Queen and Bishop versus Two Rooks

by admin on November 15, 2014

A couple days ago I read this in Wikipedia’s entry called Chess endgame:

Queen and bishop versus two rooks. This was thought to be a draw [before computer tablebases -- DM] but the queen and bishop usually win. It takes up to 84 moves.

This got me curious. Like most players, I only know the basic pawnless endgames: K+Q vs. K, K+R vs. K, K+2B vs. K, etc. My impression was that every other pawnless endgame is ridiculously rare and ridiculously difficult.

But I started wondering: could I use the Nalimov tablebases to learn something about the Q+B vs. 2R endgame? Are there some rules for playing this endgame that ordinary humans can understand?

The answer is yes! First, there are some drawn positions for Black. In fact, it’s easier to say how Black draws than to say how White wins. Here is a rule that I figured out last night:

Rule 1. Black draws if he can put his rooks side by side on the third rank, [and not on the two central files -- clarification added 11/16] in such a way that the rook closer to the side of the board pins the bishop against White’s king. There is only one exception (see below.)

Here is a typical example:

qandb1FEN: 1k6/6Q1/2rr4/8/8/2B5/2K5/8 w – - 0 1

Starting Position 1.

As you can see, the rooks are side-by-side on the third rank, the c-rook pins the bishop, and the d-rook prevents White’s king from escaping to the long side. This is important! If the rook were on b6 instead of d6, White would be winning. But here, White to play cannot make any progress. If he tries to unpin the bishop with 1. Kb3, Black plays 1. … Rb6+. Now if White continues to move the king forward, he just gets chased around forever. The rook on d6 serves as the sentry that keeps the king from escaping the box, while the other rook does the checking.

Alternatively, if White interposes the bishop with 2. Bb4, then Black simply moves the “sentry” rook to c6: 2. … Rdc6. Now White’s position is even worse than before! The White king is confined to a smaller box.

qandb2FEN: 1k6/6Q1/1rr5/8/1B6/1K6/8/8 w – - 0 3

Position after 2. … Rc6.

If we go back to Starting Position 1, you might wonder whether White can make progress with a queen move rather than a king move. The answer is no. The only way the queen can help is to pin one of the rooks, either the sentry rook or the mobile rook. Thus, in the initial position, either 1. Qe5 or 1. Qg3 would be a good try. However, if White does this, Black merely steps to the side (1. … Ka8) and White has not made progress.

A more interesting, in fact beautiful, draw arises if we move the king and bishop one rank closer.

renamed1FEN: 1k6/6Q1/2rr4/8/2B5/2K5/8/8 w – - 0 1

Starting Position 2.

This is still a draw, but it takes a miracle! Here is best play for both sides according to the tablebase.

1. Kb4 (breaking the pin) Rb6+ 2. Ka5 (the king can’t be checked here) Rdc6 (same idea as before — making the box smaller) 3. Bd3 (preparing to bring the bishop to the long diagonal) Kc8 4. Qe7 Kb8 5. Qd8+ Ka7 6. Bb5! (seemingly decisive, because the rook is overworked — it has to defend the other rook and the square c7) Rd6 7. Qc7+ Ka8 8. Be2. Once again White’s bishop is heading to the long diagonal, and this time it appears fatal.

renamed2FEN: k7/2Q5/1r1r4/K7/8/8/4B3/8 b – - 0 8

Position after 8. Be2. Black to play and draw!

Do you see the miracle draw? Hint: look for stalemates.

The answer is 8. … Ra6+!! If White accepts the sacrifice, 9. Bxa6 Rxa6+, obviously he can’t take the second rook because 10. Kxa6 is stalemate. But if he plays 10. Kb5, the rook continues its desperado ways with 10. … Rb6+!!

renamed3FEN: k7/2Q5/1r6/1K6/8/8/8/8 w – - 0 11

Position after 10. … Rb6+.

Amazingly, White’s king has no escape from the checks. If 11. Kc5 then 11. … Rb5+! Black keeps checking on the first six ranks forever — unless the king moves to the seventh rank, and then … Rb7 will skewer the queen and king and lead to an immediate draw.

Incidentally, you might be wondering, “What is so special about the third rank? Wouldn’t Black still be drawing if he has his rooks side by side on the fourth rank?” Well, the above line is one case where it makes a difference. If we moved everything down one rank in Starting Position 2, Black wouldn’t have had this stalemate trick.

The only exception to Rule 1 occurs if we move the bishop one step closer to the rooks.

qandb3FEN: 1k6/6Q1/2rr4/2B5/2K5/8/8/8 w – - 0 1

Starting Position 3.

The reason for this exception is obvious. After 1. Kb5 White breaks the pin, Black cannot play … Rb6+, and now he has to move his “sentry” rook away from d6.

White can make use of this knowledge, too. Here is another study taken straight from the Nalimov tablebase. (Actually, we’re starting at move 10 of a different variation I was looking at, but never mind that.)

qandb4FEN: 1k6/4Q3/r2r4/3K4/8/2B5/8/8 w – - 0 10

Position after 9. … Rd6+. White to play and win.

After the above discussion, this position is a piece of cake. White has only five ways to get out of check. Taking on d6 obviously leads to a draw. 10. Ke5? likewise draws immediately, because of 10. … Re6+! forking the king and queen. Both 10. Kc4? and 10. Kc5? put White’s king in the box set up by the “sentry” rook on d6, and as we have seen above, after 10. … Rac6+ White has no way to make progress.

Therefore, by elimination, the winning move has to be 10. Ke4! At first this looks crazy, because Black once again can fork the king and queen with 10. … Re6+. Now, however, White can interpose with check: 11. Be5+! and it’s mate in three after 11. … Ka8 12. Qd8+ Kb7 13. Qc7+ Ka8 14. Qb8 mate. Of course, Black can delay the inevitable by giving up the exchange with 11. … Rxe5, but that’s a book win for White. Actually, Black’s best defense after 10. Ke4 is 10. … Kc8, but 11. Be5! is still extremely strong. (See diagram.)

qandb5FEN: 2k5/4Q3/r2r4/4B3/4K3/8/8/8 b – - 0 11

Position after 11. Be5. Black to move.

The main point is that after Black’s natural answer, 11. … Rdc6, White checkmates in two moves with 12. Qe8+! Kb7 13. Qb8 mate. If the d-rook moves to any other square on the third rank, 12. Qc7 will be mate. Therefore Black is forced to disconnect his rook battery, either with 11. … Rd7 or 11. … Ra4+. Usually in this endgame it’s death for the rooks to get separated, and it’s certainly true here. I’ll let you work out the win from here.

The end of this example gives us an idea of how White typically wins this endgame. I would say that it’s a lot harder for White to win than it is for Black to draw, even though theory says that White is winning. The reason is that the usual principle of “chase the defender’s king to the edge of the board” is not completely accurate here. The winning checkmate often does not occur at the edge of the board; the above position was an example. White has to have a great deal of ingenuity to come up with these kinds of checkmates. One might say, computer-like ingenuity.

To the extent that I can give any general advice to White, it is this:

1) Centralize the king. The king is often a secret weapon in setting up the unusual checkmates required in this endgame.

2) Do not let your bishop get pinned (except if it’s on the d- or e-file). If it gets pinned, try to unpin it as quickly as possible.

3) Use unconventional checkmate threats to either force Black’s rooks to disconnect from each other or to force one of them to give itself up for the bishop.

I will close with two more examples that illustrate the last idea. “White to play and mate or convert in 3″ means that either White mates in 3 moves or Black has to give up the exchange, thereby “converting” to a book win.

qandb6FEN: 8/8/2r2r2/3K4/1B6/4k3/6Q1/8 w – - 0 1

Problem 1. White to play and mate or convert in 3.

qandb7FEN: 8/2B5/k1r4r/3K4/8/1Q6/8/8 w – - 0 1

Problem 2. White to play and mate or convert in 3.


Problem 1. After 1. Be7! if Black moves his rook — say 1. … Rg6 — then White has an “unconventional mate” with 2. Bg5+ Kd3 3. Qd2 mate. It’s clear that Black has to give up the exchange to prevent this mate.

Problem 2. After 1. Qb8! White threatens the unconventional mate¬† 2. Qa8+ Kb5 3.Qa5 mate. It’s clear that Black has to give up the exchange to prevent this mate.

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Wrong Moves and Wrong Conceptions

by admin on November 12, 2014

At Mike Splane’s last chess party, the question came up: “Is one bad move enough to lose a game?” Of course the answer is yes, if the move is really, really bad, like hanging a rook or a queen. But in games between more or less experienced players, say above a 1500 rating, outright blunders like that are relatively rare. In the great majority of games it takes more than one mistake to lose. I think that it’s only at the high master level, 2500 or beyond, where one mistake might again become enough to lose.

On the other hand, a wrong conception can easily be fatal, and Craig Mar gave us a great example of that. It was a game he played in 1986, in Los Angeles, against an “almost-master” (2198) named Sid Rubin. Craig’s rating at the time was 2420.

The game started 1. d4 d5 2. c4 e6 3. Nc3 c5 4. e3 Nf6 5. Nf3 Nc6 6. a3 (diagram).

mar reuben 1FEN: r1bqkb1r/pp3ppp/2n1pn2/2pp4/2PP4/P1N1PN2/1P3PPP/R1BQKB1R b KQkq – 0 6

Position after 6. a3. Black to move.

I discussed this position once before, in a post called The Art of Doing Nothing. This position is very well known to theory, and can arise via many move orders. Nevertheless, it is a position that many amateur players have misconceptions about.

Misconception #1: The position is not dangerous for Black.

It’s understandable why you would think this. The game has started symmetrically, and Black can keep the symmetry going if he wants with 6. … a6. White has not played any particularly aggressive moves, and his last move (6. a3) does not develop a piece and only indirectly affects the battle for the center.

Nevertheless, Black has many ways to go wrong. One of them — which I also mentioned in my previous post — is 6. … cd 7. ed dc 8. Bxc4, “saddling” White with the isolated queen pawn. (See diagram 2.)

mar reuben 2FEN: r1bqkb1r/pp3ppp/2n1pn2/8/2BP4/P1N2N2/1P3PPP/R1BQK2R b KQkq – 0 8

Position after 8. Bxc4 (analysis). Black to move.

Misconception #2: Black’s play is perfectly reasonable. Normally, when playing against the Tarrasch Defense, White gives Black an isolated queen pawn. So why shouldn’t Black do it to White, given the opportunity?

The reason is that Black has handed White a victory in the “tempo game.” White has been able to bring his bishop to c4 in one move, instead of two. Not only that, the innocent a3 move will turn out to be very useful for White, as it gives the bishop a nice square (a2) to retreat to.

In the Tarrasch Defense, Black gets counterplay for his isolated queen pawn in the form of active pieces. In this position, where White is in effect two tempi ahead of a normal Tarrasch (one by virtue of being White, and one by virtue of developing his bishop in one move), the advantage in development is not merely compensation for a pawn weakness, it is the most important factor in the position.

I kind of hinted at this in my earlier post, but Craig said it much more bluntly. He said, “I think White is almost winning here. This will get you lots of nice wins against lower-rated players.”

That’s one reason that Craig got to 2500 and I’m nowhere near that point. He has a better understanding of fundamental opening positions, called “tabiyas.” He talked about this at the party, and said that he had learned the importance of tabiyas by watching the games of IM Cris Ramayrat, who was active in southern California chess at the same time.

Anyway, Craig’s opponent did not fall into this mistaken conception. He fell into a different one. The game continued 6. … dc 7. Bxc4 Be7 8. O-O O-O 9. dc Bxc5 10. b4 (diagram).

mar reuben 4FEN: r1bq1rk1/pp3ppp/2n1pn2/2b5/1PB5/P1N1PN2/5PPP/R1BQ1RK1 b – - 0 10

Position after 10. b4. Black to move.

This was, in Mar’s opinion, the key position of the game. Black has three reasonable places to put his bishop, and he can throw in a queen trade first if he wants. What should he do?

The move that Black played, 10. … Bd6?, again looks completely reasonable. It is the most “active” square for the bishop, and it gives Black the illusion of making progress, rather than returning the bishop to e7 where it came from. In fact, 10. … Be7 was best, and Craig once again said that he considered 10. … Bd6 to be a nearly losing move.

Misconception #3: When in doubt, develop your pieces to the “most active” squares.

This is a misconception that I fall into a lot, and I have some painful losses to show for it. Active squares are also, in many cases, vulnerable squares. So to properly evaluate the position you need to ask yourself: Realistically, who is going to have the initiative? Will it be Black, with his still vague threats of playing … e5 and somehow getting an attack on the kingside? Or will it be White, who is already ahead in development and is now guaranteed to gain more tempi by placing a rook on the d-file? Black has committed one bishop to d6 and is more or less committed to putting the other one on d7. On these squares the bishops cannot be defended by pawns and they are targets.

In spite of this, 10. … Bd6 is the most popular move in this position according to ChessBase: it has been played 27 times in 49 games, while 10. … Be7 has been played 16 times in 49 games. Clearly there are a lot of people suffering from Misconception #3, and some of them have pretty high ratings. (For example, grandmaster Nikolai Krogius in 1958, against Efim Geller.)

Now to be fair, I don’t think that 10. … Bd6 is quite as terrible as Craig was suggesting. To be more precise: I think the move is okay, but it’s the conception that is bad. According to Rybka, after 10. … Bd6 White’s advantage is 0.59 pawns. That’s not a winning advantage, but it is definitely more than White’s “normal opening advantage.” It’s a sign that Black has done something wrong — namely, lose the tempo battle and misplace his pieces. Black will have to play carefully to survive.

Craig’s opponent didn’t play carefully. The game continued 11. Bb2 Qe7. Here I think 11. … Ne5 was better. Black has to realize he’s in trouble and take urgent action to trade off some of White’s attacking pieces. Instead, Black plays this whole game as if he were in no trouble at all.

Craig then played 12. Qc2 Bd7 13. Rad1 Rfd8 14. Ne4 Nxe4 15. Qxe4 Rac8. Let’s pause for another diagram, because this is a truly comic and instructive position.

mar reuben 5FEN: 2rr2k1/pp1bqppp/2nbp3/6N1/1PB1Q3/P3P3/1B3PPP/3R1RK1 b – - 0 16

Position after 15. … Rac8. White to move.

Misconception #4. “Development” means (1) Dump your minor pieces on any squares beyond the first rank. (2) Castle. (3) Centralize your rooks.

This position is the logical culmination of Black’s whole misguided approach to the opening. Reuben probably thought he hadn’t made any mistakes yet. He has just dumped all of his pieces in a little knot in the middle of the board, where they all get in each other’s way and none of them defend his king! Meanwhile, five of Craig’s pieces are poised and ready to pounce on Black’s undefended kingside. No wonder the game was over in just a few more moves.

16. Ng5! g6

Obvi0usly Black would like to play … f5, but he can’t because White would just take the pawn.

17. Rxd6! …

Deflecting the queen away from the kingside.

17. … Qxd6 18. Qh4 h5 (diagram)

mar reuben 6FEN: 2rr2k1/pp1b1p2/2nqp1p1/6Np/1PB4Q/P3P3/1B3PPP/5RK1 w – - 0 19

Position after 18. … h5. White to play and win.

At this point we had a very lively discussion at Mike’s chess party. Many in the audience, myself included, wanted to play 19. Nxf7!, and in fact this does win. If Black takes, 19. … Kxf7, then 20. Qf6+ Ke8 21. Qxg6+ Kf8 22. Qg7+ Ke8 23. Be2! is curtains.

However, Craig didn’t see 23. Be2, and instead he chose a very simple and practical move that doesn’t sacrifice material and leads to mate or a huge win of material: 19. Ne4! Qe7 20. Nf6+ Kf8 21. Qf4! g5 (only move) 22. Qxg5 Qd6 23. Ne4. Threatening the queen as well as mate in two. Black resigned.

There’s an interesting little lesson in this finish, which is that super-strong players do not necessarily play showy sacrifices at every opportunity. In fact, it’s just the reverse. They only play a sacrifice (like 17. Rxd6) if it’s the only means or the most efficient means to their goal. If there is a perfectly solid non-sacrificing move that wins (like 19. Ne4), they will almost always pick that move rather than a risky sacrifice like 19. Nxf7, which only works if you see the finesse 23. Be2 several moves later.

I definitely learned some things from Craig’s game, and I hope you did too.

Followup¬† (11/13)… Thanks to Hal Bogner for pointing out a couple of typos, which I have corrected. Also, he points out that Sid Rubin was a long-time Los Angeles master who was getting on in years by 1986. So referring to him as an “almost-master” was not really correct … as I should know very well, because I’m also a National Master whose rating doesn’t currently show it. Also, Mike Splane points out a likely move-transposition error in the comments, but I’m showing the game the way that Craig presented it.

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Carlsen-Anand: A Mathematical Analysis

November 11, 2014

Today a seismic shift happened in the world championship match between Magnus Carlsen and Viswanathan Anand. Vishy finally won a game! Last year, you might remember, Carlsen defeated Anand without even losing a single game. Even though Anand went into the match as the world champion, he didn’t even look as if he was in […]

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November 10, 2014

You can have your Stockfish, your Rybka, your Houdini. I’ve got Max.

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Another San Francisco Giant

November 7, 2014

Step aside, MadBum! There’s a new hero in town, and his name is VigPanch! The San Francisco (baseball) Giants have Madison Bumgarner, the hero of the World Series. But the San Francisco (chess) Mechanics have Vignesh Panchanathan, the #4 fourteen-year-old in the country. There’s a very good argument that he has been their most valuable […]

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November 2, 2014

A couple posts ago, I said I wouldn’t write any more about my game with Sergei Kudrin because I was planning to record a ChessLecture on it, and I didn’t want to post spoilers to my own lecture. However, an interesting point came up near the end that I DIDN’T address in my ChessLecture, so […]

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Look for the Penguins

October 30, 2014

Here’s the finish of one of my games from the recent Western States Open in Reno. It was round three, and I was White against Ganesh Murugappan, the #43 12-year-old in the country. FEN: 6k1/2p1rr1p/P2p4/1PnPpBP1/2n1P3/2B5/4K2R/7R w – – 0 81 Position after 80. … R8f7. White to move. Black has just moved his rook to […]

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Reno Odds and Ends

October 22, 2014

A few final thoughts about the Reno tournament… (1) The ratings went up today and I was surprised to see that my rating didn’t go up as much as I thought it would. Only from 2164 to 2182. This means that if I had won my last-round game against GM Sergey Kudrin instead of drawing, […]

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Almost My First Win Over a GM

October 19, 2014

What a finish to the Western States Open! In the last round, I almost… Beat my first grandmaster (a bucket list item) Tied for first in an open tournament, for the first time in 20 years Scored another historic victory with the Bryntse Gambit Got my rating back over 2200. But I didn’t. Instead, I […]

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How Could I Be So Blind?

October 18, 2014

This is a lament that every chess player utters at some point… some of us more often than others. My turn to utter it was yesterday. FEN: 7k/7p/P2R2p1/5p2/2p5/1K6/6rP/8 w – – 0 48 Position after 47. … c4+. White to move. Round one of the Western States Open in Reno. I’m playing White against Samir […]

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