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amacivn
27-May-09, 02:23
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 Rook End Game
I've just accepted the offer of a draw , my opponent offered because he doesn't think you can win with just a rook and king , i thought you could but who is right ? what is the best way to do it , if it can?
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Of course you had a clear win. If his pawn only 3 squares away from promotion then it would be a draw but it is a long way!
You can put your rook in front of the pawn (so his king must guard the pawn) and bring your king next to the pawn so you can capture with your rook: 1.Rc2 c5 2.Ke4 c4 3.Kd4 and next you can capture the pawn with the rook
I believe you know how to mate with a rook.
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You had an easy win. Yes, you can mate with a king and a rook against a king. The basic idea is to get the rook on a file in front of the king. Once you achieve a position of opposition with your kings, then you can check the king and drive him back a file. Once you have him on the last file. You force direct opposition with the king and then when the rook checks it's mate. You can of course do the same thing with ranks instead of files.
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try this site for a better explanation.
www.chesscorner.com
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amacivn
27-May-09, 06:31
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Rook End Game
I can't believe what i did , at the time i thought he needed to make a mistake , and it's very rare he does, i didn't want to chase him all over the board-my error ,i can see it now - I've not heard of that site, but will check it out - my question seems so daft now !
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I found a puzzle that might help #7107 although there might be other puzzles its just the first one that I found .
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Chess Puzzles...
There have been quite a number of K plus R vs lone K puzzles on the front page of this site recently. Has someone been listening then?
I guess the trickiest mates are these;
[a]
b
White to play is instant death (1.Ra1#), but what if it's Black to play? E.g. 1...Kh4 2.Kf4 Kh5 is no good. The surest method is, whichever way the enemy K moves, to move your rook along the file to a safe spot, i.e. at least 2 squares away from your own king, on the other side of your king from where the enemy king has moved to. Got that?
E.g. 1...Kh4 2.Rg7 (Rh7 is equally good) Now the enemy king may not go to h5, so 2...Kh3 is forced. Your own monarch sets off in pursuit: 3.Kf4 Kh2 4.Kf3 Kh1 5.Kf2 Kh2 6.Rh7#.
If the enemy K goes the other way, then the line goes:
1...Kh6 2.Rg3 (Rg2 is fine) 2...Kh7 3.Kf6 Kh8 4.Kf7 Kh7 5.Rh3#
Suppose the Kings were facing off nearer the corner?
b
Now, Black van't go into the corner because of the mate, so must come out.
1...Kh6 ...
But White's rook has no "safe" square on the other side of his King (2.Rg9 would be OK :))
Here White can adopt one of two methods:
[i] 1...Kh6 2.Kf6 and continue as indicated in the previous diagram, or there is this alternative method:
[ii] 1...Kh6 2.Rg8
Now, Black can continue 2...Kh5 3.Kf6 Kh4 4.Kf5 Kh3 5.Kf4 Kh2 6.Kf3 Kh1 7.Kf2 Kh2 Rh8# but what about 2...Kh7, then? There's no immediate mate.
White plays the rook past the King along the rank. I like to play 3.Ra8 here, but that's just a flourish. 3.Re8 is just the same.
So, from the diagram: 1...Kh6 2.Rg8 Kh7 3.Re8 Kh6 4.Re5 Kh7 5.Rh5#
[b] The second tricky situation arises from this sort of situation. Again, with White to move, it's mate on one, but what if it were Black (the defender) to play?
b
Black might try to escape on the opposite side of the rook:
1...Kh6 2.Rd7! Zugzwang! 2...Kh5 3.Rh7#
This should give the clue to what happens if Black plays 1...Kh4. White wants to set up the diagram position - or something very like it - with himself to move. He plays, then, a waiting move: 2.Re3 (say), whereat Black has no choice but to walk into the mating net.
Here's a puzzle. If you can answer it correctly (and demonstrate the answer), then you will know all you will ever need to know about K plus R vs K endings.
Imagine a chessboard of infinite size, but having one finite corner, a1. That is, from a1, the board has an infinite number of files to the right, and an equally infinite number of ranks stretching into the distance. Clearly the board has 2 finite edges - the 1-rank, and the a-file.
You have the White pieces: Your K on a1 and your R on b1. You are told that somewhere on the board, on such and such a square, stands the Black King.
The question is: is it possible to checkmate the Black King with your K plus R? If you answer "No", can you show why not? If you answer "Yes", can you show how you would go about it?
Cheers,
Ion
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Puzzle on infinite board
Obviously there can be no 50-move rule, but it seems possible to corner the black king.
1. Cut the black king of with the rook, either along a file or a rank, say a rank.
2. March the white king to a higher rank than the black king. This can be done since the black king is restricted in rank by the rook. Do not worry about files at this moment.
3. Once the white king is a few ranks higher than the black one, use the rook to cut off the black king from files to the right of it. The rook does does no longer need to restrict ranks now, the white king will make sure there is no escape along the ranks. When the rook is attacked it can move out of reach to a very high rank, but while keeping the same file.
4. The white king now marches towards the file which the rook controls, always staying on a higher rank than the black king. The white king has no problem reaching that file since it has a head start of a few ranks, so the black king can not shoulder it.
5. Once the white king comes to the file just before the one controlled by the rook, the rook comes back to one rank lower than the white king. The black king is now boxed in along both file and rank by the rook and the rook is protected by the white king.
Further restriction is simple. E.g. if the black king goes in opposition, the white king can go on the same file as the rook, one rank higher than the rook. The black king has either to give up a file to the rook or go back a rank allowing the white king to take opposition when the rook can take away a rank the next move.
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algol...
... Sounds about right.
The point is that the rook forms a kind of box that contains the king. The only point of egress for the enemy king is the square upon which the rook stands, hence the need for the WK to come and defend the rook. Once the BK has been contained, the mating process is straightforward (if lengthy!) and the BK can always be gradually driven onto an edge or into a corner.
There is an optimum method of containing the Black king that requires just 3 rook moves (though a less optimum method still fulfils the requirement of the puzzle). Suppose the Black king stood at (x,n), White moves the rook to (x+1,1), Black responds 1...K(x,n+1) where x+1 means the "letter" after x (supposing we had an infinite alphabet. It might be easier to think of squares as numeriacl coordinates, so that a1 is (1,1) ).
Now the rook goes to some rank to form a "box". What rank? The minimum rank has to be x+n+3. The rook, then, moves 2.R(x+1,x+n+3). The King, presumably, will try and get as far from the corner as possible, so 2...K(x,n+2). Now, the WK moves up the diagonal until the BK reaches ....K(x,x+n+2), whereupon White replies R(x+n+1,x+n+3). Actually, the rook can move further to the right if desired, but it must move at least to the (x+n+1)-file. Now, the BK will respond ...K(x+1,x+n+2); The WK continues along the diagonal, reaching K(x+n+1,x+n+1) just after Black reaches ...K(x+n-1, x+n+2). Now the BK is contained. It can not approach the rook and will gradually be driven back and mated.
Here an example with actual numbers. At the minimum, you will need 13x13 board to play it through:
WK at (1,1), WR at (2,1), BK at (6,3) [f3]
1.R(7,1) K(6.4)
2.R(7,13) K(6,5)
3.K(2.2) K(6,6)
4.K(3,3) K(6,7)
5.K(4,4) K(6,8)
6.K(5,5) K(6,9)
7.K(6,6) K(6,10)
8.K(7,7) K(6,11)
9.K(8,8) K(6,12) Now the rook is threatened with capture, and must retreat.
10.R(11,13) K(7,12)
11.K(9,9) K(8,12)
12.K(10,10) K(9,12)
13.K(11,11) ... And since K(10,12) is illegal (by placing the kings on adjacent squares), Bllack must begin the long retreat to checkmate. With correct play, Black's king never has the slightest chance of escaping the net as it closes in.
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Optimal Solution
Figuring the optimal solution out is a lot harder than just any method :-) Thanks for the puzzle.
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Of course if you don't move the rook far enough, it doesn't really matter. You just pull it back out of reach again, and continue moving your king along the long diagonal.
I haven't examined what happens if Black tries to stop the WK, neither. That can get pretty interesting as well. Suppose the BK were quite close (3,3), say.
1.R(4,1) K(3,2)
2.R(4,6) K(3,1)
3.K(1,2) K(3,2)
4.K(1,3) K(3.3)
5.K(1,4) K(3,4)
6.K(1,5) K(3,5)
7.R(8,6) K(4,5)
8.K(2,6) K(5,5)
9.K(3,7) K(6,5)
10.K(4,7) K(7,5)
11.R(8,9) K(7,6)
12.K(5,8) K(7,7)
13.K(6,9) etc.
Black can certainly slow White down, but there seems to be no way to avert the inevitable.
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If the King were far enough away from the finite corner (which in a random placement he probably would be), you couldn't do it in the required 50 moves
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Yes you could,
if you know that there are two methods to mate with the rook. First method is using the opposition technique, second is operating the rook near the king while confining the defending king into smaller and smaller "rectangles". The combination of both methods will mate the king in less than 20 moves.
First, move the king to the center where you want to confine the defending king in about 5x5 rectangle. It takes about 3 king's moves and 1 or two rook's moves. Here is an illustration of the second method:
1.Kc2 Ke5 2.Kd3 Kd5 3.Ra4 Re5 4.Rd4 Rf5 5.Re4
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On an infinite board, I am not sure how you would define the center. However just place him on the long diagonal from the finite corner , say about 100 squares out ( which is quite a bit short of the center) so that he is a hundred squares from the two edges and your going to have a hard time confining him to a 5x5 rectangle in 3 king moves plus 2 rook moves.
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Rook+King VS Pawn+King
I couldn't believe that the original question was about rook+King VS king alone. IMO such simple ending was supposed to be taught by someone "older" when we are taught about this game.
Endgames are supposed to be the first lesson taught to students in chess schools, especially in Russia (probably not in England). But nowadays begineers tend to spend too much time studying the openings...
Anyway, rook endings with a single pawn in the defending side is not simpler, but can be simplified if we understand the three techniques related to this ending:
(1) Cutting off the king from defending the pawn
(2) Promotion into a knight to draw the game
(3) The defending king blocks the attacking king from reaching the pawn.
(1) The rook can cut the defending king from assisting the pawn to promotion if the king is on the third rank or less. If the pawn is promoting himself without the king's assistance then the rook can attack it near the promotion rank. If the pawn doesn't want to promote himself then the attacking king will reach/capture the pawn. In the following diagram WT will move with 1.Rg5! If the pawn moves 1...c3 2.Rg3 c2 3.Rc3 and the defending king cannot do anything to help.
(2) If the pawn is not in the corner (a-pawn or h-pawn), there is a situation where it should be promoted to a knight to achieve a draw. 1.Rh2+ Kd1! 2.Kd3 c1N+! (of course it should not be promoted into a queen) 3.Ke3 Nb3! 4.Rb2 Nc1! draw (or 3.Rc3 Ne2+! draw)
(3) If the defending king is beside the pawn and the attacking king is far away, then the defending king should block the attacking king from reaching the pawn (The attacking king should reach the pawn because the rook cannot just capture the defended pawn without help from his king). Here the opposition technique also applies. In the following diagram, the attacking king has a plan to chase the pawn from b6 to e2 and capture the pawn with the rook just before it is promoted on f1. But the defending king has the tempo to block the attacking king:
1...Kf3! (If 1...f3? or 1...Kf5? the defending king doesn't have the tempo to block the attacking king)
2.Kc5 Ke3!
[based on the opposition technique, not 2...Ke2? 3.Kd4!, not 2...Ke4? 3.Kc4 Ke3 4.Kc3! Ke2 5,Kd4 f3 6.Ra2+! Ke1 7.Ke3 1-0 (still losing is 4...f3 5.Re1+! Kf2 6.Kd2)]
3.Ra3+!? (If 3.Kd5 f3! 4.Ra3+ Ke2! 5.Ke4 f2! 6.Ra2+ Ke1! 7.Ke3 f1N+! and the knight promotion draws the game)
3...Ke4! (Not 3...Ke2?? 4.Kd4! f3 5.Ra2+ 1-0)
4.Kc4 f3! 5.Ra8 f2 draw
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blake78613,
sorry, I think I misunderstood you.
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You are right...
... If the BK were at (51,51) it would take well over 100 moves just to encircle him. But in keeping with the infinite board size, we can dispense wityh the 50-move rule, can't we? I any case, I believe that in international tournaments, if you can demonstrate a win that happens to take more than 50 moves, I believe you are allowed the opportunity to try.
On a normal board, I believe from any (non-trivial) position, a K+R mate will take fewer than 20 moves.
I did wonder, yusuf_prasojo, whether in fact your original question was about K+R vs K+P. I'll get back to you on that...
Cheers,
Ion
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At one time the rule was, you were allowed twice the min no moves to mate if that number exceeded 50. I'm not sure if that rule is still in existence. I have hunted for it without any luck.
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50-move rule
blake78613,
I thought that FIDE moved away from all those endgame exceptions and the simple 50-move rule is back in its old glory. The official FIDE website has the handbook: Article 9 which deals with the drawn game does not mention those exceptions.
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ionadowman, actually it was amacivn 's question. And I think algol is right. There was the 75-move rule because of such a decisive mate with more than 50 moves. But the 50-move rule is back again now.
What I don't know (hope any of you do) yet is in blitz or rapid, 50-move rule does not apply because you don't write down your moves, right? So if you have say K+R+N vs K+R, will it automatically be drawn or you are given a chance to mate within your time limit?
Remember that there are exceptions to the commonly known draw because of specific position on the board. The K+R+N vs K+R for example, has the mating possibility if located near the corner (Remember when Kasparov controversially managed to beat Polgar!).
The same thing happened here lately in an open tournament where everyone started to complain when a GM having the knight refused a draw. The position was not in the corner, but I think he had the 50-move right to expect his opponent made a mistake (It was not rapid chess).
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yusuf_prasojo
After getting to sac a Knight for his last couple pawns, I played out that ending of K+R+N vs K+R in a USCF-rated (but non-FIDE-rated) OTB tournament a number of years ago, vs BOGG , who is also here at GK now ( & he was the #1 highest GK-rated player for a time, actually.). As you might guess, I had the side that was short of a Knight. It was a grueling affair & took us about 8 hours to finish the game, to a Draw result. But he did have the right to play it out to the 50 move rule. And indeed was correct to do so, since I slipped at one point & may have gotten into a losing sequence. But he also overlooked the refutation for just one move & that let me slip out of it (Quite by accident too, since I had not realized my close call to losing until he mentioned his oversight after the game. Of course, knowing such things is why he was Master & Champion of Region-7, the Mid-Western USA ... and I was just an Expert!)
* * * *
I think maybe it happened because it was such a tiring affair of so very many moves considered and made. It was all played in one sitting, due to being a game from the next to last round of the tournament, and those are not allowed to be adjourned; rather must be completed before the start of the Final Round. Needless to say, the tournament was delayed a bit for Final Round :)
* * * *
***
But anyway, the time control of that event was probably something like 40 or 50 moves required in 90 minutes. Which is not a "Sudden Death" time control (such as "Game in 60 min" for example). But even with a Sudden Death time control the side claiming a Draw based upon "Insufficient Losing Chances" would have to have a determination made by the TD of whether the position qualified for that. And the standard they used here was generally something to the effect that:
'the position should be able to be held by a Class-C player even against a GM'
Now that is a very tough standard, and personally, as a former TD myself ... I would not think this ending to qualify to that standard from the side that is down a Knight. Tho probably would, if it were the Knight-plus player trying to claim the Draw himself. Also, there ARE positions that start with those pieces which are Wins due to the starting position favoring the Strong-Side in that way.
* * * * *
I am wondering too however, if such position would be considered as a Draw by the World Blitz organization (started by GM Walter Browne, in early 80's I believe!? Was/is it "WBCA"?). There they had a tough stance against players who would not agree to split the point when their opponent claimed attainment of a situation known to be a Draw with best play. Perhaps trying to just run them out of time in a position known to Draw for instance. I forget if they just did declare it Drawn by the TD; or if the TD might not forfeit the stubborn player & give the game point to the underdog, as I suspect that they could then do.
So I wonder if this situation could be claimed drawn under WBCA. Or also Quick Chess or Rapid Chess rules ?!
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ccmcacollister,
BOGG once sent me a message regarding Gambit Staunton. I just realized now that both of you have the same name :))
About chess playing rule, I guess it would be better if the TD authority were taken out as much as possible. I think it is not that difficult to standardize "everything", is it?
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Speaking of Rook vs Pawn in endgames...
... Here's something from the Introduction in the book on Rook Endings published by Grigory Levenfisch and Vassily Smyslov. It is, I think, quite instructive - as you would expect - in showing in what circumstances a rook will beat the pawn, and when the pawn will hold out.
The plot begins in 1890, a game between W.Steinitz (White) and I. Gunsberg (Black). Steinitz found himself a pawn down and Black's pawn about to promote, as in the diagram (Black to play):
b
White's check is part of his plan of defence. Right now Black is threatening ...Rg1+; ...a1=Q, but has now to get out of check. White wants to capture the g-pawn, and place his hopes on threats to promote the h-pawn to force Black to exchange his rook for it and draw the game.
Black played
1...Kf3 2.Ra3+ Kf2 3.Kxg6 Rg1+ 4.Kf7 a1=Q
5.Rxa1 Rxa1 6.h5 Rh1 (Rooks go behind the passed pawn)
7.Kg6 Rg1+ 8.Kf6 Rh1 9.Kg6 Kf3 10.h6 Kf4
11.h7 Ke5 12.Kg7 ..
And Black could make no further progress. If 12...Rg1+ 13.Kh8 and the rook must again move to avoid the Stalemate. A non-check, and the White pawn will promote. Steinitz chose a well-known sort of defence in this kind of ending.
As transpires, though, Black could have won! Gunsberg's mistake came right at the beginning of this sequence, when his King went the wrong way:
1...Kd5!
Looks counter-intuitive, don't it? Where is the White King to hide from the checks? Black is happy to check all day - good enough for him! The b-file beckons, but it seems much too far away from the K-side...
2.Ra5+ Kc6 3.Ra6+ ...
Now, White could go for broke here: 3.Kxg6 Rg1+ 4.Kf7 (say; The WK dare not go onto the h-file) a1=Q 5.Rxa1 Rxa1 6.h5 Rh1 7.Kg6 Kd7
8.h6 Ke7 9.h7 Kf8 and the pawn falls. If instead 9.Kg7 Rg1+ 10.Kh8 Kg6 11.h7 Ra1 wins.
3...Kb7 4.Rxa2 Rxa2 5.Kxg6 Kc7 6.h5 Kd7
7.h6 Ke7 8.h7 Rg2+ 9.Kh6 ... (9.Kf5 Rh2 10.Kg6 Kf8, as seen already)
9...Kf7! 10.h8=N+ Kf6 11.Kh7 ... (every other move loses the knight at once; how about this one?)
11...Rg1 and the knight falls, or it is mate. Black wins.
A remarkable position!
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Original position
Original position is  game
In that position - White has an easy win...
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yusuf_prasojo ...
... gave probably White's simplest method of containing and winning Black's pawn, and then the game. Actually, has White's King stood on the h-file - at h6, say - it was still a win to White, with White to play.
What is puzzling is Black's choice of pawn move. Why advance it the one square instead of two? The threat to promote is what will save Black, if his game is to be saved. However, in the game, 54...c5 won't save Black:
54...c5
55.Rc2 Kb4
56.Ke5 c4
57.Kd4 and the pawn falls.
Even had the WK stood at h6, Black's counterattack just fails:
Position with Black to play, White's K relocated to the h-file.
b
54...c5
55.Kg5 Kb4
56.Kf4 Kb3
57.Rh2 c4
58.Ke3 ...
Now, what? 58...c3 is simply met by 59.Kd3 followed by 60.Rc2 and 61.Rxc3 winning. Nor does 58...Kc3 help as 59.Rg2 forces the BK back: 59...Kb3 60.Kd4 c3 61.Kd3 as before. Finally, 58...Kb4 59.Rc2 (is one method) ...Kb3 60.Rc1 c3 61.Kd3 etc.
So the King and pawn team is by no means a guarantee of a draw. The pawn has to be sufficiently far advanced and the enemy King sufficiently far away for a draw to be on the cards for the King/pawn pair. For instance
w
and Black is close enough to promotion to force White to exchange before his King can intervene effectively.
54.Kg5 Kb3
55.Ra8 c3
56.Kf4 c2
57.Rc8 Kb2
and now 58.Ke3 c1=Q or 58.Rb8+ Kh2 both lead to draws.
Finally, I can't leave this discussion without pointing out that in certain, very special circumstances, a rook and pawn will defeat the King and rook. Check this out:
w
The pawn is 2 squares away from promotion, but after it advances one square, the rook stands too close to the WK and is in no immediate position to hold back the pawn. He has somehow to buy time:
1.c7 Rd6+
2.Kb5! ...
Not 2.Kc5 as after 2...Rd1; 3...Rc1 Black will pick up the pawn (or queen). Nor does 2.Kb7 Rd7 give White anything more than a draw.
2...Rd5+
3.Kb4 ...
The same considerations apply as in the previous move.
3...Rd4+
4.Kb3 Rd3+
5.Kc2 ...
Whoops! Now the back rank, and hence the whole c-file is off-limits to the rook! There is no way to prevent the pawn from queening... is there?
5...Rd4!!
What a move! If White promotes, then 6.c8=Q Rc4+! 7.Qxc4 Stalemate! A draw. But What can White do about it? If 6.Kc3 Rd1 draws. The trick is, White does promote after all:
6.c8=R!! ...
You gotta be kidding me, right? how can King and rook beat King and rook? OK, White threatens mate right now... But that's easily fixed:
6...Ra4
Only move. Now how does White win from here? It all becomes clear with the next move:
7.Kg3!
Curtains. To avert the mate at c1, Black has to give up his rook, after which it's the standard win for White.
The diagram position is a famous one - a study by one Saavedra from about a zillion years ago.
Incidentally, there is one loose end to this that you might want to check out. After 1.c7, what happens if Black defends by 1...Rd2!?
Have fun... :)
Ion
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...
... Bumping, to bring it alongside a similar thread,,,
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