24 June 2011

How to solve a study? (Part II)

Before proceeding with the solving hints, I show you two examples which illustrate the items "introductory exchanges" and "dual avoidance" mentioned before.

Pietro Rossi
Magyar Sakkvilág, 2004
1. Rf7+ Bf4+ 2. Kxf4 Qxf7+ 3. Kxe3+ Re5+! 4. Bxe5+ Ka8
There have been lots of checks and captures during the first stage. Now that the king is not in danger of being harrassed anymore by all those black pieces, White can concentrate on mating. The black queen is kept under control.
5. Qb5! Qa7+ 6. Ke2! Qb6 7. Qd5+ Qb7 8. Qa5+ Qa7 9. Qb4 Qa6+ 10. Kd2! Qc8
10. - Qh6+ 11. Bf4 Qb6 12. Qe4+ Qb7 13. Qe8+ Ka7 14. Be3+
11. Qa4+ Kb7 12. Qb5+ Ka8 13. Bd6 and wins.

Norman A. Macleod
Szachy, 1987
Special Honourable Mention
1. Rd2+ Kc3 2. Ne2+ Nxe2 3. Bxe2 Ra1+
3. - Rb1+ 4. Rd1 Rxd1+ 5. Bxd1 (Kxd1?) Ra1 6. Ke2 drawn. But not 4. Bd1? Re5+ 5. Re2 Rxe2+ 6. Kxe2 Ra1 zugzwang.
4. Bd1
4. Rd1? Rxd1 5. Bxd1 Rb1 6. Ke2 Ra1 zugzwang.
4. - Re4+ 5. Re2 Rxe2+ 6. Kxe2 and it's a draw. White to play would lose, but Black to play cannot maintain the bind.
Very neat. In two complementary variations we see the dual avoidance on move four in view of the upcoming position of mutual zugzwang on the sixth move.

Knowing the name of the composer may help you to find the theme of a study. Most of them, I guess, have certain preferences.

If there are not so many pieces involved, you may consult books on endgame theory like Fundamental Chess Endings by Karsten Müller and Frank Lamprecht. Or maybe it's a special type of endgame, e.g. with rooks. There are special monographs and if you're the proud owner of such a book you could find hints there.
In general, even if you don't have additional aids at hand, you simply have to play a series of moves and see what is the outcome. Sooner or later, you either have a total mess or you can say it's a draw/win. Check the line for blunders and choose better moves. Now, reiterate through your line and look for improvements and alternative lines. Ask yourself what threats do emerge, what are important squares, etc. You will definitely discover several hidden treasures of the study.

What to do when stuck?
If you think that there's no way for Black to defend properly, that White wins/draws with ease, then you surely have overlooked something. Maybe you missed exactly the defence that even spoils all your plans for White. For example, there could be a zwischenzug instead of an immediate recapture or direct reply to a threat.
On the other hand, it may appear that there is no appropriate continuation for White. Then you could experiment with sacrifices, change the order of the moves or examine checks. Consider what ways there are to draw — stalemate, perpetual check, insufficient material, etc. Likewise, how can White win — mate, pawn promotion, material advantage, and so on.

That's all, I'd say. Of course, in case you try to solve using a real chessboard, you should make sure that all pieces are set up correctly. Especially when examining (side)lines of your supposed solution, make sure to put back the pieces in the correct places after returning to the respective superordinate line. However, from time to time, diagrams are misprinted. And databases may contain wrong positions, too. Well, that's plain bad luck.

17 June 2011

How to solve a study?

I've already mentioned a simple procedure how to tackle a study. Admittedly, that was a little bit theoretical and might not always be helpful. Let's have a look at some more concrete hints that are worth keeping in mind when making solving attempts.

Key piece
Which piece makes the first move? There are cases where it's fairly obvious as certain threats or plans by Black require immediate countermeasures, e.g. pawn promotion or capture of a piece. Look at Bazlov's study in the previous post. White has no other choice than to move away the rook.
In some way, this applies to all compositions. However, Black's intentions may only become clear after hours of intensive pondering. Maybe, we can take a short cut by applying probability theory. What...? Yes! A while ago, some guys (sorry, I don't know who, when and where) analyzed which key piece is favoured in a study. In fact, they made a comparison of several types of compositions, but for now, we're only interested in the result for studies. Their statistics was based upon all compositions to be found in the FIDE albums up to 1964. It turned out that in 26% a pawn made the key move.
I was curious and made my own statistics. This time, the source was the endgame study database of Harold van der Heijden, third edition. Guess what? The result was the very same: pawn 26%, knight 19%, rook 18%, king 16%, bishop 15%, queen 6%. So, analogous to detective stories – the murderer is always the gardener – we should keep an eye on those "suspicious" pawns.

Introductory exchanges
Often, the first moves of a study are rather a prelude to the real action. They may include captures and/or checks. Usually, the key move is a pawn capture at most. Sometimes, there is a thematic choice of captures. Then, you have to work out the differences, of course. Questions like which remaining minor piece Is better are to be answered. This should be easier for more experienced solvers or chess players.

Dual avoidance
The fact that the existence of several equivalent continuations at any stage of the solution is a blemish and devalues any composition is quite useful for the solver. Normally, composers avoid those duals as far as possible, therefore somehow providing unintentional clues. For example, you think about a march of the white king from c2 to e5 as a promising maneuver. This is feasible in different ways, though. So, that means either this idea is totally wrong or you have to find the reason why, for instance, the king should visit e4 or avoid d3.
However, the famous Troitzky held other views, as to duals. So, be careful in that respect.

(to be continued)

10 June 2011

What's cooking?

Hopefully you're not too disappointed that I'm not gonna write about culinary goodies. My writing is still about chess problems. Nevertheless, I want to mention cooks — a contradiction? Only, if I intended to mention those guys preparing delicious food in the kitchen. — Problem chess and cooks? Where's the link?

In simple terms a cook is a flaw in a chess problem. This might be an unintended (additional) solution or a possible defense was overlooked by the composer, so that there is no solution at all. Thirdly, the solution may not be unique due to so-called duals. Of course, all thes possibilities spoil a problem.

It's not absolutely clear, where this term cook comes from. The general opinion is that it's named after the nineteenth-century problemist Eugene Beauharnais Cook (1830-1915) who was famous for a phenomenal solving talent. Emanuel Lasker came up with this explanation. On the other hand, the problemist Benjamin Glover Laws (1861-1931) traces the term back to a statement of Josef Kling. Moreover, I've read that cook is probably derived from the word's English slang meaning (to tamper with or foil).

Anyway, cooks are so annoying! And this leads us back to the endgame studies. There are very strong solving programs with which you can check a great varity of chess problems. But what to do with those studies? Sure, you can use powerful chess engines and query endgame tablebases. But there is no general foolproof method to check a study for correctness. How to spot the best moves and defenses? At which point can the composer (in the previous post, it was the solver to ask) say "and wins" or "and draws" without doubt, unless a tablebase position or a book draw/win (stalemate, insufficient material, a forced mate in x, etc.) is reached? You and/or your engines might still miss a critical move, possibly exactly the one that spoils it all.

Guess what? When writing last week's post, at first, I had selected a cooked study. I only noticed when I compared the given solution in a book with the one in Harold van der Heijden's endgame study database. So, cooked chess problems are also irritating for authors like blog writers! Grrrrrr. Anyway, I do my best to pick only sound studies for you.

By the way, in his book Studies and Games, Jan Timman shows several of his compositions with all the flaws they have/had – e.g. anticipations, duals, being unsolvable. It's very interesting to read about the backgrounds of his works and how he managed to repair or further develop the cooked problems. I think it's quite rare that a composer writes so much about his unsuccessful attempts. Kudos to GM Timman!

In 2007, there was an international composing tournament with the thematic task "Studies for Practical Players". It was held in recognition of Mark Dvoretsky's 60th birthday. Obviously, most composers were making active use of computer programs and of endgame tablebases. Nevertheless, there were also 21 cooked problems! Here are some of the prize winners for you to enjoy:

N. Rezvov
S. Tkachenko
Dvoretsky-60 JT, 2007
1st Prize
1. Bf6!
Not 1. Nxe6?, as after 1. - b2 2. Bg5+ Kf2, White would have to give up the bishop for the pawn: 3. Be4 b1=Q 4. Bxb1 Nxb1.
1. - b2!
Weaker is 1. - Nxc5+? 2. Kxa3 +-
2. Bxb2 Nc4
This gets the knight away from attack with gain of time.
Again, 2. - Nxc5+ 3. Kxa3 is lost.
Now, where should the bishop go?
3. Bh8!!
Tempo play does not work: 3. Bc1+? Kf2! 4. Bd5 Nxc5+ 5. Kb5 Nd3 and the knights will reunite on the next move.
Also, 3. Ba1? Nxc5+ 4. Kb4 Nd2,a5 only turns out to be in favour of Black.
3. - Kf2!
Black has all the time to harrass the bishop. The knight on c5 can wait, it's not going anywhere.
4. Bh1!!
This move to the corner drives the black king further away.
The premature 4. Ba8?! analogous to the previous move fails: 4. - Nxc5+ 5. Kb5 Nd7! 6. Bd4+ Ne3! 7. Be4 Nf8! 8. Kc6 Ne6.
4. Bh3? Nxc5+ 5. Kb4 Kg3! also does not win.
4. - Kg1!
4. - Nxc5+ 5. Kb5 Ne3 6. Kxc5 Ng2 7. Bd4+! and the (temporarily) trapped bishop is save. The two bishops win versus the knight.
5. Ba8!! Nxc5+
5. - Nb6+ 6. Ka,b5 Nxa8 7. Nxe6 +-
6. Kb5! Nd7 7. Bd4+! and wins. Now, there is no Ne3 that saved Black before with his king on f2.

Three times, the bishops have to hide in the corners in their battle against the knights that goes on across the whole board.

Y. Bazlov
Dvoretsky-60 JT, 2007
2nd Prize
Apparently, this position is clearly better for Black, isn't it? It seems quite probable that sooner or later that game is lost for White. But, unlike in an OTB situation, we do know that there is a way to save this!
First question: Where to put the rook? 1. Rd2? Qh6+ 2. Nh3 Qxd2+ or 1. Rd3? Qf2+ 2. Kh3 Qf5+ fails immediately.

1. Rf1! Qb2+
1. - Qh6+ is not dangerous: 2. Nh3 Qd6 (2. - Ne4 3. Ng4) 3. Rf5 Qe6 4. Rh5 Ne4 5. Nf4 Qa2+ 6. Ng2=.
2. Kh3
Of course not 2. Kg3? Ne2+.
2. - Qe2 3. Rf5
Though everthing is protected, White is still not out of the woods yet.
3. - Qh5+ 4. Kg2
4. Kg3? Ne2+ 5. Kg2 Nd4 6. Ne4 Qe2+ and one of the white pieces will be captured.
4. - Nd5
4. - Ne4? is weak, for the rook is indirectly protected: 5. Nxe4 Qxf5 6. Nd6+. Now, how to neutralize the threat Ne3+?
5. Kg3!
The knights can't move. 5. Ne4? is not the same as before: 5. - Ne3+ 6. Kg1 (otherwise the rook is captured with check) Qd1+ followed by 7. - Nxf5. Also, 5. Nd7? Qg4+ is clearly lost.
5. - Ne7 6. Ng4!!
White sacrifices the rook without obvious compensation. But he has to, there is nothing else: 6. Kf4? Qh2+ (6. - Nxf5? 7. Kxf5=) 7. Kg4 (7. Ke4 Qc2+) 7. - Qg2+ 8.Kf4 Nd5# Oops, a mate in the middle of the board!
Okay, White threats the fork on f6. But Black comes first and captures with check.
6. - Nxf5+ 7. Kf4 Qg6 8. Ne5 Qf6 9. Ng4
The last stumbling block is 9. Ne4? Qe6 10. Ng5 Qc8 and Black wins. The black queen has not many squares from where it can both protect the knight and avoid a fork.
9. - Qf8 10. Ne6 Qf7 11. Ng5 Qg6 12. Ne5 and draws. Black can't escape from the continuous attack.

S. Didukh
Dvoretsky-60 JT, 2007
3rd Prize
1. Nh5!
Insufficient tries:
1. Rh1? Kxg7! (but not 1. - Nf2? 2. Rh2 Kxg7 3. Kc7) 2. Rxh3 Nd6+! 3. Kd7 Nf5 4. Rd3 Kf6 and Black has built a fortress.
1. Ne8? e5+ 2. Kd8 exd4 3. Rh1 Ng5=; according to the tablebases, 3. Rd1 Kh7 4.Rxd4 is a drawn position.
1. - e5+!
1. - Kg8 2. Kd8 leaves Black no chance at all: White gradually realizes the advantage of the exchange by purely technical means. For example: 2. - Kf7 3. Ra7+ Kf8 4. Ra3 Bg4 5. Re3 Nd6 6. Ng3 Nc4 7. Re1 Kf7 8. Kc7 Kf6 9. Ne4+ Ke7 10. Nc5 Kf7 11. Nd7 Bf5 12. Ne5+.

Now, White has a difficult choice: where to go with the king? It seems reasonable to let it approach the black pawn: 2. Kc7? exd4 3. Rh1 Bg2 4. Rh4 Kg8 5. Rg4+ Kh7! 6. Rxg2 d3 7. Rg1 d2 8. Rd1 Kg6 9. Nf4+ Kf5 10. Nd3 Kg4 11. Rf1 Nc3 12. Nb2 Nd5+!! 13. Kd6 Ne3, draw!
A different check will spoil things with the king on d8: 2. Kd8? exd4 3. Rh1 d3! 4. Rxh3 Nf2 5. Rg3 d2 6. Nf6 and the black pawn promotes with check! Therefore ...
2. Kb8!! exd4
2. - Bg4 3. Re1!
3. Rh1 Bg2
Now, the variation 3. - d3 4. Rxh3 Nf2 5. Rg3! d2 (5. - Kh7 6. Nf6+ Kh6 7. Ng4+!) 6. Nf6 d1=Q contains no check, so White continues with 7. Rg8#.
4. Rh4 Kg8 5. Rg4+

A) 5. - Kh7!
5. - Kf7?! 6. Rxg2 d3 7. Rg7+ Ke6 8. Nf4+ +-
6. Rxg2 d3 7. Rg1! d2 8. Rd1 Kg6 9. Nf4+ Kf5 10. Nd3! Kg4 11. Rf1! Nc3 12. Nb2 Kg3
Unfortunately, there is no longer enough time to bring the knight over.
13. Nd1! and wins.

B) 5. - Kf8 6. Rxg2 d3 7. Rg1 d2
7. - Nf2 (7. - Nc3 8. Rf1+! Ke7 9. Rf2) 8. Rf1 d2 9. Rxf2+
8. Rd1 Ke7 9. Nf4 Kd6 10. Nd3 Kd5
10. - Kc6 11. Ne5+
11. Nf2! Nxf2 12. Rxd2+ and wins.

Surely a difficult study. White wins a piece by force and is a rook up. But this advantage in material can't be converted with ease. The remaining pawn gives Black serious counterplay. Only the foresighted second move brings the win for White.

03 June 2011

Back to the real (problem chess) world

Looking back at last month's posts, one might get the impression chess problems mainly deal with all kinds of boards, strange chess pieces, special rules and lots of other weird stuff. Examining all that through the glasses of a chess player, this might not be overly attractive. In fact, fairy chess is not even fascinating all problemists! So, let's return to compositions which are most probably more appealing to the majority of chess enthusiasts — endgame studies.

Though a lot of endgame studies look as if they occured in an actual chess game, they're still made up, products of composers' creative activity. As to the number of moves, there is no restriction. Nevertheless, the aim - draw or win with the white pieces - has to be achieved in a unique way against any defense.

Most probably, a study with, say, at most ten pieces is what a casual solver would accept as a composed endgame. But, as already mentioned, a study is not an endgame in terms of the final stage of a game. Therefore, there can be way more pieces on the board. Actually, I have seen some studies with a piece count of 15 and more. But I can't say I like many of them.

An interesting question is how to solve a study. You only have the stipulation, nothing else. Unlike in a mate problem with its constraint to deliver checkmate after the given number of moves, you don't have exact hints when you have found the complete solution of a study. For example, at which point can you say it's a draw as demanded? Not all variants of a study end with a stalemate or the position king vs. king, so that you can determine the result easily.

Recently, I saw a nice recipe how to proceed when making solving attempts:
  1. Examine the material.
  2. Examine the stipulation.
  3. Examine the position.
  4. What are Black's threats?
  5. Can you list the White defenses to the threats? Play one of them.
  6. What are White's threats?
  7. Choose a reply for Black.
  8. Repeat steps four to seven as long as necessary.

We might try that now. Obviously, I have found something appropriate for demonstration purposes. ;-)

A. A. Troitzky
Novoye Vremya, 1895
White to move and draw (3+3)
  1. Examine the material.
    White has a rook against a bishop. This is a normal draw.
  2. Examine the stipulation.
    White is to draw, but as it is a normal draw anyway there must be a catch somewhere.
  3. Examine the position.
    The catch is clear. Black has a pawn about to queen resulting in an enormous material advantage.
  4. Black's threats?
    As already stated: Black will promote on g1.
  5. White's defenses?
    This is not easy. 1. Kh3 does nothing about the threat, and 1. Rg3 Bxg3 makes things even worse. So, knowing that there is a solution, we hunt for clues. One clue is that, for drawing purposes, White has too much material. He needs only to capture the g2 pawn at any price to settle the result. There do not seem to be any other clues. That the stipulation is a draw suggests a stalemate possibility, but only an experienced solver would suspect stalemate here. Even if there seems no point, let's try a rook sacrifice. 1. Rf4+ Bxf4 2. Kf3 g1=Q is a dead end for White, so try 1. Rd3+.
  6. White's threats?
    Of course, White wants to play 2. Rd1 on the next move.
  7. Black's reply?
    The only way to spoil White's intention is 1. - Kxd3.
  8. Black's threats?
    Black still threatens to queen his pawn.
  9. White's reply?
    2. Kh3 still is not good, as it wasn't before, but 2. Kf3 attacks the black pawn, blocks the white pawn, and invites 2. - g1=Q (or R), which ... is the stalemate we hoped to get. Weeeeeeeeee! White's rook sacrifice did three things: 1) got rid of a superfluous piece; 2) enticed the black king onto a desired square (completing the stalemate net forcibly); 3) vacated a square for the white king.
    What about other Black promotions, to knight or bishop? No stalemate then. But after 2. - g1=S+ 3. Kg2, White takes one of the black pieces and it's a draw. 2. - gl=B leaves Black with two bishops on the same colour, and no black pawns — draw.

Argh! Due to lack of time, this post got shorter than intended. Watch out for more, soon!