Monday, September 17, 2007

A very difficult endgame


This is the position after 45...Kb6 in the Kramnik - Grischuk game. Kramnik played 46.Kg2 and the game ended in a draw. However, can White win this?

I have not read any analysis which shows a win for White. Having said that, I would take a shot with 46.h4 here instead if 46.Kg2. That is my intuition speaking. What is your take?

This is another good position to stufy from and for IM Ken Regan, the premier chess analyst to dissect :)
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20 comments:

Adrenaline101a said...

Im working this out in my head (as usual no chess sets cluttering up my desk) but isn't this a win for white?
white's bishop can get to the pawns black pawns a lot faster than black's night. and white's king is also a bit closer.
starting with Be8, then f7 then g8 etc etc can't whites bishp force blacks pawns forward? sooner or later black's pawns will be coming up against white's pawns AND white's king. all white needs is 2 king moves and black will require 4. that's got to generate a passed pawn with proper oppsition, no?

Anonymous said...

Rybka (2.1) - Crafty (20.9):

1. Be8 f6 2. Bf7 e5 3. Kg2 Kc5 4. Bg8 h6 5. Kh3 Kd6 6. Bh7 g5 7. Kg4 Nb3 8.
h4 Nd2 9. Kh5 e4 10. Kxh6 e3 11. fxe3 Nf1 12. h5 Nxg3 13. Bd3 g4 14. Kg6
Nxh5 15. Kxh5 g3 16. Be4 Ke5 17. Bf3
{Black resigns} 1-0

But Rybka - Fruit (2.3.1) was a draw.

Anonymous said...

Black can extract its Knight which is temporarily dominated by the wB.
The pawns are on one side of the board, which makes the wB less advantageous (over the bN) than it might be.
I don't see a win for White here. Can't Black just stick its Ps on black squares and stand its ground?

Anonymous said...

Interesting: how about trying Crafty (20.9) - Rybka (2.1).

Anonymous said...

> Interesting: how about trying Crafty (20.9) - Rybka (2.1).

Draw after 37 moves.

Beco said...

I was thinking in this variation.

The diagram shows the game at move 45...Kb6. But the next moves I think is accurate.

Let the game go until move

45.Ba4 Kb6 46.Kg2 Kc5 47.Kf3 Kb4 48.Be8 f6 49.Bf7 Nb3

Now here, instead of 50.e3, I suggest:

50.Bg8 h6 51.Bf7 g5 52.Kg4 Nc5
53.Kh5 Kc3 54.Kxh6 Kd2 55.h4 gxh4
56.gxh4 Kxe2 57.h5 Kxf2
58.Kg7 Ne4 59.h6 Ng5
60.Kxf6 Nxf7 61.Kxf7

1-0!

What do you think about this line?

Best wishes,
Beco

Adrenaline101a said...

"Can't Black just stick its Ps on black squares and stand its ground?
"
Black can indeed do this but that puts them closer to white's king than they are to Black's king. It just becomes a simple race and white gets there first. The trick if black does this is to not move whites' pawns too far forward and block white's king from going around/through on the white squares

Anonymous said...

How about Rybka 2.1 - Rybka 2.1.

I guess Rybka sometimes gets it wrong but it surely can't be that often these days.

Fábio said...

Empate.

KWRegan said...

Someone can read my mind well :-), as I was up past 1am analyzing this endgame, in particular some ideas raised on the PlayChess server during the game. My PGN file is about half-done, and I'll post whatever state it's in by bedtime (US ET) tonight.

First a disclaimer: I do analyze with engines, on hardware no worse than what Kramnik faced last Nov.-Dec., and 90% of my accuracy comes from that. However, there is still room for human skill in being an "Engine Whisperer". (The reference is to "dog whisperer" or "Horse Whisperer"---and note the analogy that a human on a horse is 3x faster than a human off one, but still must guide the horse in a race.) And this extends even to cases I've pointed out on the server where one should "switch off" or "throw away" the engine!

I believe there are several such cases here. The line in the second comment (anonymous) is similar to one communicated during the game as recommended by the engine "Deep Sjeng". With move numbers from the game (after Grischuk's 45...Kb6), it goes:

46.Be8!? f6 47.Bf7 e5 48.Kg2 (White can also play 48.Bg8 straightaway, but maybe it makes no difference to the timing of Black's idea?) Kc5 49.Bg8 h6 50.Kh3 Kd6 51.Bh7.

Now engines will tell you 6...g5, but as shown in the comment this allows infiltration by White's King and a passed h-pawn, whose danger versus a Knight is well-known to humans but (I infer) slow to be realized by engines.

Instead, leave the g-pawn en-prise and play 51...Ke7! 52.Bxg6 Kf8! Engines will tell you Black is more than a full Pawn worse, since the Black Knight is still in the corner, Black's Pawns are split, and White even has weaksquares f5-e6 by which to "penetrate". However, White's Bishop cannot quickly find squares to trap Black's Knight again like after 45.Ba4 in the game, and most to the point, after ...Kg7 Black will have a dark-square fortress. Unlike in any other kind of ending, a single Bishop can never budge a King off an opposite-colored square by forceful means---the only way is by Zugzwang. Nor can White ever assail the "weak" pawns on f6 and h6, except by Zugzwangs which I believe do not exist here. The final points are that the f6-e5 pawn formation is well-placed to stop White from marshalling his majority, much like the recommended f7-g6-h5 formation in a R+4 vs. R+3 ending, and White's Bishop is the "wrong color" to control h8. The only way White can make a passed pawn is by pushing f4 and later e4-e5. But after swaps on f4 and e5, White's only other pawn is the h-pawn. Black can then willingly chase down and sacrifice his Knight for White's e-pawn, leaving an h-pawn + wrong-color Bishop ending that is a theoretical draw.

Yes, I've run several engines to high depth on positions after 53.Bxg6 Kf8, noting that the +1.10--1.60 or so evals never go much higher, but the point is that the defensive idea came from human knowledge. One has to believe first, then verify afterward! The interesting question is how much Kramnik and Grischuk themselves were aware of which B+4P versus N+3P positions were promising to White.

Later around Move 50, several have noted that Kramnik had much more substantial winning tries. 50.e3!? was fine and well-principled, since the semi-forced 50...Nc5 obstructed the direct return of Black's King, but 51.h4?! was too slow, allowing an effective counter-attack. Based on my incomplete analysis, however, I believe that Black can survive by similar well-timed early Pawn sacs---and here I'm going further out on a limb: only by a particular well-timed sac of the h-pawn, defending the g-pawn initially by a fork on e5. Since I don't have my PGN file in my office right now (or even an engine:-), I'm not sure whether this was with Beco's 50.Bg8 or with 50.e3 first. More on this later, but meanwhile I'll be interested to see other ideas that readers of this blog come up with.

Jerry MacDonald said...

I would get into a position where I could sacrifice my bishop for 2 pawns. :)

Anonymous said...

b a4 to e8 black will go f7-f6 then just go down and start taking pawns,use king to defend your pawns and try to promote one to a queen.

KWRegan said...

I should add that I also prefer Susan's suggestion of 47...Kd4(!) in her real-time comments, and my analysis so far last night supports it as holding comfortably. Thus Grischuk's 47...Kb4 deserves "?!", not just post-facto.

I've also just noticed that Vasily Lebedev's analysis for Crestbook.com (here, in Russian) includes the second pawn-sac line I mentioned. He gives 50.Bg8"!" (as-per Beco's comment) Nc5 (per my stated idea) 51. Bxh7 Nd7 52. Bg8 Nf8 53.h4. Now last night, I had played 52.h4 first, and I got the impression that 52.h4 Nf8 was inaccurate timing for Black, preferring 52.h4 Kc5 first. But Lebedev's 52.Bg8! first seems to be a key finesse, and as my boldface-"only" hints, Black may be in trouble here.

Lebedev also gives the same pawn-sac idea after 50.e3 Nc5 by 51.Bg8(!) h6 52.Bf7! (more accurate than Bh7) Nd7 53.Bxe6. Compared to the line in my previous comment, White will be able to make a passed e-pawn when not just h-pawns but also g-pawns are on the board, and this may make a big difference. He also gives a main line if Black tries to preserve his pawns: 52.Bf7! g5 53.Kg4 f5+ 54.Kh5 g4 55.Kxh6 Kc4. Black's activity with ...f5+ and ...g4 was to deny White a passed h-pawn, and ideas to get one by f2-f3 allow Black counter-chances, but here White can explode Black's pawn chain at its base by 56.Bxe6! Nxe6 57.Kg6. Besides 57...Nc5 58.Kxf5 Nd3 59.Kxg4 Nxf2+ 60.Kf5 being a win in 28 according to the online up-to-6-piece tablebases maintained by K4IT.com and ShredderChess.com, I have verified to my satisfaction that 57...f4 58.gxf4 also wins for White.

Martin said...

this is the type of positions where only Topa can drain, exhaust and outsmart the oponent and win

Anonymous said...

kwregan is suggesting that engines help with 90% of the analysis, and clearly recommends their unapolgetic and enlightened use as assistants. Fair enough!
What engines are Susan and Paul using when commentating?

SusanPolgar said...

I mostly use my brain :) I prefer not to use any engine except the database to see if various lines have been played. It's more fun for me to calculate things out. I actually do not trust the analysis of computer in some situations. The only time I turn the engine on is when the position is too complicated for the human brain :)

Best wishes,
Susan Polgar

Anonymous said...

Susan, tfy reply. My question was what engine you use.
There's a big move to Rybka: my bet would be that you use Rybka too, just because it's reckoned to be the best now.

David Small said...

These sorts of positions are incredibly difficult. Intuition is about the only tool you can use. Analysis tends to get you only so far. My hunch is that the only way white can win is by disrupting the pawns and moving in the king quickly. The bishop only has an advantage as long as the K and N are far from the action. The compact nature of the pawn structure means that the N is at least the equal of the B if the K and N can get back.

So my hunch is that h4 is wrong in principle. Kg2 (and/or Be8) makes sense as the K needs to get in to the weakened black Ps for white to win. h4 is very commital and I am not sure that it shouldn't be held back in reserve. I think Kramnik's h4 later on was a declaration that it was probably a draw.

The right plan seems to be Bf8, Bf7, Kg2, Kf3, Kg4... or am I missing something? My hunch is that white can win, but that h4 was a mistake.

KWRegan said...

Sorry---I know I said I would post the PGN file in whatever state, but...the whole position is many times deeper than I thought! And already this evening I've had to take Susan's advice before I noted her 5pm comment: engines off, chess set out! This found a very dangerous idea against her 47...Kd4 suggestion:

From the diagram, 46.Kg2 Kc5 47.Kf3 (played) Kd4!?, now 48.h4!? as Kramnik might have had in mind, to judge from his move 51 in the game. The main point is that 48...f6 49.g4(!) h6 gets hit by 50.g5! since after 50...hxg5 51.hxg5 fxg5 52.Kg4 Kc3 53.Kxg5 Kd2 54.e4!, White wins. And 51...f5 loses the g6-pawn and eventually White's King comes around thru the h-file to escort the g5-pawn home (though there are pitfalls here too, including the fact that WKg5,WBf5,WPg6,f4; BKg7,BNe2, Black to move draws by ...Nc3! as the Knight reaches a blockade on f6!). The only defense seems to be 49...g5 50.hxg5 (or e3+ first) fxg5, which looks like it should lose, but after 51.e3+ Kd3 Black seems to hang on. I'm still not sure---need more time with the chess set, but the "Nalimov server" at www.k4it.de tells me that 52.Bb5+ Kc3 53.Ke4 Nb3 54.Ke5 Nc5 55.f4 gxf4 56.exf4 Kd2 57.f5 exf5 58.exf5 is uniquely defended by 58...Nb7! White has other ideas---47...Kd4 is not so "comfortable" as I thought.

I've also seen 46.h4 suggested somewhere, and it too is dangerous. Here's an entertaining line: 46.h4 Ka5 47.Be8 f6 48.Bxg6?!? hxg6 49.g4 Nc2/b3 50. h5 Nd4 51.h6(?---can you find a move to hold?) Nxe2+ 52.Kh2 Nf4 53.Kg3 Ng6 54.h7 (else ...Nf8!), and alas 54...f5! wins for Black. But the idea comes better with 48.Bf7 e5 49.Kh2!? (to avoid Nd4-xe2-f4 being check!). when K-moves by Black run into 50.Bxg6! So it seems Black must pitch a pawn by 49...Nc2 50.Bg8 h6 51.Bh7 with a skewer, and trying to build a fortress with BN on g7 fails because it gets trapped by an eventual f4-f5!

Thus I currently believe 46.h4 Ka5 would lose. The quieter 46...Kc5 (like in the game) transposes into the first dangerous line above after 47.Kg2 Kd4 48.Kf3, but with this move order White has the extra positional option of an immediate 47.g4(!), when Black can't stop g5 fixing some pawns on white squares. So far Rybka and DF10 are not impressed, HIARCS 11.2 a little more, but...that's why I need my chess set as that should be bad for Black. (I did do this entirely without a machine, and it was upheld 100% by 6-man EGTs, but it took a week, so if one wishes it on a modern Internet time cycle, let's have the engines...:-)

Nor have I gotten back much to moves 50 and 51. The pawn-sac line I had examined was with 50.e3 Nc5 first, so 50.Bg8(!) is fairly new to me, and certainly looks good! All this is great fun, maybe too much fun...

KWRegan said...

Update: I think Lebedev's 50.Bg8 can be met by the same (human!) defensive idea I put in my first comment, but it's hairier. The idea is to blockade with Black King on g7 and Pawns on h6, f6, e5 versus White's 4 pawns, but Black's King is a long way from g7! This formation ensures that Black can trade two pairs of pawns before White creates a passed pawn, and if one of the remaining White pawns is the h-pawn, Black can sacrifice his Knight for the other one, drawing because White's Bishop is the "wrong color" to win with an h-pawn---a known theoretical draw. Concretely [this is most but not all cut-and-paste from my still-not-ready PGN file, so apologies for any typos]:

------------------
50.Bg8 h6 51.Bf7 (White has other ideas too, not yet examined...), and my idea here is 51...Nd4+(!). White has:

(a) 52.Ke3 Kc5 53.Bxg6 e5 {Importantly, the Black e-pawn and Knight keep White's King from getting to h5.} 54.Kd3 Kd6 {Black also has 54...Kd5, but this shows the idea directly} 55.e3 {55.f4 is a dangerous try needing more analysis} Nb5! {Re-routing to d6} 56.Ke4 Ke7 57.Kf5 Nd6+ {Very fortunately for Black, White's Bishop blocks Kg6!} 58.Kg4 Kf8! {and the King reaches g7 just in time, with the fortress formation in place.} White also has the idea 57.Bh5 Nd6+ 58.Kd5, which looks menacing, almost a Zugzwang as Black's King must stay glued to e7. But I think Black is always OK shuttling his Knight out of and into d6. Those who trust in brains and/or engines are challenged to try to break Black down here!

(b) 52.Kg4 {Certainly principled---focus is on the h-pawns! Now 52...Nxe2 53.Bxg6 may be survivable since Black has after all traded a pawn, but I doubt it. Instead, Black delays White by not taking the e-pawn, rather setting up ...Nf3+ as a reply to e2-e3!} 52..f5+! and now:

(b1) 53. Kh4 Kc3! 54.Bxg6 Kd2 {This counterattack looks convincing, but amazingly it only barely saves Black} 55/Kh5 Kxe2 56.f4 Kf3 57. Kxh6 Kg2 58. h4 Kxg3 59. h5 Kxf4 60. Kg7 Nf3 61. h6 Ng5 {Just in time, and the e-pawn allows Black to escape Zugzwangs.} 62. Kf6 Kg4 63. Be8 Kf4 64. Bd7 e5 65. Bxf5 e4 {Equal, as verified by the "database" Susan mentioned of perfect play with 6 or fewer pieces on the board, at http://www.k4it.de/index.php?topic=egtb&lang=en. But put White's King
on g6 instead, and this is winning, as White can take on e4 and the recapture is not check!}

(b2) 53.Kf4 53... Nxe2+ 54. Ke5 g5 55. Bh5 Nc1 56. Kxe6 f4 57. gxf4 gxf4 58. Bg6 {To stop Nd3, but a tempo loss all the same.} (58. Kf5 Nd3 59. f3 Kc3 60. Kg6 Kd4 61. Kxh6 Ne5 62. Kg5 Ke3= {Black queens same time as White}) 58... Kc5 59. Ke5 f3 60. Kf4 (60. Kf6 Kd4 61. Kg7 Nd3=) 60... Kd6 61. Kxf3
Ke5 62. Kg4 Kf6 63. Kh5 Kg7= {Once again, Black is just in time.})

(c) 53.Ke4!? Nxe2 54.Bxg6, and now I think to stop Kf3-g4 with tempo, Black should plunge ahead by 54...Kc3 55.Kf3 Kd2! White again seems to be too slow to get to h6.
--------------------


I note that IM Andrey Devyatkin, in his always-spirited live commentary for Chesspro.ru (here, in Russian), gives 50.e3 Nc5 (as played) 51.Bg8 Nd7"!!" 52.Bxh7 Nf8 "and the Knight holds everything" 53.Bg8 Kc5. But this is actually the line I meant in my second comment above (2:17pm Monday) where I thought 52...Nf8 was inaccurate move order, as I think 54.h4 still gives White chances. But 52.Bxh7 Kc5(!) still holds g6 by the fork, and allows meeting 53.Bg8 by ...Kd5! Again, it takes even more study to see whether this fine-point is really important.

Devyatkin also has this topical note to 46...Kc5, if I'm translating Russian correctly:

"A really interesting struggle...and now in my gut I had the sensation that I was doing my commentary in a 'computer parlor'---i.e. that two computers were playing! True, one of them started with balky wiring getting him [Grischuk] into time trouble [and he might have added, White blew a fuse just before time control], but if you take my gut-feeling seriously, it actually means that the level of the game was extremely high."

(Aided by Babelfish, since my Romanov dictionary is not here in my office, but if you try pasting Devyatkin's Russian here you'll see that Babelfish is not as good an engine as Littlefish (Rybka).:-)