queen if the rooks can’t coordinate in time:

[Event "Leipzig m 8990"]
[Site "Leipzig"]
[Date "1889.??.??"]
[Round "4"]
[White "Mieses, Jacques"]
[Black "Lasker, Emanuel"]
[Result "0-1"]
[ECO "C25"]
[Annotator "Illingworth,Max"]
[PlyCount "86"]
[EventDate "1889.??.??"]
[EventRounds "8"]
[EventCountry "GER"]
[Source "ChessBase"]
[SourceDate "1999.07.01"]

1. e4 e5 2. Nc3 Bc5 3. g3 Nc6 4. Bg2 a6 5. d3 d6 6. Nge2 Nge7 7. Nd5 O-O 8. O-O
Be6 9. Kh1 Qd7 10. Nxe7+ Nxe7 11. f4 Bh3 12. Bxh3 Qxh3 13. f5 Qh5 14. f6 gxf6
15. Rxf6 Kh8 16. Qf1 Ng8 17. Rf5 Qg6 18. Qf3 f6 19. Bd2 Ne7 20. Rh5 f5 21. Rf1
Qg8 22. exf5 d5 23. Bh6 Rf7 24. Rg5 Qe8 25. Qg4 Ng6 26. Re1 Ne7 27. Bg7+ Rxg7
28. Rxg7 Qf8 29. Rg5 Ng8 30. Nc3 Nf6 31. Qf3 Qd6 32. Nd1 Re8 33. Nf2 e4 34. Qe2
Qc6 35. dxe4 $4 (35. Ng4 $1 exd3 36. Nh6 $1 {threatening Nf7 mate was the only
way to retain a winning advantage. And if} Qd7 $2 37. Qxe8+ $1 {spectacularly
forces mate.}) 35... Nxe4 {Now it is Black who is winning!} 36. Nd3 ({Even
more brutal is} 36. Nxe4 Rxe4 37. Qf1 Rxe1 38. Qxe1 d4+ 39. Kg1 d3+) 36... Nf2+
37. Nxf2 Rxe2 38. Rxe2 Bxf2 39. Rxf2 {Perhaps Mieses saw to here and thought
he was just winning with the plan of f6-f7-f8=Q, but the best players continue
pushing ahead in their analysis where others stop, and Black claimed the full
point with a nice tactic:} d4+ 40. Kg1 ({or} 40. Rg2 d3 $1) 40... d3 $1 {The
problem for White is that he can't defend against ...dxc2 by taking on d3 as
then ...Qc1 picks up the rook on g5. If you put that rook on just about any
other square, White would be winning.} 41. c3 (41. f6 dxc2 42. Rxc2 Qxc2 43. f7
{was the best try, although with} Qb1+ 44. Kg2 Qxb2+ 45. Kh3 Qg7 $1 {Black
transitions into a won pawn endgame.}) 41... Qe4 $1 {Now the passed d-pawn
will be faster, and a queen and pawn definitely beats a lone defending rook.}
42. h4 (42. f6 d2 $1 {is the key point: either Black will queen with check or
win both rooks with} 43. Rxd2 Qe1+ 44. Kg2 Qxd2+ 45. Kf3 Qxg5 {.}) 42... d2 43.
f6 d1=Q+ {White resigned.} 0-1 

Our next game is perhaps the most famous example of the queen vs. two rooks battle (at least it’s the first one I thought of when this topic was suggested to me). It’s from the first game of the World Championship and shows the queen vs. two rooks imbalance in almost its most pure form (of course, queen vs. two rooks with no pawns on the board is a draw unless one side can win a piece or mate right away):

[Event "World Championship"]
[Site "Brissago"]
[Date "2004.09.25"]
[Round "1"]
[White "Leko, Peter"]
[Black "Kramnik, Vladimir"]
[Result "0-1"]
[ECO "C42"]
[WhiteElo "2741"]
[BlackElo "2770"]
[Annotator "Illingworth,Max"]
[PlyCount "130"]
[EventDate "2004.09.25"]
[EventRounds "14"]
[EventCountry "SUI"]
[Source "ChessBase"]
[SourceDate "2004.11.11"]

1. e4 e5 2. Nf3 Nf6 3. Nxe5 d6 4. Nf3 Nxe4 5. d4 d5 6. Bd3 Nc6 7. O-O Be7 8. c4
Nb4 9. Be2 O-O 10. Nc3 Bf5 11. a3 Nxc3 12. bxc3 Nc6 13. Re1 Re8 14. cxd5 Qxd5
15. Bf4 Rac8 16. h3 Be4 17. Be3 Na5 18. c4 Nxc4 {An interesting simplifying
combination leading to a material imbalance.} 19. Bxc4 Qxc4 20. Nd2 Qd5 21.
Nxe4 Qxe4 22. Bg5 Qxe1+ 23. Qxe1 Bxg5 {I may return to this part of the game
in a later post as it is quite fascinating how Black manages to keep the
balance, but for now I'll just examine the queen vs. two rooks part of the
struggle.} 24. Qa5 Bf6 25. Qxa7 c5 26. Qxb7 Bxd4 27. Ra2 c4 28. Re2 Red8 29. a4
c3 30. Qe4 Bb6 31. Qc2 g6 32. Qb3 Rd6 33. Rc2 Ba5 34. g4 Rd2 35. Kg2 Rcd8 36.
Rxc3 Bxc3 37. Qxc3 {If we count the material using the standard piece values,
White is up 0.75 pawns (queen = 9.75, rook = 5, pawn = 1), but in fact only
Black can win this position as the position is quite fixed and Black can
target White's pawns one by one without running into immediate perpetual check
(as his pawns cover his king). The first task is to win the a-pawn and it is
instructive to see how Kramnik coordinates his rooks to do so.} R2d5 $1 {
Preparing ...Ra8 and ...Rda5.} (37... Ra2 38. Qc6 $1 {stops ...Ra8, after
which it is hard to win the a-pawn as} Rd4 $4 {loses the rook to} 39. Qe8+ Kg7
40. Qe5+ {. Indeed, you might have noticed by now how much better the rooks
coordinate when they defend one another and can avoid forks from the queen.})
38. Qc6 Ra5 {Now there's no way to avoid the loss of the a-pawn, though White
can create enough kingside play to draw if he's careful.} 39. Kg3 Rda8 40. h4
$1 {Absolutely the correct decision, intending h5 to swap more pawns and
thereby get closer to a draw.} R5a6 (40... h6 $5 {is interesting, intending}
41. h5 g5 $1 {like in the game when obviously Qxh6 loses the queen to ...R8a6.
The difference compared to the game is that White can still exchange pawns with
} 42. f4 $1 gxf4+ (42... Rxa4 43. Qxh6 {is also equal.}) 43. Kxf4 R5a6 44. Qc1
Rxa4+ 45. Kg3 {and that proves sufficient for a draw as Black can't bring his
other rook to attack the g4-pawn without running into perpetual checks.}) 41.
Qc1 Ra5 $1 {A very strong practical move to discourage White's intended
kingside counterplay; the automatic} (41... Rxa4 42. h5 {gives White ideas of
h6 and Qb2 to counterattack Black's king, and the alternative} gxh5 43. Qg5+ {
gives White an immediate perpetual check.}) 42. Qh6 $2 {Technically speaking
this doesn't throw away the draw, but it gives Black the chance to press for a
long time with the rooks.} (42. h5 $1 gxh5 43. Qf4 {would maintain the balance
as Black can't take on a4 without allowing perpetual check with Qg5, and} hxg4
44. Qxg4+ Kf8 45. Qb4+ {is the same story.}) 42... Rxa4 43. h5 R4a5 {This
innocent-looking move sets a powerful trap.} 44. Qf4 $2 {And White falls for
it! The problem is that, once the pawns become completely fixed, the rooks
will be way better than the queen and Black will no longer have the problem of
perpetual check that we've seen in some of the earlier variations.} (44. hxg6
hxg6 {is a draw with best play, but White needs to know to place his pawn on
g5 to fix Black's kingside structure. Then after a later f4, the best Black
will be able to do is exchange his two rooks for the queen and f-pawn, and the
resulting king and pawn endgame will be a theoretical draw. If this
explanation doesn't make any sense to you, it will when I delve into this
endgame next week in Part Two.}) 44... g5 $1 45. Qf6 {White is hoping for h6
and Qg7, but Black's move is a silent crusher.} h6 $1 {White can't take the
pawn because of ...R8a6, but otherwise Black will place both his rooks to
attack White's f-pawn, with decisive consequences. It takes a bit of shuffling
but Kramnik gets there in the end.} 46. f3 R5a6 47. Qc3 Ra4 48. Qc6 R8a6 49.
Qe8+ Kg7 {There's nothing White can do to ultimately stop Black's rooks
getting to the f-file, after which the f3-pawn will fall.} 50. Qb5 R4a5 51. Qb4
Rd5 52. Qb3 Rad6 53. Qc4 Rd3 54. Kf2 Ra3 55. Qc5 Ra2+ 56. Kg3 Rf6 {Now the
final part of the plan is to get the other rook around to f4.} 57. Qb4 Raa6 58.
Kg2 Rf4 59. Qb2+ Raf6 60. Qe5 (60. Qc3 Rxf3 61. Qxf3 Rxf3 62. Kxf3 Kf6 63. Ke4
Ke6 {and ... f5 wins the pawn endgame.}) 60... Rxf3 {The rest could be done in
Kramnik's sleep.} 61. Qa1 Rf1 62. Qc3 R1f2+ 63. Kg3 R2f3+ 64. Qxf3 Rxf3+ 65.
Kxf3 Kf6 {A nice piece of endgame technique by the former World Champion.} 0-1 

There’s a lot more to learn about this material imbalance, but let’s recap the basics:
a) Although the rooks are materially worth more than the queen, if the rooks aren’t coordinated properly at the start of the endgame, the queen can swoop around and grab material.
b) The queen is much more competitive with the rooks when minor pieces are thrown into the mix.
c) The rooks, when coordinated, are much stronger than the queens (with no other pieces).
d) The side with the rooks is quite happy to have at least 3 pawns shielding his king from enemy checks (along with the rooks if necessary).
e) When both sides have passed pawns, tactics will determine who comes out on top.
f) A fixed pawn structure is calamitous for the queen as the pawns will just drop off.
I’ll be back next week with more on this interesting material imbalance!