White to move and win. Can you find the winning pattern?
R7/6k1/P6p/5p2/5Pp1/4K1P1/r6P/8 w – – 0 1
Dvoretsky, 2003
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This is too deep for an exact continuation, but it appears one would want to leverage the ‘a’ pawn. I would start by pushing it, essentially locking Black’s rook to defending against the promotion. At that point you can try to get your King over there to help promote, but that probably won’t work because there isn’t any protection for the King and Black can just check you away whenever he wants. Black’s rook can just move up and down the ‘a’ file, keeping White’s rook locked down protecting it.
But, after doing all that, it looks like you should be able to maneuver the King over into Black’s pawn territory. I don’t see how Black could ultimately protect the ‘f’ pawn. Once that falls, it should be reasonably easy to promote and win the game.
Easy. March the king to b6 then move the rook out of the way. Next is to queen. 1-0
1. a7
Now, the black rook must stay on the a-file, and the black king must stay on g7/h7 to prevent white from playing Rh8.
Well, the black rook can leave the a-file temporarily to check the white king, but has to return to the a-file, or else the a7 pawn will queen.
So, the strategy for white is to move the king up and win the f5 pawn. Black g4 pawn will also fall. If …h5, then the h-pawn will also fall.
Trying to force the issue with the king on the q-side is much harder… because black will check the king from behind on the b-file, c-file, etc. If the king tries to attack the black rook, the rook can move up and down the a-file.
However, don’t see a way for black to save the f5 pawn. If …Ra5, then the white king goes to b4, and drives it away, then moves to the 5th rank and if necessary, the 6th rank, and sooner or later, the white king will be on e6 or e5. The black king cannot come to f7 for f6 or g6, and the black rook cannot stay on a5 forever.
One possible scenario though, is the following: white king on e6, black king on g7, white pawn on a7, and black rook on a5, and white to move. At this point, it’s appears a little hard to make progress. if Kd6, Kh7. or if Ke7, Ra6.
The solution then is
1. Re8 Rxa7
2. Re7+ Rxe7
3. Kxe7
and white wins the king and pawn ending (the f5 pawn falls).
A similar situation happened in an Anand-Kramnik game, and Joel Benjamin showed how to make progress. In that game though, Anand had a way out into stalemate.
I am trying to see what the subtlety is that prevents the obvious from winning. Mark Dvoretsky is too good an endgame composer to waste his time on something that appears so simple – unless it isn’t.
pawn to a7 first. Then black king must stay on g7 or h7. Black rook can go to a4 to stop white king advancing, so king moves to b file to advance to 5th/6th ranks, then moves across to attack f5 pawn. When white king reaches e6, black rook must sit on a5. Then Re8, Rxa7, Re7+, RxR, KxR, Kg6, Ke6 is a won pawn ending
Not easy at all. Black has a defence and conterattack. Black takes on h2 and moves his h-pawn. King stays on g7 or h7.
First, marching the king over to b6isn’t quite the solution it appears at first sight. The black rook can check the king from a distance as I will show below.
Now, with that out of the way, it seems to me, at first look, that the first move has to be a7, otherwise, black has time for Rh2 and back to a2 to cover a8. After that, I don’t readily see how white can win this. So, black has three basic replies, king moves, pawn move, or rook moves:
1. a7 Kf7 (Kf6 2. Rf8 wins)
2. Rh8 Ra7
3. Rh7 bagging the rook. This takes care of the king moves.
Rook moves:
1. a7 Ra4
2. Kd3 h5
3. Kc3 Ra5
4. Kb4 Ra1
5. Kb5 Rb1
6. Ka5 Ra1, and if white persists, black is going to claim a draw by perpetual.
Now, bringing the white king into play has to be part of the solution, but where is the target?
Black’s f-pawn seems to be the prime weakness. Might white be able to attack it immediately?
1. Kd4 Rh2
2. Ke5 Rg2
3. a7 Ra2 (seems forced to me)
4. Kf5 and the g-pawn falls, too, giving white a decisive edge, and a win even a patzer like me could bring home. The other major lines for black seems no better,
1. Kd4 Rh2
2. Ke5 Kg6
3. a7 Ra2
4. Rg6 Kf7
5. a8(Q) winning the rook
Or,
1. Kd4 Re2 (cutting off Ke5)
2. a7 Ra2 and the rest is the same as above.
To the Anonymous commenter at 1:25 PM,
Marching the king to b6 is no solution that I can see:
1. Kd4 Rh2
2. Kc5 Rg2 (threatening to win g3)
3. Kb6 Rg3
4. Rc8 Rb3
5. Ka7 g3
6. Rc2 Kg6
7. Kb8 Rb3
8. Kc8 Ra3 and how does white make progress here? If the king marches back to the b-file, black simply checks again, and if the white rook attempts a return to ranks 6-8, black advances his pawn.
I should also add one addtional line:
1. Kd4 Ra5
2. a7 h5
3. Kc4 Ra4 (what else?)
4. Kd5 Ra5
5. Ke6 Kh7 (any rook move loses)
6. Kf6 and now black is in zugzwang, he must either lose the h-pawn, give up the a-file, or give up the f-pawn.
The real point of this problem is that Black’s King can hide out on h5 and that White’s King can be checked by Black’s Rook as long as White’s King is in the open on the Q-side. As such, simply marching the White King to b6 really doesn’t work as it becomes open for target practice by the Black Rook. So, what at first looks like a straight-forward win by White, is actually a difficult problem.
LOOKS LIKE A-7, THEN THE THE KING MARCH TO ASSIST THE R+P!?
As a follow up to my previous post, if White’s King ever decides to place itself on f6 and Black’s King is on h5, Black can play …Rxa7! with a stalemate if White takes, and, with the a-pawn gone, there goes White’s win.
just a7 and maneover to get the king to the king to the 6th rank..
As a follow up to my previous post, here’s a line demonstrating one of the points to the problem: 1.Kd4 Kg6; 2.a7 Kh5; 3.Ke5 Re5+; 4.Kf6? Rxa7! and if 5.Rxa7 it’s stalemate. 5.Re8 Rf7+!; 5.Ke6 (5.Kxf7 is stalemate) Rf6+!; 6.Ke5 Rf7 with a probable draw.
1.a7 1…Ra4 2.Kd3 2… Kh7 3.Kc3 3… Kg7 4.Kb3 4…Ra6 5.Kc4 5… Ra5 6.Kb4 6… Ra1 7. kc5 ra6 8.kd5 rA1 9. ke5 ra5+ 10 ke6 kg6 11. h3 ra6+ 12ke7 gh 13 rg8+ kh5 14 a8=Q rxa8 15 rxa8 kg4 kf6 1-0
Ah… now we are getting somewhere 🙂
1. a7 Kg6 2. Rg8 Kh5 3. a8Q Re2+ with a possible draw.
1. Kd4 is right, but because it threatens also 2. Ke5
Black is threatening Rxh2. so 1.a7 is the first move as far as i can see. This move will limit the activity of black’s king and rook. The King cannot march to any 6th rank squares without the disastrous check on f8 or g8. White King can penetrate into the black’s camp via e6 and capture pawns on f5 and g4.BUT this plan looks easy.
Have a second look. Black can set a trap and split the score by stalemate. Can you see it? By moving his King to 1..g6 2.Rg8+ Kh5 3.a8=Q
Now DO NOT take the queen, instead give an endless check to the King since the rook is taboo.
Now let’s have a third look LOL!
Ah yes I see – and 1. a7 Kg6 2. Rg8+ Kh5 3. a8Q and the R checks up and down the a-file. If the Q or K takes the R it is stalemate, and if the K runs to the 8th rank then R:a8+ x-rays the white R.
1. a7 Kg6 2. Rg8+ Kh5 3. Rf8 R:a 3. R:f5+ and 4. Rd5 allows white to transform this into a winnable ending. (4….Ra2 5. Rd2 and the R will get behind the f-pawn.
1.a7 must win.
Black stays with the king on g7-h7, rook on 4-th rank.
Wihite plays with the king to b3-b4-c5-d6
then with black king on g7:
on
..Ra6+ Ke5
..Ra5+ Ke6
..Kh7 Kf6
black still has some moves:..h5,
but white wins with Kg5-Kg7 Kxh5-Kh7 Kg5-Kg7 Rb8-Rxa7 Kxf5
aam, I believe your solution is correct, as is your critic of the king march to b6 which was my first idea but I believe you forgot something
In the variation where you play (Ra8/Ra5 Ke6 /Kg7) 1. Re8 Rxa7 2.Re7+ RxR 3. KxR Kg6 4. Ke6 then Black should save the game with the stalemate pattern 4…Kh5!!
white’s first move should be Kd4, threatening Ke5. If Black defends the f5 pawn with Kf6 then white moves the king towards the black rook (Kc3). White’s aim is to get his king to b3, chasing away the black rook from the a column. After that white can move the a pawn to a7 with black not able to check his king. Then, white moves his rook out of the way with a check and promotes the “a” pawn.
Timothée Tournier, you are right about the stalemate!
Can white force the black king to h7? If the white king is on e6, and the black rook on a5, guarding f5, and it’s black to move, then …Kh7 will be forced.
0. … Kh7
1. Rf8 Rxa7
2. Rf7+ Rxf7
3. Kxf7
and 4. Kf6, and 5. Kxf5
Given the stalemate, Black can also try
1. a7 Kg6
2. Rg8+ Kh5
3. a8(Q) Re2+
and keep checking the king. don’t see an easy way for white to get out of this mess.
Given the stalemate pattern, does white have to play
1. a7 Kg6
2. h3!
Then if 2…gxh3, 3.Rg8+
Or 2…Kh5, 3.hg, fg; 4.f5
But, I can’t see a way around Timothee Tournier’s problem of the stalemate on h5 after the rooks have been exchanged on e7, in which case 1…Kg6 might actually be a mistake!!
1…a7 and is draw. The best strategy would be getting the king to a7 and free the rook. Note that the black king can not get too close to the white pawn because of the threat of R-h8.
1…a7 and is draw. The best strategy would be getting the king to a7 and free the rook. Note that the black king can not get too close to the white pawn because of the threat of R-h8.