|
|
| |||||||
| From | Message | ||||||
|---|---|---|---|---|---|---|---|
|
 Another Endgame thread.To kick this off, I will look at something that when I first encountered it as a schoolboy, gave me a better appreciation of the possibilities in an endgame. It was this: White to play draws, as he simply promotes the pawn. But what if it were Black's move? 1...Qb6ch White could defend the pawn by 2.Kc8, but Black would then take the opportunity to bring his King closer the action by 2...Kg2. White can do better: 2.Ka8! ... No, not insanity, for 2...Qxc7 is Stalemate! Since he can't take the pawn without Stalemating, Black has at least to stop its promotion (2...Qc6, say) whereat 3.Kb8 protects it again. White's king is too far away to break the deadlock. In fact, given this cofiguration of WK, WP and BQ, the BK has to be standing at one of the squares shown here by the rooks and the king itself in order to achieve a win for Black: E.g. King at e6 simply plays 1...Kd7 and wins the pawn King at a5: 1... Kb6 2.c8=Q ... Underpromoting to a knight will enable White to survive a move or two longer. Otherwise 2.Ka8 Qc6ch and mate next move. 2... Qd6ch 3.Ka8 Qa3ch 4.Kb8 Qa7#. To be continued... Rook's pawns vs Queen. |
||||||
|
|
||||||
|
A rook end game... (This is a very long posting...) One of the things I have noticed on Gameknot, is the number of rook end games I have had to play. Some of them were straightforward wins with extra material, others I have has to fight hard to save, usually - but not always - with success. I thought I would show this one from 2008, not especially special, but in which, despite the reduced material, tactics play their part. You will see the 'two pawns vs rook' motif make a brief appearance as well... Here's the plot: White: archduke_piccolo (2041) Black: webb31260 (1738) Early in the middle game White won a pawn, and the King side attack subsequently mounted by Black cost him another pawn trying to break through. The repulse of that attack, then, left Black two pawns down, but they were not going to be so easy to exploit with his active 'rook on the seventh'. Black had just played 38...Nh5-f6 when this story resumes from the diagram. 1.b5! ... Tactics. White has spotted an attractive idea and offers Black the d-pawn to bring it about. But embedded is the thematic idea of levering open the way for the c-pawn by the threat of b5-b6 - with suitable preparation, of course. 39... Nxd5 40.Bxg7 Kxg7 41.Rxd5 Rxf2 What has this flurry of exchanges achieved? The game has been reduced to a 'pure' rook and pawn end game, and White's lead reduced to one pawn only. The break 42.b6 won't do because after 42...cxb6, White can't really bring the rook betimes behind the pawn. Well, he can, but it won't work: 43.b6(?) cxb6 44.Rc5(??) dxc5 45.c7 Rf8. But such wasn't my plan. It was this: 42.Rxd6! ... And here's were the two pawns vs rook comes in. The idea is that after 4...cxd6, White wins with 5.c7 or 5.b6 as he chooses. 42... Rf1ch 43.Kg2 Rb1 Clearly Black saw through my cunning plan. But it meant I got away with an extra pawn, and recovered my earlier two-pawn advantage. 44.Rd7ch Kf6 45.Rxc7 Rxb5 46.Rd7 ... Protecting the passed pawn from the front is awkward, especially when the pawn is so close to promotion. Ideally I want the rook behind the pawn, but Black will want his rook there as well. However, protecting the passer from the side will be an improvement, and allow time to bring the White King into the action. 46....Rb2ch 47.Kf3 ... I was prepared to give up a pawn to bring the King up to the battle front. 47...Rxh2 48.Ke4 ... Another idea was 48.Rd6 at once. 48... Ke6 49.Rh7 Kd6 50.c7 Rc2 Forced, of course. 51.g4 ... What White would now like to see is 51...Rxc7 52.Rxc7 Kxc7 53.Kf5 Kd6 54.Kg6 ... Whether Black tries to defend by bringing his King across to the King-side, or counter-attacks by going after the a-pawn (probably the better plan) White is winning in this line. So... 51. Rc5 An attempt to hold back the White King. 52.c8=Q Rxc8 White is going to rely on his g-pawn to bring home the win. 53.Rxh6ch Kd7 it is unclear why Black chose this instead of ...Ke7. Possibly he was hoping to induce 54.Kd5 (Opposition) whereupon 54...Rg8 would have been a little bit embarrassing. 54.Ra6 ... White is not especially going after the a-pawn, though I'll take it given the chance. But it is a threat to distract Black's attention from the main action on the g-file. 54...Rc4ch 55.Kf5 Ke7 56.Ra7ch Ke8 Again, slightly puzzling. ... Kf8 was what I would have expected. 57.g5 Kf8 It is possible that Black had decided a move earlier that he did not want the king to be standing on f8 already, though it is hard to see that makes a huge difference, given that the rooks on both sides can make 'tempo' (i.e. temporizing, or 'waiting') moves. True, Black is more restricted there, but all you need is one (...Rc4-d4 and ...Rd4-c4). 58.Kg6 Ke8 Black was practically in a 'zugzwang' - a situation in which one is forced to move, but every move is bad. 58...Kg8?? would have been mate in two; 58...Rc6ch would have led to 59.Kh7 and White wins. Mind you, Black might have tried for a 'Marshall Swindle' in this line: 58...Rc6ch 59.Kh7 Rc4 60.g6?? Rh5 checkmate! Of course, White would instead have played 60.Ra8ch Kf7 61.g6ch Kf6 62.g7 and after 62...Rh5ch, 63.Kg8 ... 64.Kf8; or 62...Rc7 and White can choose between 63.Ra6ch Kf5 64.Kh8; or 63.Kh8 Rxg7 64.Ra6ch Kf7 65.Ra7ch Kf6 66.Rxg7. Finally, a 'tempo' move like 58...Rd4 led to 59.Ra8ch Ke7 60.Kg7 ... 59.Kg7 Re4 60.g6 Rc4 61.Kg8 ... Black resigned at this point, figuring the situation was hopeless. But I think there was still a little bit of resistance in the position, with some tricky but 'useful to know' manoeuvring to close out the win. So, let's have a diagram of the final position: 61...Rg4 62.g7!? ... Probably 62.Kg7 is better, but let's go with this advance. There's some interesting stuff, here. 62...Rh4! A very awkward situation for White! 63.Ra8ch ... I believe this finesse improves upon moving the rook at once to a5. 63....Ke7 64.Ra5 ... The plan here is fairly complicated to state, but actually quite simple. White needs to give the King cover to get out from in front of his pawn. The threat here is to check the BK away from the e-file so White can play Kf8. [A] If Black plays 64...Re4, then 65.Rh5 seals the deal: the pawn won't be stoppable after Kh8 or Kh7. [B] If Black moves his rook along the h-file somewhere, White could simply play Rxa5, and win with two extra pawns. That supposes White has no better plan (and he probably would have had). So we are left with: [C] 64... Ke8 65.Re4ch Kd7 66.Kf7 Rf4ch 67.Kg6 Rg4ch 68.Rg5 wins; This sort of cover you really should pack away into your end game bag of tricks! [D] 64...Ke6 Not ...Kf6; Kf8 ... wins at once (...Rc4; Ra6ch ... or Ra8 ..., followed by promotion). But now, what follows is really cute. It took me by surprise when I found it! 65.Kf8 Rf4ch 66.Ke8 Rg4 67.Ra6ch ... Or, maybe, Rxa4?! 67... Ke5 68.Kf7 Rf4ch 69.Ke7 Rg4 70.Ra5ch Ke4 71.Rxa4ch Kf5 72.Rxg4 ... And White wins. There's quite a few interesting motifs in this end game - one at least that surprised even me, now that I have come to investigate the 'what-ifs' more closely. Enjoy! |
||||||
|
|
||||||
|
What result? game You will see playing though it that it's a pretty large scale battle, swirling all over the board. During the course of the end game, Black (Janet) had to give up a rook for small change. At the final position, still with only three pawns for a rook, Black was surprised to receive the offer of a draw. She was dead certain that Black ought to win. I find these asymmetric end games most interesting. What I'll do here is examine the final position, and see whether indeed White can force a win from there. In another posting, I hope later to see whether he might have had better chances earlier. Here's the position, White having played 64.Ba1-b2 and offered a draw. Before making any moves, let us examine the salient features of the position: 1. Black has three pawns for a rook. 2. Two of those pawns are close to promotion. 3. The other pawn provides a fine safe central square for the bishop... 4... from which it protects all 3 pawns on their present squares. 5. Bishops of 'opposite colours' means that the White bishop can not come at Black's pawns. 6. The Black King in on the edge of the board, and could have been locked there if White had played 64...Rg8. What all that means is that White can not plan to go directly after pawns, as all Black has to do his hang tough with her King, playing tempo moves with the bishop if necessary. White also has to be take care that the h-pawn in particular doesn't run away on him before he can reel it in. White's plan, then, must be, by means of a mating attack, induce the advance of one of the flank pawns onto unprotected square. Black's defensive plan will be to keep the King active, if she can, whilst seeking out opportunities to stretch White's pieces with threats of promotion. Fascinating! My first thought was that this had to be a draw: Black had set up what amounted to a 'fortress' - and impregnable position by an inferior force. But then I thought maybe White could force a zugzwang. So I tried... 64...Kg6 65.Rh8! Now look! The Black King has no moves. The flank pawns may not advance. If Black were to try 65...f6? then comes 66.Rf8 Kg7 (66...h2 67.Rh8; 66...Kh7 67.Bxf6) 67.Rxf6 h2 68.Rxe6ch Kh7 69.Re1 (or Re8). Any bishop move towards the a-pawn loses the h-pawn. Bishop to c8 or g4 are obviously useless, but how about 65...Bf5? White plays 66.Rg8ch Kh7 67.Rg7ch Kh6 68.Kxf5 h2 69.Rg8 and mates shortly. Where does that leave Black? Precisely one move remains: 65...Bd7! Although this leaves the a-pawn unprotected, after 66.Ra8 Be6, then what? Now White has to form a plan. The one I came up with seems as good as any: manoeuvre the WK to f6 and search for checkmate or skewer possibilities on the h-file. 66.Rg8ch Kh5 Of the alternatives, ...Kh6 may be just as good, but I would not recommend ...Kh7 on account of 67.Rg7ch Kh6 68.Rxf7 ... and if 68...h2 69.Rf8 with the skewer (Rh8ch) to come. The reason for ...Kh5 is to advance the Black King whilst White advances his: 67.Ke5 Kh4 68.Kf6 Be6!?* This move I shall return to, but it seems pretty reasonable at the moment. 69.Be5 ... This places more responsibility on the bishop than it can comfortably handle: covering the approach marches of both flank pawns. But in fact it helps out the rook against the h-pawn e.g.: 69...h2 70.Rh8ch Kg4 71,Rxh2, safely picks up the pawn. So: 69... Bb3 A tempo move. There may be a better! 70.Bg3ch Kh4 71.Rg5ch Kh6 72.Ra5! ... Changing of the guard! I think 72.Be5 ... would have been a good alternative. +++As an exercise you might like to check out what might happen after 72.Be5 a1=Qch or 72.Be5 h2+++ Meanwhile, the threat is 73.Bf4ch Kh7 74.Rh5ch Kg8 75.Be5! Be6 76.Ke7! ... and an imminent checkmate. So: 72... Bd5! The bishop is immune! 72.Ra4! a1=Qch Immune to capture on d5, the bishop is not on c4! 72...Bc4 73.Be5! Kh5! 74.Rxc4 h2 75.Rc1. 73.Rxa1 ... Having knocked over one of the Black advanced pawns, White will be able to concentrate his forces in subsequent operations. *All this looks pretty promising for White, but recall the asterisk (*) at Black's 68th move? Let's go back there and have a look: We then thought that 68...Be6 looked reasonable. But how about this move: 68...Bg4!? Abandoning the a-pawn? Yes, but in a good cause. If now 69.Ra8, h2 70.Rh8ch Bh5. There you see the purpose of the bishop move: to obviate the skewer. 69.Rh8ch Bh5 Now the bishop is committed, but it is much harder for the White pieces to reel in the advanced pawns. 70.Kf5 h2 71.Bf6ch Kh3 (...Kg3 is just the same) 72.Rxh5ch Kg2 There is nothing more to be done: 73.Rg5ch Kf1 74.Rh5 Kg2; or 73.Be5 h1=Q 74.Rxh1 Kxh1 and a simple draw. Much the same sort of thing would have happened if Black had delayed playing ...Bg4 for one move. I am forced to conclude at this point that White's draw offer, based upon the belief that Black had enough resources, was correct after all. The key to Black's defence seemed to be ...Bg4! played at move 68 or 69 in the line we have been exploring. The notion of masking the potential skewer is not one that immediately sprang to mind! |
||||||
|
thats very interesting Ion. |
||||||
|
|
||||||
|
BTW |
||||||
|
archduke_piccolo 23-Sep-15, 19:18 |
Deleted by archduke_piccolo on 23-Sep-15, 22:02.
|
||||||
|
Editing... |
||||||
|
game And, this was the position. My last move 49...c3, but it was not to win a pawn. Instead, my goal was to promote because I watched a video and a game where when you attack a pawn, instead of taking, the opponent advanced with the plan being to promote. So, he played 50.bxc3, and instead of taking with 50...bxc3 (which would've ended in a draw by repetition), I played 50...b3 as I was planning, long term, how to promote with no way for white to stop it. However, what I overlooked was just how close his K was to my pawns. If it were further back, say on f4 or g4, the plan might have worked, and it definitely would've on h4 However, being where it was, he was able to move his K, and from then on, it was over. Oh yes, he also promoted, and for a while, I remember what I previously studied from ION that sometimes, one extra pawn, alone, isn't enough to win. And, I also remembered previous mistakes I made in the B+N mate which I failed by allowing what would've been a draw, which is in the end game study thread. With that being said, once I went wrong, I thought I could trick white into making a mistake so that the game would end in draw by 50 move rule, since no captures were going to be made. Well, I was wrong, and about 10 moves later, I resigned because Julio had an inevitable mating sequence with no way out. Best was 50...bxc3, and after 51.Kd3, it would've been an automatic draw. |
||||||
|
Mistake... Although Black's 50...b3 was a mistake that compromised the draw and led to the loss, in fact (the GK Engine notwithstanding) the position after 50...b3? 51.Kd3 Kg5 ...was not yet losing for Black! What the mistake has done is to make Black work a little longer for the draw, whilst leaving himself open to making a fatal error later on. This he did, and lost the game. But it was still salvageable at this point: 52.c4 Kf5 53.Kc3 Ke5 I would have preferred ...Ke6, but there is really nothing at all wrong with what Black played... 54.Kxb3 Kd4?? ...except that it permitted this fatal mistake! The right move was 55....Kd6, which led to a 'book' draw: 55...Kd6 56.Kb4 Kc6 (preventing White's King from getting in front of the pawn whence it could guide the pawn home) 57.c5 Kc7 58.Kb5 Kb7 59.c6ch Kc7 60.Kc5 Kc8! (The other K-moves lose. This is a vital thing to remember from this drawing technique) 61.Kb6 Kb8 62.c7ch Kc8 63.Kc6 Stalemate. 55.Kb4 Ke5 56.Kc5! ... Most accurate, though 56.c5 and 56.Kb5 also led to a win. From in front of the pawn, the King lead the pawn to promotion: a true example of political leadership! From here the win is straightforward and assured. |
||||||
|
|
||||||
|
|
||||||
|
game Now, in this position, I advanced, with the idea of connecting three pawns and promoting. So, now it's white to move, as I just played 49...g5?? Doing this not only allowed Ron to win back a pawn, but he almost got a draw, so although it seemed like an easy way out, this is where it became a real challenge, as I had to think about what to do to prevent a draw. Remembering those difficult mating courses and how I failed, it would be so much worse if I allowed a draw in a won position since it is the deal. So, I had to go back and forth coming up with my own variations. Best, however, was 49...Kg5, as now, not only can the pawns advance, but my K would've prevented him from taking.
|
||||||
|
@jkarp... 50.Rxh5 Re3ch I would have played 50...Rg2ch 51.Kf1 Ra2 here, but there are several roads to Rome. 51.Kf2 g4? This is the real mistake. Much better is 51...Ra3, and then advance the pawn. Reason? Now Black could play 52.Rxf5ch Kxf5 (It's no use playing 52...Ke4 on account of 53.Re5ch!) 53.Kxe3 Kg5 54.Kf2 Kh4 55.Kg2 g3 56.Kg1 Kh3 57.Kh1 g2ch 58.Kg1 Kg3 Stalemate. 52.Rh1? g3ch 53.Kg2 Re2ch 54.Kh3 ... This seems best, though Black could cut to the chase with another pawn sacrifice by 54...Rh2ch!? 55.Rxh2 gxh2 56.Kxh2 Kf3 57.Kg1 Ke2 and Black wins. 54...g2 55.Rg1 Kf3 56.Kh2 f4 57.Rd1 Kf2 58.Rg1 f3 59.Rc1 Re4!? Here I would have preferred 59...Re1, which pretty much wins at once. If White tries 60.Rc2ch Black plays 60...Kf1 and that's pretty much the end of the story. But the text move certainly does not compromise Black's winning advantage. After another 6 or 7 moves, Black forced a pawn through and White resigned. |
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
Look before you leap... (Longish posting)game This situation at move 44 was what engaged my attention: White was in check; his move is obvious: 45.Kxd3 ... Now came an obvious piece of tactics from Black: 45...Rxe4 The plot is clear: if the King takes the rook, then ...Nd2 forks K and R, leaving Black with the piece ahead in a N-and-P vs bare pawns ending. In view of this, White elected to keep his rook as offering his best chance, and played: 46.Rb4 ... After 46... Rg4 47.Rxc4 Rxg3ch 48.Ke2 ... (K to the 4th rank would have been disastrous after ...Rg4ch and the rooks come off) 48... Rxa3. Two pawn down in a rook and pawn ending, White went on to lose. But what intrigued me was the notion of letting Black play out the fork! Let's review the situation after Black's 45th Let's see what happens: 46.Kxe4! Nd2ch 47.Kd3 Nxb1 48.a4 Na3!? * (It turns out Black has a better move than this, but you'll have to wait until the second-last paragraph of this posting to find out what it is - unless you can figure it out already!) 49.Kc3 ... Check it out: the knight has but one reasonable move: 49...Nb1ch but then comes 50.Kc2! Na3ch 51.Kb3 and a repetition! Draw! So Black would have to look at alternatives if he wants to seek out the win: a] 49...a6 The idea is to give up the knight for a temporary win of a pawn and hope to have time to obtain a decisive advantage on the K-side. 50.Kb3 Nb5 51.axb5 axb5 52.Kb4 g6 53.Kxb5 ... Not hxg6 which helps Black on his way. 53...gxh5 (I'll leave 53...g5 for you to look at, but I reckon that is drawn at best for Black) 54.Kc5 Kg6 55.Kd4 Kg5 56.Ke3 Kg4 57.Kf2 ... It is clear there is no win for Black here! b] 49...Kg8 To bring the King into action whilst White is busy going after the knight. 50.Kb3 Kf7 51.Kxa3 Kf6 52.Kb4 Kg5 53.Ka5 Kxh5 54.Ka6 Kg4 55.Kxa7 Kxg3 56. a5 h5 57.a6 h4 58.Kb6 h3 59.a7 h2 60.a8=Q ... and White wins! Clearly this will not do for Black! C] 49...g5! This has the same idea as [B] but clears the way for a shorter route for the Black King. Now, by 'counting moves, one discovers that one's instinct NOT to play 50.hxg6 e.p. ch is correct: it simply helps Black on his way, the rook-pawns notwithstanding. So: 50.Kb3 Kg7 51.Kxa3 Kf6 52.Kb4 Kf5 Observe how neither side moves the rear pawns. The reason is that it would simply gain time for one's opponent. The pawns are goners, so the best they can do is delay the inevitable by staying put, and causing the opponent to spend more time in their liquidation. The point is that it takes so much longer to clear the routes to the queening squares for White's a-pawn and Black's g-pawn. 53.Kb5 Kg4 54.Ka6 Kxg3 55.Kxa7 Kh4! 56.a5 g4 57.a6 g3 58.Kb8 g2 59.a7 g1=Q 60.a8=Q ... Draw? By no means! 60... Qg8ch 61.Kb7 Qxa8ch 62.Kxa8 Kxh5 63 Kb7 Kg4 64.Kc6 h5 ... ...and the pawn simply runs home to Queen. D] 49...g6 Without going into details, I have found this line also wins for Black. So now we know why White did not after all allow Black to carry out the K-R fork. It is unlikely that either player analysed the position as deeply as this, simply judging (correctly) that after the position reached at move 48...Na3 49.Kc3 (as discussed here) or, better yet after 47...Nxc1 48.a4, advancing the 'backward' g-pawn would have led to a winning ending for White. The ...g5 thrust is stronger played a move earlier, at move 48, as it takes so much longer for the White King, after taking out the knight on b1, to intervene to attack on the Q-side or to defend on the K-side. Ain't end games fun, though? I was quite struck by the depth of the tactic inaugurated by Black's 45th move. |
||||||
|
archduke_piccolo 04-Jan-16, 03:50 |
Deleted by archduke_piccolo on 04-Jan-16, 12:34.
|
||||||
|
You say it is whites move although the black king is in check? ? |
||||||
|
Damn - I thought I had checked the position, too... GM Wei Yi had White this position in a game at last week's Qatar Open tournament. Now, with a move like 1.a3 or, say 1.Kf3, White could draw. But instead White played 1.Qxc4. The question is, what was the result of the game? Had White seen something to win the game... or missed something that would lead to a win for Black? If so, what was it? Over to you... |
||||||
|
Two months... In the diagram above, After GM Wei Yi played 1.Qxc4, the game ended VERY quickly: 1.Qxc4?? bxc4 2.Kf4 ... White has no choice. Any other move, and the c-pawn gets away on him. 2...f5!! The killer! White promptly resigned. There really isn't a lot he can do, now. Committed to reeling in Black's c-pawn, he can't take Black's f-pawn, nor can he bring the g-pawn to protect his h-. So: [A] 3.g4? fxg4 and one of Black's pawns will queen. [B] 3.Ke3 Kh6 4.Kd4 Kxh6 5.Kxc4 Kg4 6.Kd4 ... (6...Kd5 won't be quick enough) 6...Kxg3 and nothing will stop the g-pawn. [C] 3.a4 Kh6 etc. [D] 3.h6ch Kxh6 is no help at all. |
||||||
|
Maybe this on will elicit a response: Nothing much to this, is there? K-R-N vs K-R is normally a 'book' draw, but the defender often has to work for it. The diagram position ought to have been a draw, too. Black is in check, and has three possible moves. In the game, he chose the only move of the three that lost. What did Black play, and how (or why) did White win? |
||||||
|
|
||||||
|
It is nice... 1...Kh5 does look wrong, doesn't it - voluntarily moving to the edge of the board to a place where the King has no moves!? But then you need a follow-up. Joe's line overlooks at one point the rook at a2. As it turns out, if White doesn't check the king, Black gets the chance to move his own rook and place the WK in check. Can we drive the BK into a mating net with checks? 2.Rh1ch Kg4 (...Kg6 also escapes) 3.Rh4 Kf3 4.Rh3ch Kg2 5.Rg3ch Kf2 and the BK is still at large. 1...Kh3 seems equally counter-intuitive, but Black escapes to a draw this way too. The reason I posted this is that, amazingly enough, the safest-looking move is the one that loses! 1...Kf3?? 2.Nh4ch ! ... Spotted it yet? Black has three possible moves, with these outcomes 2...Kf2 3.Rg2ch K moves 4.Rxa2 2...Ke2 3.Rg2ch K moves 4.Rxa2 2...Ke3 3.Rg3ch K moves 4.Rg2ch K moves 5.Rxa2 In all three, Black falls into a King-rook skewer, with an elementary win for White. |
||||||
|
Speaking of 'elementary' wins... Say, a position like this: This was from an enquiry about a draw, in which the enquirer wanted to know how much longer she had to survive to claim a draw by the 50-move rule. Well, I looked at the game, and at that point 90-odd moves had been reached, of which something like 44-45 moves had been this K+R vs K end game. I told her she simply needed to hang on for another 5-6 moves then she could claim the draw. What I didn't tell her - for obvious reasons - was that in the position then on the board, that was going to be no problem. Barring accidents, there was no forced mate in the time remaining. Clearly her opponent had no idea how to force a mate with a K and R versus a lone King. In fact, at the outset of this endgame, he could have forced the mate in three or four moves, as I recall. The game would have ended at move 49. Now, I don't want to enlarge on this unless there is a need for it. But to anyone who reads this, here is a little 'thought puzzle' to think about. Imagine a chess-board with just one finite corner, the a1-square, but which stretches to infinity, bounded by the a-file and the first rank. We shall identify the squares by numeric (Cartesian) pairs (x,y), where x is file and y is rank. Our e4 would be identified as (5,4). Now, you have the white pieces, King standing at (1,1) [a1] and the rook at (2,1) [b1], and standing somewhere out yonder, at (x,y), is the enemy king. If you can answer the following two questions confidently and correctly, you will have no problems in respect of KR vs K end games. 1. Can White force checkmate on such a board? 2. [a] If you answered 'Yes' to Q1, how? [b] If you answered 'No' to Q1, why not? Answer... another time. |
||||||
|
I was hoping for some response... I did hope, too, that someone might have had a crack at my puzzle. That really is disappointing. Imagine this board continuing up the screen to infinity, and to the right to infinity. The White pieces are standing at (1,1)(K) and (2,1)(R); the Black King at (8,8). Can White, however many moves it takes, force checkmate? Note: we have to rule out the 50-move rule here. Otherwise the puzzle would have no meaning if the Black King was standing at (432876, 2340987)! Q1. Can White force checkmate? A1: Yes. Checkmate can be forced. Q2: How? A2: Not so easy to answer in this forum. The plan goes like this. We'll use the above diagram, noting that it extends to a 9th, 10th etc file and a 9th, 10th etc ranks... 1. Reduce the King's mobility. In effect the board represents a box open on two sides. The rook will close those two sides. So the first move would be in the diagram position R(2,1)-(9,1). The enemy Will try and create as much room for himself, so will run up the 8 file 2. Bring our king up along the diagonal to the file one short of the rook's file, i.e. the 8th, the same file as the enemy King is on. 3. Slide our rook along the file, four squares beyond the enemy King (which will be standing at (8,16) by this, so we bring the rook to (9,20). We have closed the box, except for one little hole: the square upon which the rook stands. We have to stop up this hole. Black will still try and escape through it. 4.Continue our King's journey along the diagonal until Black's attacks the rook. By this time, our King will be on a file to the RIGHT of that upon which the rook is standing. Positions will be WK(10,10) WR (9,20); BK (8,19). 5.Slide the rook along a rank to the long diagonal square (20,20). Actually it need not go so far - (18,20) will do, but no harm in caution. The BK will now be constrained along the rank. 6. Continue with our King's diagonal moves. You will reach a point at which The BK can neither move up not to the right: the box has been closed off completely. relative positions: WK (18,18), WR (18+,20): BK (16,19). 7. Drive the BK by gradually reducing the size of the box, never letting the King escape. That's the easy bit! You can try this out on a 10x10 board as a game. The White King and rook stand at a1 and b1 as before; the Black King at c3. (Imagine this board with two extra ranks and files - 10x10). White has to checkmate the Black King. But Black wins if his King reaches any square on the 10th rank or the 10th file - the j-file, shall we call it. White wins by: 1,Rd1 Kc4 2.Kb2 Kc5 3.Kc3 Kc6 4.Rd10 Kc7 5.Kd4 Kc8 6.Ke5 Kc9 7.Rh10 Kd9 8.Kf6 Ke9 9.Kg7 Kf9 10.Kh8 Kf8 11.Rf10ch ... and White forces the mate. Note that Black might vary, but that merely brings the win closer. |
||||||
|
|
||||||
| |||||||
