KQ vs. KR

[ASTROBOY]

Wrong e-mail appeared on the other post. The right one is
s156...@uottawa.ca

[How to mate with King and Queen versus King and Rook?]

Thierry Angers

[Sensaru]

how much time do you have?
if time is not a concern take your time and make sure you dont stalemate.
the difference the rook has to mate on the edge of the board. whereas the queen
simply has to command the kings field.

live and be well
marc.

live and be well
marc.

[Pierre G. Boutquin]

ASTROBOY wrote in message <34B3C4...@nova.astro.utoronto.ca>...

Thierry:

Below's an excellent summary of the theory.

HTH!

/Pierre
----------------------------------------------------------------
How To Win Queen Vs. Rook

by NM Roger Poehlmann

As this discussion seems to be a source of recent debate on
games.rec.chess and elsewhere I decided to take a closer look at this
ending. Computers have uncovered some undocumented defensive
techniques involving voluntarily separating the King and Rook to
threaten checks when there is no way for the queen to pick off the
rook.

What's important to me as a practical player is being able to win this
position with the Queen, and put up the most practical defense as
Black.

First let's define some "basic" positions that are clear wins so we
know what we're heading for. Then we'll handle a normal looking
position and go from there.

THEORY

(1) The Draw Position: Qe6, Kf8, Rf7, Kh6 (Black to move)

Black plays 1..Rh6+! 2.Kg6 (2.Kxh7 stalemate) and checks forever. If
Ke5, then ..Re7 pins the queen. This is right out of BCE.

(2) The Fianchetto Position: Kc6, Qh1, Ka8, Rb7

So named because the rook is "fianchettoed" on b7, but this is known
theory too. White wins with either side to move by getting his Queen
to d8 or a5 with Black to move, and then the rook has to leave the
king, with fatal consequences. White to move gets this position
quickly (1.Qd5 etc.) so let's give Black a chance to defend:

1..Ka7 2.Qg1+ Ka8 3.Qg3+ (White inches closer, so Black tries a trick)
3..Ka8 4.Qg5! (White must *unprotect* a7 and b8 to avoid any rook
check stalemate ideas. Here 4.Qd6?? looks like progress, but 4..Rb6+
draws.) 4..Ka7 5.Qa5+? Kb8 (The winning position, but we need Black to
be on move) 6.Qd8+ Ka7 7.Qd4+ Kb8 8.Qf4+ Ka7 9.Qa4+ Kb8 10.Qa5! (And
now Black is stuck with the move: 10..Ra7 11.Qd8 mate, so the rook has
to make a run for it.) 10..Rh7 11.Qb4+ Ka8 12.Qa3+ Kb8 13.Qb3+! (The
last trick. On 13.Qb2+ Kc8! and there's no quick knockout, since the
Rh7 stops the mate on h8!) 13..Ka8 14.Qa2+ Kb8 15.Qg8+ Ka7 16.Qxh7+
wins.

(3) The 3x3 Box: Kd7, Qa5, Kb7, Rb6

White naturally seeks to compress Black down to the Fianchetto
Position at which point the win has already been demonstrated. Most
humans would defend this position by: 1..Ra6 2.Qc7+ Ka8 3.Kc8 Rb6!
4.Qc4! (Again, note the *unprotection* of b8 and a7 defuses the
stalemate traps) 4..Rb8+ 5.Kc7 5..Rb7+ 6.Kc6 and we have reached the
Finachetto position.

However, my computer seems to like 1..Rh6! here, a more annoying
defense: there's no way to pick the rook off, Black's threatening
checks, and if White checks then Black's king runs out of the corner!
Very discouraging. But if you keep your wits about you, you'll see
that Black's king isn't going ANYWHERE. Notice the c1-h6 diagonal?
Any check on that diagonal wins the rook. Now from that c1-h6
diagonal, imagine the cross-diagonals e1-a5, f2-a7. Maybe you want to
put pennies on these squares to show that Black dare not put his king
on them. Similarly, the 3rd, 4th and 5th ranks are war zones too
since Qe3+, Qf4+ or Qg5+ will pick the rook off. So where can Black
go with complete safety? Only b7, a6, and a8 are safe squares!
Black's freedom is illusory and it is now an easy matter to manuever
around and put the queen on a square where h7 is covered:

1.Qd5+ Kb6 (Flaunting his temporary freedom, since White can't get
back to e3 just yet) 2.Qd4+ Kb5 3.Qd3+ Ka4 4.Qc2+ (White's queen
finally gets on the right track, ready to jump on the killer c1-h6
diagonal and Black has to return to the squares without pennies on
them) 4..Kb5 5.Qf5+ Ka6 6.Qd3+ Kb7 7.Qe4+ Ka6 8.Kc7! (Now White
threatens Qa4 mate, and only the a6 square is safe for Black's king!)
8..Ka5 9.Qf5+ Ka6 10.Qd3+ Ka5 11.Qd2+ Ka6 12.Qxh6+ winning.

Remember this trick with the pennies, it will come in very handy
whenever Black's rook goes for a walk.

(4) The 4x4 Box: Kf5, Qd8, Kf7, Rg7

This reduces to a 3x3 Box by losing a tempo: 1.Qh4 Ke8 2.Qh8+ Kf7
3.Qd8! (It is now Black to move in the same position) 3..Rh7 4.Qd7+
Kg8 5.Qe8+ Kg7.

Active defense fails in the same way as in the 3x3: 3..Rg1 4.Qd5+ Ke8
5.Qb5+ Kf7 6.Qc4+! Ke8 7.Kf6! (Just as in the 3x3, White threatens
mate with Qc8 and the queen covers the f1 checking square, and the
king cannot return to its safe squares.)

(5) Third Rank Blockade: The Incredible Flying Rook: Kd5, Qh7, Kd8,
Ra6

This is the defense Browne ran into and the most interesting of the
rook separation defenses. The position we're aiming for here is Kc5,
Qf7, Kd8, Ra6 with Black on move; the rook is on the "short side".
The King covers b6, c6, and d6, and the Queen guards e6, f6, and g6.
If ..Rh6 then Qf8+ spears the rook, so h6 is covered too. If Black
moves ..Kc8 then Qe7 tightens the grip. So Black cannot maintain the
blockade.

1.Qf7! Ra5+ 2.Kd6! Ra6+ 3.Kc5!

As far as I know, this is all original analysis, so I claim the Kc5,
Qf7, Kd8, Ra6 position with Black to move as the "Poehlmann Zugzwang":
(a) 3..Ra3!? 4.Kb6! Re3 5.Qd5+ Ke8 6.Qh5+ (Trying to get on the c1-h6
diagonal: Black has only e8 and c8 as safe squares) 6..Kd7 7.Qb5+ Kd8
7.Qg5+! Re7 (Saving the rook?) 8.Kc6! and Black can choose between
getting mated by 8..Ke8 9.Qg8 mate or losing the rook (I told you so!)
by 8..Kc8 9.Qxe7 Kb8 10.Qb7 mate.

(b) 3..Kf8 4.Qe7 (a simpler case of the 3..Ra3!? defense) 4..Ra3 5.Kb6
Rb3+ 6.Ka7! (notice how Black's king is "knight-forking" White's king
and queen) 6..Rd3 7.Qc5+ Kd8 8.Qa5+ Kd6 9.Qd8+ Ke5 10.Qxd3 wins.

There are other ways to break the bind, but this is a clear and easy
way to smash through. Black has to try (b) and play 4..Kg8 instead,
which is a 3x3 Box discussed above.

GAMES

Let's start with a "typical" position: Black pieces in the center, and
see how these methods actually play out. My trusty Psion program is
more than happy to play the other side, and doesn't mind a bit if I
put pennies on the board.

Poehlmann-Psion (486/66, 30 seconds/move)
Ka2, Qf3, Kd4, Rc5

1.Kb2 Ke5 2.Qe3+ Kd5 3.Kb3 Rb5+ 4.Kc3 Rc5+ 5.Kd3 Kd6 6.Qf4+ Ke6 7.Kd4
Rd5+8.Ke4 Rb5!? (The fourth rank blockade? Same procedure) 9.Qh6+ Ke7
10.Qc6 Rh5 11.Kf4 (The Poehlmann Zugzwang, only one rank back!)
11..Rh2 12.Kg5 Rd2 13.Qe4+ (This is 5(a) above with the flying rook,
we just have one extra rank--let's try the same method) 13..Kd7
14.Qa4+ Ke7 15.Qb4+ Rd6 16.Kf5 Kd7 17.Qb7+ (This was mate in 5(a) but
here it just forces black's king to the back rank) 17..Ke8 18.Ke4 Rh6
19.Qg7 Rb6 20.Qc7 Rg6 21.Qc2! (losing a tempo) 21..Rh6 22.Qc8+ Ke7
23.Qc7+ Ke8 24.Kf5! (The Poehlmann Zugzwang, see 5(a)) 24..Rh3 25.Kg6
Rd3 26.Qe5+ Kd8 27.Qa5+ Ke7 28.Qg5+ Ke6 (everything loses) 29.Qf5+ Kd6
30.Qxd3+ and wins

1.Kb3 Rb5+ 2.Kc2 Rc5+ 3.Kd2 Rc4 4.Qb3 Rc5 5.Qb4+ (I call this the
"Candy Cane" position because of the shape of the pieces on the board.
It's key because Black can't play 5..Rc5 6.Qd6+ Ke4 7.Qd3+ winning the
rook! So he has to move the King back.) 5..Kd5 6.Kd3 Rc7 7.Qb4+
(Candy Cane again) 7..Kd6 8.Kd4 Rc1 9.Qe5+ Kc6 10.Qd5+ Kc7 11.Qf3 Rg1
12.Qf4+ Kc6 13.Kc4 Re1 14.Qh6+ Kc7 15.Kd5 Rd1+ 16.Kc5 (Giving Black
the opportunity to bring the wandering rook home) 16..Kd7!? (And he
refuses!) 17.Qh3+ Kc7 18.Qg3+ Kd8 19.Qg5+ Kc7 20.Qf4+ Kd8 21.Kc6 Ke7
22.Qh4+ Kf8 23.Qf2+ Kg7 24.Qg3+ Kh6 25.Qh4+ Kg6 26.Qg4+ Kf6 27.Qxd1
and wins

1.Qf2+ Kd5 2.Kb3 Rb5+ 3.Kc3 Rc5+ 4.Kd3 Rc7 5.Qf5+ Kc6 6.Kd4 Rd7+ 7.Kc4
Kd6 8.Qf6+ Kc7 9.Kc5 Rd1 10.Qf7+ Rd7 11.Qf4+ Kb7 12.Qe4+ Kc7 13.Qe8
Rd1 14.Qe5+ (Get out the pennies again...d8 and c7 are the only safe
squares, so White wants to play Qf4+ and then Kc6) 14..Kd7 15.Qf5+ Kc7
16.Qf4+ Kd8 17.Kc6 Ke7 18.Qe4+ Kf6 19.Qf3+ Ke5 20.Qxd1 and wins

In these last two Black didn't get a chance to set up the blockades
but we did see some wandering rooks. Maybe I can do better with
Black:

Psion-Poehlmann

1.Qf4+ Kd5 2.Kb3 Kc6 3.Kb4 Rb5+ 4.Kc4 Rc5+ 5.Kd4 Rd5+ 6.Ke4 Rd6 7.Qc1+
Kd7 8.Qc4 Ke8 9.Ke4 Rg6!? (Let's see if it can break the blockade!)
10.Qc8+ Ke7 11.Qc7+ Ke8 12.Qb8+ Ke7 13.Qb7+ Ke8 14.Qe4 Rb6 15.Qa4+ Kd8
16.Qa7 Rh6 17. Qe3 Rc6 18.Qa3 Rb6 19.Qc5 Ra6 20.Qc4 Rb6 21.Qd4+ Kc7
22.Qc5+ Kb7 23.Kd5 Ka6 24.Qc7 Kb5 25.Qc2 Ka6 26.Qe2+ Kb7 27.Qe8 Kc7
28.Kc5 Ra6 29.Qe7+ Kb8 29.Kb5 Ra7 30.Qe5+ Kb7 31.Qd4+ Kb8 32.Kb6 Rb7+
33.Ka6 Ka8 34.Qd5 Kb8 35.Qxb7 mate

Psion-Poehlmann

1.Qf4+ Kc3 (Attack!) 2.Qe4 Rc4 3.Qe3+ Kb5 4.Kb2 Kb5 5.Kb3 Rc7 6.Qd4
Rc1 7.Qd5+ Kb6 8.Qd2 Rc5 9.Qd7 Rc7 10.Qd6+ Rc6 11.Qb4+ Kc7 12.Qe7+ Kc8
13.Kb2!? Rc7 14.Qe8+ Kb7 15.Qb5+ Kc8 16.Qd5+ Rd7 17.Qg5+ Kc8 18.Qf5
Kd8 19.Qf8+ Kc7 20.Qc5+ Kd8 21.Qa5+ Ke7 22.Qe5+ Kd8 23.Kb3 Rc7 24.Qd6+
Kc8 25.Ka4??= Ra7+ 26.Kb5 Rb7+ 27.Kc5 Rc7+ 28.Kb6 Rb7+ 29.Ka5 Ra7+,
draw.

So I got lucky. Psion doesn't know the Draw Position (1) that we
looked at at the start of this article, but hey, I don't always
remember to pick up my socks on the floor.

CONCLUSION

The Flying Rook defenses are interesting and offer great practical
chances for a draw. Objectively, however, there is no draw, and you
don't have to be running at 350 Gigahertz or be 2600 to force the win.
You do need to know these key positions, though, and a jar of pennies
can come in handy too.

NM Roger Poehlmann

[Steve Haataja]

Pierre G. Boutquin wrote:
>
(stuff deleted)

> (5) Third Rank Blockade: The Incredible Flying Rook: Kd5, Qh7, Kd8,
> Ra6
>
> This is the defense Browne ran into and the most interesting of the
> rook separation defenses. The position we're aiming for here is Kc5,
> Qf7, Kd8, Ra6 with Black on move; the rook is on the "short side".
> The King covers b6, c6, and d6, and the Queen guards e6, f6, and g6.
> If ..Rh6 then Qf8+ spears the rook, so h6 is covered too. If Black
> moves ..Kc8 then Qe7 tightens the grip. So Black cannot maintain the
> blockade.
>
> 1.Qf7! Ra5+ 2.Kd6! Ra6+ 3.Kc5!
>
> As far as I know, this is all original analysis, so I claim the Kc5,
> Qf7, Kd8, Ra6 position with Black to move as the "Poehlmann Zugzwang":

(more stuff deleted)

The position you reached after 3.Kc5 can be found in Nunn's "Secret's of
Pawnless Endings" on page 58. It is diagram 79, after 1. Kd5-c5. Once
again, there is nothing new under the sun.

If Black plays 1. ... Rb6 from your position, we reach diagram 78 in
Nunn's book. Apparently it is the most difficult third rank position to
crack. Nunn points out that winning this position requires playing at
least one counter-intuitive move, so he suggests playing one
immediately: 2.Qf4. Note that the Black Rook cannot presently move.
Nunn indicates that understanding diagrams 78 and 79 are sufficient to
break down the third rank defense. Your analysis of diagram 79 looks to
be on the mark, Roger.

Presenting a complete analysis diagram 78 here would take far more time
than I presently have available, but here is one line from Nunn. 2.Qf4
Kd7 3.Qa4+ Kc7 4.Qa7+ Rb7 (the third rank defense is broken) 5.Qc5+ Kb8
6.Kd6 Rg7 (Rf7 or Rh7 are most simply met the same way) 7.Qe5 Rc7 8.Qe8+
Rc8 9.Qb5+ Ka7 10.Kd7 Rb8 11.Qa5+ Kb7 12.Qe5 (diagram 64 in Nunn, which
is Berger, 1899) Ka7 13.Kc7 Rb7+ 14.Kc8 Rb6 15.Qa5+. BTW most of
White's moves are optimal, and all of Black's are.

Nunn's three "Secrets of ..." books make for fascinating reading. I
have since also purchased Ken Thompson's three CD database as well.
Playing Q vs. R against it is quite interesting!

All apologies, Roger, but I haven't yet had time to read more of your
post. Since the third rank defense is most critical, I jumped to it,
and recognized the key position.

Was the third rank defense known before endgame databases? I seem to
recall that it was not, but am not sure.

--
Steve Haataja
remove z's to obtain email address
------

[Pierre G. Boutquin]

Steve Haataja wrote in message <34B520...@sd.cyberznex.net>...

>Was the third rank defense known before endgame databases? I seem to
>recall that it was not, but am not sure.
>

Hi Steve!

I have a different recollection, but am not sure either.

/Pierre

[Don C. Aldrich]

I think not. Back in the late 70's/early '80's, Walter Browne played
two "matches" against Cray Blitz, with Browne having the Q. Cray
played the defense, and Browne was unable to crack it the first time
around, and barely the second [mating on move 49 or 50]. I recall
that they felt some of the positions Cray was coming up with were new.

==Dondo

"He thinks too much. Such men are dangerous."
Julius Caesar, Act I, Sc. 2.

[Timothy E. Vaughan]

Sensaru wrote:

> if time is not a concern take your time and make sure you dont stalemate.
> the difference the rook has to mate on the edge of the board. whereas the queen
> simply has to command the kings field.

After reading the original poster's question carefully, I think he meant that he
was
interested in KQ vs. KR ending, NOT a comparison of the ending KQ vs. K to the
ending KR vs. K, which is what your message assumed.

[Pierre G. Boutquin]

Don C. Aldrich wrote in message <34b863fc....@news.skypoint.com>...

>>>Was the third rank defense known before endgame databases? I seem to
>>>recall that it was not, but am not sure.

>I think not. Back in the late 70's/early '80's, Walter Browne played
>two "matches" against Cray Blitz, with Browne having the Q. Cray
>played the defense, and Browne was unable to crack it the first time
>around, and barely the second [mating on move 49 or 50]. I recall
>that they felt some of the positions Cray was coming up with were new.

Anybody have the Cheron volumes on the Endgame? That's where I thought I
might have read about it.

/Pierre

[Achim Engelhart]

>>>Was the third rank defense known before endgame databases? I seem to
>>>recall that it was not, but am not sure.
>I think not. Back in the late 70's/early '80's, Walter Browne played
>two "matches" against Cray Blitz, with Browne having the Q. Cray
>played the defense, and Browne was unable to crack it the first time
>around, and barely the second [mating on move 49 or 50]. I recall
>that they felt some of the positions Cray was coming up with were new.

> Anybody have the Cheron volumes on the Endgame? That's where I thought I
> might have read about it.

Just recently I tried very hard to win against fritz5 (includes the KQ vs. KR
database automatically) in this ending, and it took seven tries
until I succeeded to win in less than 50 moves. After that I checked several
endgame books (unfortunately I didn't check Cheron, but I will do), but the only
one where I found this defence (and the correct winning lines)
was Euwe's "Das Endspiel" (from the 1950s I think). It is not called
third rank defense there, but all the variations are there ... in great detail, by
the way
(whereas e. g. Keres' Practical Endgames doesn't treat it)