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Pandolfini's Puzzler #55: Winning the Hard Way the Easy Way

  • NM brucepandolfini
  • | Aug 15, 2014
  • | 4021 views
  • | 28 comments

Professor: Good day, class.

The class smiled back, some of the students even said “hi.”

Professor: Are there any questions before we begin today’s session?

Hale: I was wondering if I could show the final moves from a blitz game I had the other night.

Professor: Certainly. Let’s see them.

Here Hale went up to the board and set up the following position.

Question 1: How does White win material?

Hale: I had White and it was my turn.

Zephyr: That’s comforting to know.

Hale: It was a straight 5-minute game, and we both had very little time left.

Thomas: Just queen and rook vs. queen and rook?

Hale: Everything else had been traded off.

Ryan: You don’t see that too often.

Hale: Anyhow, I thought I had a winning line here.

Idris: You do, but it becomes queen vs. rook, and that’s not so easy to win.

Hale: I know, especially with my lack of endgame skill.

Idris: Don’t be so hard on yourself. Analytic engines have shown that type of ending to be quite tricky.

Hale: Fortunately, my opponent blundered into mate.

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The class was amused once they saw what happened.

Professor: That was fun, Hale. Thank you for showing it.

Hale: I doubt that I could have won the position if my opponent hadn’t faltered.

Rachel: I wonder if any of us could have won it, especially in a speed game.

Idris: Rachel makes a good point.

Professor: Not today, but at some future time, we should review the queen vs. rook techniques and methodology.

Zephyr: So what are we going to do today?

Professor: Let’s follow up on what Hale has shown us. Please consider this related position.

Question 2: How can White force a win?

The class needed a little time to analyze, but it didn’t take long to find the winning line, with Idris spearheading the investigation.

Rachel: It’s definitely similar to Hale’s position.

Ryan: Heck, it’s practically the same.

Idris: Well, not exactly.

Professor: Different or not, let’s move to our next position.

Question 3: How can White force a win?

Idris: The maneuvering of the white queen is interesting, though winning the black queen is again not hard.

Lucian: Well, maybe not for you.

Rachel: One still must know how to play positions of queen vs. rook.

Lucian: Aha.

Zephyr: Is that an “aha” moment?

Professor: Whatever it is, let’s use it as a lead-in to our next problem.

Question 4: How can White win a queen for a rook?

Professor: As expected, White’s real target is the black queen.

Idris: Isn’t this a Troitzky position?

Professor: That’s right.

Lucian: How did he know that?

Zephyr: He seems to know everything else. Why not that?

Professor: How about one more position?

Zephyr: Okay. How about it?


Question 5: How does White win a queen for a rook?

Once again, the class had no trouble dissecting the position. But this time, there was a surprise. Zephyr beat Idris to the solution.

Professor: Very nice, Zephyr!

Zephyr: You didn’t think that Idris was the only one in this class who could play chess, did you?

Professor: No, I knew you were all smart kids.

Zephyr: You knew that?

Professor: Yes, Zephyr, I knew that.

Answers below -- Try to solve NM Pandolfini's puzzles first!



Answer 1: Hale gained a material advantage with 1. Ra2+ Kb8 2. Qe8+ Qc8 3. Ra8+ Kxa8 4. Qxc8+, which gave her the advantage of queen vs. rook.

That situation can often require very precise play to bring home the point. In time pressure, however, her opponent blundered by 4…Rb8??, allowing 5. Qa6 mate.

Answer 2: This position, with analysis first published by Horwitz in 1862, is analogous to the one that developed in Hale’s game.

Here, the centralized white queen is ideally placed. White wins with the powerful intrusion, 1. Qf6!. This prevents a black queen check at h6 and constrains Black to move the king (if 1…Qg8?, then 2. Rh1+). Thus, after 1…Kg8, White wins by 2. Qd8+ Kf7 3. Rf1+, and mate soon follows.

Some sample variations: if 3…Ke6, then 4. Rf6+ Ke5 5. Qd6+ Ke4 6. Rf4+ Ke3 7. Qd4+ Ke2  8. Rf2+ Ke1  9. Qd2 mate. 

Or if instead 3…Kg6, then 4. Qf6+ Kh5 5. Rh1+ Kg4 6. Rg1+ Kh3 (for instance) 7. Qf3+ and mates next move.

Answer 3: In this position, which is a sub-variation of a Kasparyan composition, White wins by 1. Qg2+ Qg7 2. Qd5+ (another powerful centralization) Qf7 (2…Rf7 walks allows the pin, 3. Rg2) 3. Rg2+ Kh7  4. Qe4+ Qf5 5. Qh4+ Qh5 6. Qxh5 mate.

Answer 4: The winning line begins with 1. Re6+! (a clearance sacrifice, opening up the a6-f1 diagonal) Rxe6 (else Black loses a rook; note that e6 is now obstructed) 2. Qa6+ Kd5 (if either 2…Kd7 or 2…Kc7, White has 3. Qa7+) 3. Qc4+ Kd6 (if 3…Ke5, then 4. Qc3+) 4. Qc5+ Kd7 5. Qa7+, skewering Black’s king and queen.

Answer 5: In this 1926 composition by Rinck, White wins with 1. Qc5+ Kd8 (on either 1…Ke6 or 1…Kf7, a queen check, say 2. Qf5+, wins at least the black rook) 2. Kh6!. This subtle king-move leaves Black without a good reply.

If 2…Qa8, then 3. Qf8+, skewers king and queen.

If instead 2…Qxc7, then 3. Qf8 is mate.

If instead 2…Rxc7, then 3. Qf8+ wins the black queen.

If the black rook instead moves to a safe place along the d-file, say 2…Rd1, White has 3. Qe7 mate.

Meanwhile, the black rook can’t safely move along its 2nd rank (thanks to 2. Kh6!).

Finally, if 2…Ke8, then 3. Rc8+ is more bad news for Black.


Take note:

The queen vs. rook “basic mate” is not so simple, as many students soon discover. Even strong players have trouble winning it. They often miss astonishing resilience at key moments.

Good teachers have trouble teaching it. They typically describe it more than they explain it. Indeed, computers have shown that the beauty of general guidelines often fails when confronted with the ugliness of specific, aggravatingly resourceful moves.

But that’s just the way it is. Hey, who said chess was easy?


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Comments


  • 2 months ago

    DM_knight

    Wow, At first glass it seems drawish but after some thought it becomes very interesting and that last problem 2.Kh6! really difficult to find

  • 2 months ago

    yk333218

    outrageous! I would have dropped my guard and offered draw in Q+R + Q+R

  • 2 months ago

    j2009m

    “A general “law of least effort” applies to cognitive as well as physical
    exertion. The law asserts that if there are several ways of achieving the
    same goal, people will eventually gravitate to the least demanding course
    of action.” 

    “Intelligence is not only the ability to reason; it is also the ability to find relevant material in memory and to deploy attention when needed.” 


    ~Daniel Kahneman, in his book: Thinking, Fast and Slow

     


  • 2 months ago

    mrdinth

    Thank you NM brucepandolfini for your puzzles, I enjoyed them very much; I have to admit that I didn't see the combinations myself.

    One thing I'd like to point out about the last problem. You say "on either 1…Ke6 or 1…Kf7, a queen check, say 2. Qf5+, wins at least the black rook". In the game window you show 1...Kf7 as a side variant, and your answer is 2. Qf5+. In the case of 1...Kf7, there is also the most obvious move 2. Rxd7+ and mate follows quickly. See the diagram below.

    After thorough analysis I realise that 2. Rxd7+, 2. Qf5+ and 2. Qd5+ are all equally fast winning moves. In the case of 2. Qf5+ Kg8 I was struggling with 3. Rxd7? Qg3+! Later I saw this can be prevented with 3. Qxd7!! So these three variations all lead to mate in move #6, if played correctly.

    Your puzzles were a good challenge. I thought I had seen a better solution, but it turns out just to be equal. Thank you for the entertainment. Smile




  • 2 months ago

    Randal_Pejelagarto

    Pandolfini, do you spick Spanish?

  • 2 months ago

    titust

    Nice! The problems are hard this time. I like that.

  • 2 months ago

    NM brucepandolfini

    mirelch  It is amazing that even when there are a limited number of pieces on the board, the position may contain deep mysteries. But that's one of the things that draws many of us to chess. I think there are some simpler problems coming up soon. Thanks for sharing your opinion.

  • 2 months ago

    NM brucepandolfini

    EliasAStern Thank you! It's fun to solve chess puzzles, it's also fun to think them up.

  • 2 months ago

    mirelch

    this was really hard

  • 2 months ago

    EliasAStern

    great puzzles. I also love chessercizes: checkmate!

  • 2 months ago

    NM brucepandolfini

    NM londonsystem22 You've described it well. The defender's potential resilience has been known for many years, particularly since the days when Ken Thompson's Belle Lab program gave GM Walter Browne considerable difficulty. I believe they had at least a 3 or 4 game match, and Browne had real trouble winning in fifty moves.

  • 2 months ago

    NM brucepandolfini

    j2009m Intriguing quote. Thanks for sharing. If you have others, I'm sure rthe readership would love to see them.

  • 2 months ago

    NM brucepandolfini

    love_romance13 I appreciate your very nice comment. But I have to say, Josh Waitzkin is so talented, he would have succeeded at any endeavor in life he pursued, with or without help. He really is quite remarkable. But thanks for your good words.

  • 2 months ago

    NM brucepandolfini

    morgondag I agree with what you've said. Amateurs should beat other amateurs easily enough in the Q vs. R endgame, especially because the quality of defense may leave something to be desired. Teaching the subject to amateurs, however, if it is done correctly, can be more problemsome. This is especially so because playing the endgame well is not just a matter of principles and generalities, as you know. One must also be armed with a knowledge of specific positions, how to arrive at them, and how to play them precisely afterward. Strong players can do all that, of course, but average players, well, that's another matter.

  • 2 months ago

    NM brucepandolfini

     Bab3s Interesting variation. Thanks for pointing it out. As far as the degree of difficulty for the problems, from week to week they vary greatly. We try to mix it up, realizing the readership extends over a big range. But, like you, I like harder problems, too. I think the kids in the class do as well.

  • 2 months ago

    NM londonsystem22

    May be worth it to mention that the best way to try and hold Q vs R is to (counter-intuitively) keep the rook and king distant, while avoiding forks that win the rook.  I think even Morozevich failed to defeat Jakovenko in 2006 or something when Jakovenko used the idea of keeping king and rook distant.

  • 2 months ago

    j2009m

    "Chess is a contest between two people in which they attempt to plan, prepare, and anticipate the arrangement of pieces better than the other. The winner executes a better strategy."

    ~Josh Monroe (Me)

  • 2 months ago

    love_romance13

    very nice article sir bruce pandolfini like always now i know how josh waitzkin(Tiger) become great chess player under your guidance

  • 2 months ago

    NM Bab3s

    For the last problem, I came up with 1. Qe3+ Kd8 2. Qc5 but missed 2...Rd5+, the real reason why Kh6 is essential. Very hard problems this time, much harder than they usually are. I like that.

  • 2 months ago

    morgondag

    In practical play against a player of similar strength, though, Q vs R is not very hard to win. At least on amateur level. If the R stays next to the K it gets pinned, if it moves away it gets skewered or forked. The computer defenses with the R separated from the K are very hard to find for most humans.

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