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Queen vs Two Rooks
by Arthur E. Holmer
One of the more common, materially unbalanced endings is the queen and pawn(s) vs two rooks and pawn(s) endgame. This ending is inherently difficult to assess due to the large difference in the nature of the queen moves as compared to the rook moves. Most players find this situation uncomfortable and are concerned about finding themselves in a position that leads to quick disaster.
Most beginning players will turn to a section in a chess manual labeled as The Value of the Chessmen, e.g. Alburt, p. 24,1 for help in evaluating these positions. See also Table of Relative Values. This type of section is used to introduce the relative material value of the pieces. The following values are usually given: queen 9 points, rook 5 points, bishop 3 points, knight 3 points and pawn 1 point. The idea is to help players evaluate if an exchange is even, a loss or gain of material. If you use this method to evaluate the queen vs two rooks, you get 9 points for the queen and 10 points for two rooks. This indicates that the rooks are worth slightly more (a pawn) than the queen. To make the material balance, queen and pawn are said to be approximately equal to two rooks and should lead to a draw. It is important to understand that this type of evaluation is just a starting point as the position of the pieces on the board can heavily influence the situation. Let’s look at two examples to show how the board position can change everything.
|Diagram No. 1 - Black to move|
This is position 1096 on page 567 of Reuben Fine’s Basic Chess Endings3 and is attributed to Centurini, 1885. Fine says the position is a draw and gives “After 1. … Kh7 2. Qb1+ Rg6 3. Qf5 Rh8, White can prevent the fatal discovered check: 4. Qf7+ Rg7 5. Qe6 Rg6 6. Qf7+ Kh6 7. Qe7 Rh7 8. Qf8+ Rhg7 9. Qf4+ Kh7 10. Qf5 Kh8 11. Qc8+ Rg8 12. Qc3+ Kh7 13. Qc7+ R6g7 14. Qc2+ Kh8 15. Qc3, etc.” This is an excellent example of how the position is more important than the material count. However, Fine shows how sensitive the outcome is to piece position by giving the following diagram.
|Diagram No. 2 - Black to move|
Fine summarizes the theory for pawn-less positions on page 566 of Basic Chess Endings3, “Without pawns, the game is most often drawn. If the enemy king is confined to the edge of the board, the rooks may win; if the rooks are not adequately defended, the queen may win.” Above is position 1097 on page 5673, also attributed to Centurini, 1885. Fine now says that Black wins after this one square shift in the king position and gives “1. … Rh8 2. Qa2 (he must stop … Kg8+) 2. … Kg6+ wins the queen:3. Kg2 Kf5+ 4. Kf3 Rh3+ 5. Ke2 Rh2+, etc.
It is clear that the queen vs two rooks ending is not so simple and straight forward as it might appear to be. What about the next step, queen and pawn vs two rooks? It turns out that a draw is very common, but things are once again more complicated than expected. The following position, from a study attributed to Mikhail Platov, 1927, is an excellent example of some of the possible complications.
|Diagram No. 3 - White to move and win|
ChessVideos.tv2, attributed to Mikhail Platov, 1927. As this is a study, you should expect some interesting and instructive twists. And that is exactly what you get when you put this position into the six piece Nalimov tablebase. The tablebase gives you a total of 15 possible moves for White with the following distribution: one winning move, four drawing moves and ten (!) losing moves. Once again, the position overrules the theoretically even material. In case you are having trouble solving this study, the results for all the moves are given at the end of this article.
GM Lev Alburt gives another example of the queen and pawn vs two rooks ending on p. 269 of Chess for the Gifted and Busy1.
Alburt comments “Is the queen + pawn = two rooks equation true? It is in many late endings, with no other pieces left, as in the diagram above. The a4 pawn is a goner and, after its disappearance, Black’s f pawn becomes a target. White threatens to play Ra2 and Rfa3, winning the a4 pawn, with the f7 pawn as the next target. Thus, Black can’t simply sit and wait; he must do something. Some sample lines: 1. … Qe4! 2. Rf4 Qc2 3. Raxa4 g5! 4. Rac4 Qa2 5. Ra4 Qc2 6. Rac4, and White has to repeat the position. Otherwise, f2 will fall with check, and Black will be better. (If White plays 3. h4, Black’s drawing idea is similar: 3. … h6 4. Raxa4 g5.)” So, a more typical board position of the queen and pawn vs two rooks endgame is drawn.
Fine summarizes the theory for this ending on p. 5663. “Queen and pawn are normally equivalent to two rooks. This means that the queen and pawn vs two rooks is generally drawn.” It does appear that Fine’s assessment is a bit oversimplified, as we have seen with the Platov study and the Alburt example. The ending may or may not be a straightforward draw, or maybe not a draw at all. It all depends on the position.
If one pawn may or may not do the job for the queen, what about two pawns? As it turns out, the second pawn gives the queen more chances to win but the pawns’ position still heavily influences the outcome. Fine gives the following excellent example from his game with Edward Lasker where the queen has two additional pawns and manages to win.
|Diagram No. 5 - White to move, Black wins|
This is position no. 1101, Edward Lasker-Reuben Fine, New York 1940, given on p. 570 of Basic Chess Endings3. It is important to note that the side with queen is up two pawns (six pawns vs four pawns), but this is still a late ending, as Alburt discusses above. However, the extra pawns can influence the outcome as Fine’s analysis given below clearly demonstrates. Fine teaches “1. Kh1? A waste of time. The correct plan is to exchange one pawn on the queenside, then double rooks against Black’s remaining pawn there, and finally win it. For instance, 1. Rab1 b6 2. a4 e5 3. a5! bxa5 4. Ra1 Qc3 5. Ra4 f5 6. gxf5 gxf5 7. Rda1 e4 8. Rxa5 e3 9. R5a3 Qe5+ 10. Kh1, and if 10. … e2? 11. Re1 Qb2 12. Re3! eventually winning both pawns. 1. … Qa3 2. Rd7 2. Rdb1 is still better. To get both rooks to the seventh is useless in these endings. 2. … b5 3. Re1 Qxa2 4. Rexe7 a5 5. Rd8+ Kg7 6. g5 (threatening 6. Ree8) 6. … Qc4! 7. Rdd7 (7. Ree8 Qc1+ 8. Kh2 Qxg5) 7. … a4 8. Rc7 Qf1+ 9. Kh2 Qf4+ 10. Kg1 b4 and wins.”
Fine’s analysis is quite amazing, but there is always an exception to the rule. Here is a CCLA game that shows that two rooks on the seventh rank are not always useless.
|[Event "Summer Server Series, S02072"]|
|[White "Wright, Jason"]|
|[Black "Ischler, Mark"]|
1. e4 c5 2. Nf3 d6 3. Bb5+ Bd7 4. Bxd7+ Qxd7 5. c4 Nc6 6. Nc3 g6 7. d4 cxd4 8. Nxd4 Bg7 9. Be3 Nf6 10. h3 O-O 11. O-O Rac8 12. b3 Rfd8 13. Qd2 a6 14. Rad1 Qc7 15. Rfe1 Nxd4 16. Bxd4 e5 17. Be3 b5 18. Bg5 Rd7 19. Bxf6 Bxf6 20. Nd5 Qd8 21. cxb5 axb5 22. Qb4 Rc5 23. Nxf6+ Qxf6 24. Qxc5 dxc5 25. Rxd7 Qc6 26. Rd5 c4 27. bxc4 bxc4 28. Rc1 f6 29. Rd3 Qa4 30. Rdc3 Qxa2 31. Rxc4 Qa5 32. Rc7 Qd2 33. Ra1 Qd8 34. Raa7
|Diagram No. 6 - Black to move|
The rooks now demonstrate their usefulness: 34. … f5 35. Rg7+ Kf8 36. Raf7+ Ke8 37. Rg8+ 1-0 (37. ... Kxf7 38. Rxd8, "a Rook ahead wins by force" — Reuben Fine.)
Fine summarizes the theory for positions where the queen is two pawns up as “Queen and two pawns win against the rooks only when the rooks are not united, or when there are connected passed pawns.”
This is a good time to look at some more positions where the rooks have the same number of pawns as the queen.
|Diagram No. 7 - White to move|
This is a position from page 37 of Lasker’s Manual of Chess4. Here World Champion Emanuel Lasker teaches “The queen is weaker than the two rooks if the hostile king is protected against checks, otherwise it may be stronger. Ceteris paribus, (Latin phrase for "all other things being equal") it would appear the queen is a trifle weaker than two rooks.” It is interesting that these positions with equal numbers of pawns on both sides are similar to the first pawnless positions we considered. Lasker continues “White plays here Rc3, then Rhc1, thus doubling the rooks to assail the c7 pawn and winning it. To win the a6 pawn would, it is true, be difficult, because the rooks have to protect the king against checks. It is evident, however, that the rooks have the initiative and that Black’s hope is to merely draw by perpetual check.”
Fine gives a more complicated example of queen and two pawns vs two rooks and two pawns on p. 569 of Basic Chess Endings 3:
|Diagram No. 8 - Black to move wins|
This is diagram No. 1100, Chigorin-Janowski, Carlsbad 1907, p. 5693.
Fine teaches “Here White’s pawns are isolated and cannot support each other. The continuation was 1. … Rcd6! 2. Kc4 h4 3. Kc5 Kg5! 4. d5 h3 5. Qe8 Kf4 6. Qe1 Rh6 7. Qf2+ Kg4 8. Qg1+ Kf5 9. Qf2+ Kg6! 10. Qc2+ (if 10. Kxd6 h2 11. Qg3+ Kf7+ wins) 10. … Kf6 11. Qb2+ Kf7 12. Qb7+ Kg8 13. a6! This manages to stop the h pawn but leads to a loss with two rooks and pawn vs queen because of the bad position of the queen. 13. … Rxa6 14. Qb8+ Kh7 15. Qb1+ Rag6 16. d6! h2 17. d7 h1=Q 18. Qxh1 Rxh1 19. d8=Q Rg4! (forcing the king into a mating net) 20. Kb5 Rh5+ 21. Kb6 Rg6+ 22. Ka7 Rf5 23. Qd3 Rgf6 Now the ending is won because the White queen must guard against the mate possibilities and cannot pay attention to the pawn.” Fine gives additional analysis to move 42 when White resigned, but the key part is up to move 23. Fine summarizes the theory for positions of equal numbers of pawns as “the rooks are superior and win.”
To conclude our examination of various queen vs two rook endings, we must look at a position where the rooks have more pawns than the queen. Fine gives the following example:
|Diagram No. 9 - White to move, Black wins|
This is diagram No. 1099, Steinitz-Pillsbury, Nuremberg, 1896 on p. 568 of Basic Chess Endings3.
Fine notes “No. 1099 is the minimal position where two rooks plus pawn win against a queen. Yet even here Black cannot advance his a-pawn by any straightforward series of moves: he must combine the possibility of advancing with a threat against White’s pawns.
The game continued 1. Qe6 Rfd8 2. Qa6 h6 3. h4 Rf8 4. Kh3 (4. g4 Rf2+ 5. Kg3 Rdf7 is worse for White) 4. … Kh7 5. Qc6 Rd3+ 6. g3 Re3 7. Qc2+ (the threat was Rf6-g6) 7. … Kh8 8. h5 Re5 9. Kh4 a5! (at last!) 10. Qa4 Rb8 11. g4 Rg5 12. Qc6 Rg8 13. Qa6 Rd8 14. Qc6 Rgd5 15. Qa4 Ra8! 16. Kh3 Rd3+ 17. Kh4 Re3 18. Qc6 Rf8 0-1. Black has the dual threats of mate (... Rff3-h3) and advancing his outside passer. Fine summarizes the theory for positions where the rooks have more pawns as simply “the rooks win”.
Here is a chart that summarizes GM Fine’s assessment of the various types of queen and pawn(s) vs two rooks and pawn(s) endgames that we have studied.
Queen vs two Rooks
|1) Most often drawn.|
|2) If king is confined to edge of board, the rooks win.|
|3) If rooks not properly defended, the queen wins.|
Queen and pawn vs two Rooks
Queen and two pawns vs two Rooks
|1) Queen only wins when the rooks are not united.|
|2) Queen wins when there are connected passed pawns.|
Queen and pawn vs two rooks and pawn (also equal pawns on both sides)
|1) Rooks are superior and win.|
Queen and pawn vs two Rooks and two pawns (Rooks up a pawn, various amounts of pawns)
|1) Rooks win.|
The above chart should be used as a general guideline. It is very clear, from the positions we have reviewed, that where the pieces are located on the board more often determines the outcome of the game, not just a simple piece value total.
Nalimov Tablebase solution for the Platov Study (Diagram 3. above)
The winning move for White is Ra2-a4. However, it still takes 25 moves to win. Ke1-e2, Ke1-d2, Rc2-e2 and Rc2-c4 all draw. The following 10 moves all lose in the number of moves given in the parentheses: Ra2-b2 (53), Rc2-b2 (53), Rc2-d2 (44), Ra2-a7 (38), Ke1-d1 (35), Ra2-a5 (35), Ra2-a6 (35), Ra2-a3 (33), Rc2-c7 (17), Rc2-f2 (16).
1. Alburt, Lev, Lawrence, Al, Chess for the Gifted and Busy, Second Revised Edition, W.W. Norton, New York, 2015.
2. ChessVideos.tv, https://www.chessvideos.tv/endgame-training/two-rooks-vs-queen-pawn-30.php
3. Fine, Reuben, Basic Chess Endings, David McKay Company, New York, 1941, Benko Revised Edition, Random House, New York, 2003.
4. Lasker, Emanuel, Lasker’s Manual of Chess, David McKay Company, New York, 1947, (Dover Edition, 1960).