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Chess and problem rambles by PW

28 Jan. 2018 – New digital subscription for ‘The Problemist’

The Problemist is undoubtedly one of the best chess problem magazines in the world. Produced by the British Chess Problem Society, each issue contains top-quality articles, news reports, original compositions (in six sections), selected problems (typically prize-winners), and tourney awards. Further, each instalment is bundled with The Problemist Supplement – also with originals and articles – which caters for newcomers to problems and is expertly edited by our own Geoff Foster. Starting from this year, you can subscribe to the electronic version of the publication at a greatly reduced rate. The annual membership cost is £5 (about AU$8.60) and it obtains six issues of the magazine in the PDF format. This is excellent value when you consider that the normal subscription is £25 for the hard copies (which is still available). Go to the British Chess Problem Society site for details on how to become a member.

Ilija Serafimović
Youth Chess Composing Challenge 2016
2nd Place, 1st Hon. Mention
Mate in 2

Here are two selections from the November 2017 issue of the publication. The first features in the inaugural C. J. Morse Award for two-move tasks and records, named in honour of the late Sir Jeremy Morse. Two-movers from any sources (not just The Problemist) that demonstrate a maximum effect of some sort were eligible for this tourney, which covers the 2012-2016 period. Instead of the award winner, I will quote one of the top eleven entries mentioned, by a young composer who was a successful entrant in our Guided Chess Problem Composing Competition. This delightful work by Ilija brings about a terrific number of knight promotions. The key is thematic, naturally – 1.g8(S)! with the threat of 2.Bg3. Two defences by the a8-rook allow White to deliver knight promotion mates: 1…Ra4 2.c8(S) and 1…Re8 fxe8(S). Black can also defend by promoting various pawns to knights, and these moves result in different queen mates: 1…f1(S) 2.Qd4, 1…gxh1(S) 2.Qg6, and 1…d1(S)+ 2.Qxd1. (Also, 1…Re7 2.Bxe7.) The total of six knight promotions (three white and three black) constitute a new record for single-phase two-movers.

Vasil Krizhanivsky
The Problemist 2015
1st Prize
Helpmate in 2
6 solutions

All originals published in The Problemist automatically take part in its (mostly) annual informal tourneys. Given the quality of the problems that such a prestigious journal attracts, the prize-winners in these tourneys invariably impress. The helpmate above won the 2015 two-move section by achieving what could be a first: a doubling of the cyclic Zilahi theme without the use of twins. In the first three solutions, the white officers rotate their roles in getting captured by the black queen and giving mate: 1.Qxe4 Rf6 2.d5 Sc6, 1.Qxd4 Bf5 2.Qf4 Rd5, and 1.Qxd6 Sc6+ 2.Ke6 Bf5. In each phase, the white piece that’s not part of the Zilahi scheme (i.e. it is not captured and doesn’t mate) always moves to guard flights. Hence there’s a formally perfect 3x3 cyclic change of functions (sacrificed/guard/mate) for the three white pieces. Such a theme rendered would be sufficient to make a very good helpmate, but here the composer has managed to produce another 3x3 cycle of function change that again incorporates a Zilahi. In this second triplet of solutions, it’s the black king that commences the cyclic play by making the thematic captures: 1.Kxe4 Re6+ 2.Kf4 Se2, 1.Kxd4 Bd3 2.Re3 Rxd5, and 1.Kxd6 Sb5+ 2.Kc6 Bxd5.

12 Mar. 2018 – Stockfish and a modern classic more-mover

The rise of chess engines in the last decade or so is an interesting topic from which I’ve been somewhat insulated, because of my focus on problem chess. Frequenting the Chess.com site has helped me to catch up with the advances of these incredible programs, which perform at superhuman levels on modest hardware. Thus I learnt that Stockfish, one of the strongest engines with an Elo rating of around 3500, is open source software that is accessible for free. And you don’t even have to install it on your computer; you can play against Stockfish directly on Chess.com, or set up a position on the site for the engine to analyse.

As a problemist, I was naturally curious to see how efficiently Stockfish deals with long directmate problems. And the answer seems to be “very.” It solved the great majority of more-movers of up to about 12 moves that I tested in mere seconds, and even cooked a few. (Note that when you run Stockfish on Chess.com, its speed still depends on your own computer’s processing power.) Although this is impressive, Stockfish is of course no substitute for a specialised problem solver like Popeye, which uncovers all of the variations in a problem and provides certainty to its soundness. Stockfish is designed to keep looking for the best move indefinitely, or it stops analysing according to a time-limit, so you can’t tell if any forced mating sequence it has found is in fact the shortest possible. Furthermore, Stockfish can be inconsistent in being unable to crack some not-very-long directmates in a reasonable time. Here is an excellent 9-move problem that stumped the engine, but was solved by Popeye in less than eight minutes.

Theodor Siers
Die Schwalbe 1935
Mate in 9

White’s plan is to mate on e7 with the bishop, while avoiding stalemate from capturing the knight. Black is almost in zugzwang, since most knight moves allow the bishop mate and 1…Sd5/Sc6 is answered by the waiting move 2.Bc5, after which the knight must unguard the mating square. However, White has to move the king first to fend off 1…Sc2+. 1.Kb2? fails to 1…Sxd3!+ 2.K-any Sc5 3.Bb4 Sxe4!, creating an escape square on f5 for the black king. White therefore plays 1.Kb1!, but after 1…Sd5, 2.Bc5? is premature because of 2…Sc3+!, again winning the vital e4-pawn. If 2.Kc2? instead, Black counters with the resourceful 2…Se3+! 3.K-any Sf5!, which simultaneously protects e7 and attacks g7, thus dislodging the white rook. So where should the white king go? No progress is made if it stays on the queen-side, because the black knight can continue to switch between b4 to block the bishop and d5/c6, where the knight either checks directly or (if White plays Bc5) executes a fork that will give the piece access to e4 or f5, as previously seen. Correct is 2.Kc1! forcing 2…Sb4, and then 3.Kd1! Sd5.

At this point, you might guess that the theme of the problem is that the white king marches all the way from a1 to h1 without leaving the first rank. Hence not 4.Bc5? or 4.Ke2? because of 4…Sc3+ again, but 4.Ke1! Sb4 5.Kf1! Sd5 6.Kg1! Sb4 7.Kh1! Sd5, and finally the king is safe from checks by the pesky knight – 8.Bc5 S-any 9.Bxe7. The solution exploits a curious geometric feature: h1 is the only white square on the board that cannot be attacked in one move by a knight on either d5 or c6. The maximum-length orthogonal trip by the white king is superbly engineered in this first-rate composition.

When Stockfish tackled this position, it took a few minutes to find a forced mate in 13, starting with 1.Rxh7. After a couple of hours, it picked the right first move, 1.Kb1!, but based that on a wrong continuation, 1…Sd5 2.exd5?, which lets the black king escape to f5, and this leads to mate only on move 12. Are there directmates even shorter than this 9-mover that cannot be solved – within an hour, say – by Stockfish? With few clues on what would give the engine trouble, I threw some random 7- and 8-move problems at it, but most were handled quickly. Then it occurred to me that I could try using the current problem by Siers but with the first few moves of its solution shaved off; at which point of the shortened variation will Stockfish get it right? As it turns out, the engine found the solution only at the mate-in-5 stage. That means the shortest forced-mate sequence I know of that cannot be solved by Stockfish is a mate-in-6, with the white king starting on d1 and the black knight on d5. Can anyone unearth a mate-in-5 position that is too difficult for Stockfish!?

18 Apr. 2018 – ‘Esling’s Memories Expanded’ and ‘Ken Fraser – A Quiet Achiever’

Bob Meadley has sent me two splendid e-books that he published some years ago. Although their problem contents are somewhat peripheral, anyone keen on chess and especially its historical aspects will find much of interest in these well-researched documents. The first is Esling’s Memories Expanded (2009), which Bob compiled with the late Ken Fraser. Frederick Karl Esling (1860-1955) was the first official Chess Champion of Australia. He was also a railway engineer in charge of many important projects in Melbourne, Victoria, including the rebuilding of the Flinders Street Railway Station. Both of his careers, chess and professional, are covered in this comprehensive biography. Esling also composed some good problems that are tough to solve, and a small (incomplete) selection of his works is included. Below I quote one of his easier but appealing three-movers. At a sizable 268 pages, this document is divided into four PDF files which you can download here: Part 1, Part 2, Part 3, Part 4.

The second e-book is Ken Fraser – A Quiet Achiever (2014). Ken Fraser was the curator of one of the greatest collections of chess books in the world, the M.V. Anderson Chess Collection in the State Library of Victoria. Under the main heading, “The Letters from Ken,” Bob chronicles Fraser’s work as a chess researcher and the invaluable assistance he gave to other chess writers and historians, including Bob himself. “Problems are mentioned quite a lot in the pages,” wrote Bob, who indicated that the State Library intends to add the document (in whole or part) to its website.

Frederick Esling
Melbourne Leader 1941
Mate in 3

The diagram position contains a short set line, 1…f4 2.Rxf4, but most of the black rook’s moves – including some strong captures – are not prepared with white continuations. The key-move 1.Bf4! (waiting) removes the set variation but provides for 1…R~file by crossing over d6, so that 2.Rd6 (short mate) no longer interferes with the bishop’s control of e5. (An unimportant dual follows 1…Rc5 with both 2.Rd6+ and 2.Re6 working.) The main variations occur when the black rook stays on the 6th rank. After 1…Rxf6, 2.Sg7 puts Black in zugzwang as the rook cannot maintain its focus on the knight’s mating squares: 2…R~rank 3.Sxf5 and 2…R~file 3.Se6. If 1…Rb6, then 2.Sc7 brings about similar focal play: 2…R~rank 3.Sb5 and 2…R~file 3.Se6. Accurate by-play follows the remaining rook defences: 1…Re6 2.Rxf5 (threat: 3.Rd5) Re5/Rd6 3.Be5, and 1…Ra6 2.Bxa6 Kd5 3.Rd6.

27 May 2018 – The greatest masters of both the game and problems – Part 1

The world of composed problems and endgame studies, though derived from competitive chess, has developed into a sophisticated art form that is quite distinct from the practical game. The specialised skills required in each of these two disciplines of chess means that it’s rare for individuals to truly excel in both. In this two-part Walkabout, I will consider such exceptional talents and present the greatest masters who have attained prominence in both areas. The first part here lists my top-five grandmasters of the over-the-board game who are also accomplished problemists. The second instalment will proffer the top-five elite problem composers who also play the game at the international level.

Such “greatest” lists are inevitably subjective, but I will be guided (not ruled) by a number of tangible measures of achievement in the game and problems:

(1) Titles. The familiar titles of Grandmaster, International Master, and FIDE Master in OTB play all have their counterparts in problem composition, as conferred by the World Federation for Chess Composition. An obvious criterion for my lists is the attainment of such titles, ideally in both fields. In cases where a person doesn’t hold an official title in one activity, I will give an estimate of their skill level.

(2) Best World Rank. The highest ever ranking of a player as calculated by Chessmetrics provides a simple but effective way to (indirectly) compare masters from different eras. Such a measure of relative strengths seems more revealing than Elo ratings, which are fraught with issues such as inflation.

(3) FIDE Album points. The FIDE Albums, dated from 1914 to the present, are anthologies of the world’s best chess compositions. The selection for inclusion in these Albums also determines the aforementioned titles awarded to composers. The title requirements are based on a point system; each problem selected gains 1.00 point while an endgame study earns 1.67. A composer must accumulate the following number of points to acquire the corresponding title: 12 for FIDE Master, 25 for International Master, and 70 for Grandmaster.

Honourable Mentions: The World Champions
Many World Champions in the past also engaged in chess composition. Steinitz, Capablanca, Botvinnik, and Smyslov all produced endgame studies, while Lasker and Euwe devised both directmate problems and studies. Each of these individuals’ output was good in numbers, suggesting a serious interest in the activity. However, their works were not exceptional in quality, and none of these World Champions are represented in the FIDE Albums.

Honourable Mentions: Solving Grandmasters
The solving of composed problems represents yet another major branch of chess. Akin to the competitive game, there are international solving tournaments in which participants could gain norms and titles. Only six people hold the distinction of achieving the grandmaster titles in both solving and OTB play: Jonathan Mestel, Ram Soffer, John Nunn, Bojan Vučković, Kacper Piorun, and Alexander Miśta. Since solving problems and playing the game are relatively similar (both are about finding the right moves), the overlap in expertise here is less surprising. That is one reason why these double-GMs don’t make my top-five list, with one exception…

5. John Nunn (1955-)

Game: GM, Best World Rank: 10
Solving: GM
Composing: Expert-level
Photo: Lovuschka
Wikimedia Commons

The standout among the OTB/solving GMs is the English player John Nunn, whose accomplishments in both the game and composition are well ahead of the rest of the group. His best results as a player include winning the prestigious Wijk aan Zee tournament three times, and obtaining two individual gold medals at the Chess Olympiads. On the problem side, Nunn has been crowned World Champion for solving on three occasions. His book Solving in Style guides you through the thinking process of a master solver and it also serves as an excellent introduction to the different types of chess problems. He is a fine composer as well, adept in a variety of genres including endgame studies and helpmates. In the problem below, he makes a rare foray into directmate territory.

John Nunn
The Problemist 2012
5th Prize
Mate in 3

Key: 1.Sec4! (threat: 2.Bxg2+ Rxg2 3.Se3). 1…Rbb2 2.Sc2 (3.Bxg2) Rxc2 3.Sb6, 2…S~ 3.S4e3. 1…Rab2 2.Sb5 (3.Sb6) Rxb5 3.Bxg2. 1…Raxa1 2.Sc2 (3.Bxg2) Rxf1/Re1 3.Sb6, 2…S~ 3.S4e3. 1…Rbxa1 2.Sb5 (3.Sb6) Ra6 3.Bxg2. The Wurzburg-Plachutta mutual interferences seen in 1…Rbb2 and 1…Rab2 are complemented by the 1…Raxa1 and 1…Rbxa1 pair.

4. Paul Keres (1916-1975)

Game: GM, Best World Rank: 2
Composing: Expert-level, FIDE Album points: 3.33
Photo: Daan Noske/Anefo
Wikimedia Commons

The Estonian grandmaster Paul Keres is regarded by many as the greatest player never to have become World Champion. He won the famous AVRO tournament of 1938 and could have been the world title challenger to Alekhine if not for the outbreak of WWII. As a composer, Keres created about 200 works, mostly directmates of various lengths and some studies. The thematic contents of his directmate problems indicate a standard that is generally a class above that of the World Champion/composer group.

Paul Keres
Norsk Sjakkblad 1933
1st Prize
Mate in 2

Key: 1.Bg2! (threat: 2.Sf3). 1…Sc7 2.Be5, 1…Se7 2.Bc5, 1…Sb6 2.Sc6, 1…Sf6 2.Se6, 1…Sc3 2.Qf2, 1…Se3 2.Qb2, 1…Sxb4 2.Rxb4, 1…Sxf4 2.Rxf4, 1…Bxd3 2.Qxd3. The eight black knight moves are answered by different mates – the knight-wheel theme.

3. Oldřich Duras (1882-1957)

Game: GM, Best World Rank: 4
Composing: Master-level, FIDE Album points: 17.50
Photo: Wikimedia Commons

FIDE officially introduced the grandmaster title in 1950, and among the select group of 27 first recipients was the Czech player Oldřich Duras. He was an elite tournament player a few decades earlier; one of his best results was equal first place at Prague 1908 ahead of Rubinstein and Marshall. In composition, other than studies Duras focused on three-move directmates. He belonged to the Bohemian school which emphasises elegant model and echo mates. Although he had sufficient FIDE Album points for the FIDE Master title, when the award was established it was not conferred retroactively to deceased problemists.

Oldřich Duras
České slovo 1922
Mate in 3

Key: 1.Kg5! (waiting). 1…Kd8 2.Ba4 (threats: 3.Qd7/Qe8) Ke7 3.Qf6 [model], 2…Kc8 3.Qxa8 [model]. 1…a5 2.Bg4+ Kb8 3.Qb5 [model], 2…Kd8 3.Qd7. 1…Kb8 2.Bf3 (3.Qxa8/Qb7/Qe8) Kc8 3.Qe8 [model]. 1…Rb8 2.Bg4+ Kd8 3.Qd7. Four model mates are shown, two of which are echoes.

2. Richard Réti (1889-1929)

Game: GM-level, Best World Rank: 5
Composing: Master-level, FIDE Album points: 15.00
Photo: Wikimedia Commons

The great Slovak-Austrian player Richard Réti was a proponent of the Hypermodernism school which revolutionised chess theory in the 1920s. His most celebrated victories were perhaps those over Capablanca and Alekhine in the New York 1924 tournament, using the opening that now bears his name. Réti was also a world-class composer of endgame studies. His classic K+P vs K+P Draw must be one of the most famous positions in chess history. The high quality of his compositions makes up for his fairly small oeuvre of about 50 studies. Many of his best works, displaying great depth and complexity, are all the more remarkable considering they were constructed before the advent of computer-testing.

Richard Réti
Tagesbote 1925
White to play and win

Not 1.a5? Kb5! 1.Ba5! (threats: 2.Bd2/Be1… 3.a5) Kb3 2.Bc3!! Kxc3 (2…Bxc3 3.a5 c4 4.a6 Bd4 5.a7! Bxa7 6.g7 c3 7.g8(Q)+; not 5.g7? Bxg7 6.a7 c3 7.a8(Q) c2=) 3.a5 c4 4.a6 Kd2 5.a7 c3 6.a8(Q), e.g. 6…c2 7.Qa5+ Kd3 8.Qe1 Bh6 9.Kg2 Bg7 10.Qc1 Be5 11.Kf2 Bd4+ 12.Kf3 Kc3 13.Ke2 Bg7 14.Qd2+ Kb3 15.Kd3. Paradoxical first-move blocks the white pawn, followed by a double-sacrifice.

1. Pal Benko (1928-)

Game: GM, Best World Rank: 17
Composing: IM, FIDE Album points: 40.00
Photo: F.N. Broers/Anefo
Wikimedia Commons

A top grandmaster for three decades from the 1950s to the 1970s, the Hungarian-American Pal Benko won the US Open Championships a record eight times. He qualified for two Candidates Tournaments which determined the world title challenger. The Benko Gambit is named after him. As a problemist, he is both prolific and versatile, producing hundreds of compositions in all genres. He has published studies, directmates of various lengths, helpmates, retro-analytical problems, and even some unorthodox or fairy compositions. He remains the only person to have officially gained both the GM title for OTB play and the IM title for composing.

Pal Benko
Magyar Sakkélet 1975
3rd Hon. Mention
Mate in 3
Twin (b) Pb7 to e7

Part (a): Tries: 1.b8(Q)+/f8(Q)+/f8(S)? Kc6! Key: 1.b8(S)! (threat: 2.f8(Q)+ Ke6 3.Qe7). 1…Ke6 2.f8(S)+ Kxf6 3.Sd7, 2…Kd6 3.Rd7. Part (b): Tries: 1.e8(Q)?=, 1.f8(Q)/f8(S)? Kc6! Key: 1.e8(B)! (2.f8(Q)+ Ke6 3.Qe7/Bd7). 1…Ke6 2.f8(B) Kxf6 3.Rh6. Two pairs of underpromotions.

28 Jun. 2018 – The greatest masters of both the game and problems – Part 2

In this instalment, we continue our survey of the greatest chess masters who have attained prominence in both the over-the-board game and problem composition. Whereas in Part 1 we focused on famous OTB grandmasters who are proficient problemists to boot, here I give my list of top-five outstanding problem and study composers who also play competitive chess at the master level. My selection is once again partly based on three measures of an individual’s achievements: (1) chess titles acquired, (2) Best World Rank as determined by Chessmetrics, and (3) FIDE Album points, indicative of the number of first-class compositions produced.

All but one of my picks are official grandmasters of chess composition, a title bestowed to those who have gained at least 70 FIDE Album points. I want to stress how this simple-sounding requirement is in fact extremely stringent, so that on average only a handful of people per year would qualify. Indeed, since the title was established in 1972, only 88 people have ever earned the distinction, as this complete list of Grandmasters for Chess Compositions shows. Hence unlike the grandmaster title for the OTB game, now held by about 1500 players, the corresponding title for composition is in no danger of devaluation!

In passing, I should also mention a select group of eight brilliant problemists who have obtained the grandmaster titles for both composing and solving problems: Milan Velimirović, Marjan Kovačević, Michel Caillaud, Aleksandr Azhusin, Miodrag Mladenović, Andreï Selivanov, Michal Dragoun, and Ladislav Salai Jr. The last of these double-GMs also appears in my top-five list.

5. Ladislav Prokeš (1884-1966)

Composing: IM, FIDE Album points: 38.33
Game: Master-level, Best World Rank: 36
Photo: Wikimedia Commons

The Czech composer Ladislav Prokeš deserves a place here not only because of his impressive highest playing rank of 36, but also for his style of endgame composition. He was dubbed “the player’s composer” as his studies often have natural-looking positions with few pieces and their solutions are typically short but surprising – an appealing blend for the practical player. Remarkably prolific, Prokeš devised over 1,200 studies and also some directmates. He became an International Judge for composition in 1956. His International Master title for composing was awarded posthumously in 2016. As a player, he jointly won the Czechoslovak Championship in 1921 and represented his country at three Chess Olympiads (once with Réti as a teammate).

Ladislav Prokeš
Louma Tourney 1941
1st Prize
White to play and win

1.d7 Ra1+ 2.Ba2! (not 2.Kb3? Ra8 3.Bd5 Rb8+ 4.Kc4 Kxe5 =) Rxa2+ 3.Kb3 Ra8 4.e6 Ke5 5.e7, 1…Rd1 2.Bd5! Rxd5 3.e6 Ke5 4.e7, 1…Rh8 2.Bg8! (not 2.Bf7? Kxe5 3.Be8 Rh4+ 4.Kb5 Rd4 =) Rxg8 3.e6 Ke5 4.e7. The white bishop is sacrificed three times, each on a different square.

4. Yochanan Afek (1952-)

Composing: GM, FIDE Album points: 77.39
Game: IM, Best World Rank: 791
Solving: FM
Photo: Stefan64
Wikimedia Commons

The Israeli Yochanan Afek is the epitome of professional chess versatility, being the only person to hold five FIDE titles: Grandmaster and International Judge for composition, International Master and International Arbiter for the game, and FIDE Master for solving. He’s also a chess trainer, tournament organiser, and writer! As a composer, Afek is best-known for his endgame studies – which make up the majority of his output of more than 400 works – but he has additionally published directmates, selfmates, and helpmates of excellent quality. In competitive play, his best result was winning the 2002 Paris City Championship, which earned him a GM-norm. His expertise in both studies and the game makes him an ideal author of books such as Extreme Chess Tactics.

Yochanan Afek
Probleemblad 1980
3rd Prize
Mate in 2

Try: 1.b6? (threat: 2.Ra5). 1…Qd4+ [a] 2.Bd6 [A], 1…Qxe5 [b] 2.Bc5 [B], but 1…Qc3! refutes. Key: 1.Kc7! (2.Re8). 1…Qd4 [a] 2.Bc5 [B], 1…Qxe5+ [b] 2.Bd6 [A], 1…Qe1 2.Bb4. Virtual and actual play show a reciprocal change of white battery mates (labelled [A] and [B]) in response to the same pair of black queen defences ([a] and [b]).

3. Ladislav Salai Jr. (1961-)

Composing: GM, FIDE Album points: 87.35
Game: IM, Best World Rank: 524
Solving: GM
Photo: YouTube

Ladislav Salai Jr. of Slovakia recently joined the exclusive club of double-GMs by gaining the composing title last year, having been a grandmaster solver since 2011. He is an International Master for playing the game as well, and this triple accolade seems to be unique. In composition, he’s equally proficient in studies, directmates, helpmates, selfmates, and unorthodox problems that employ armies of fairy pieces. He tends to favour very complex themes that involve a formal relationship between the variations. In the OTB game, he played for Slovakia at the 1996 Chess Olympiad, and won the Slovak Championship of 1997. Incidentally, his late father Ladislav Salai Sr. was also an accomplished problemist.

Ladislav Salai Jr.
Czechoslovakia–Israel Composing Match 1992
6th Place
Mate in 2

Tries: 1.Sd3? (threat: 2.Rd4 [A]). 1…Se6 2.Sf6 [B], but 1…Ra4! 1.Bd7? (2.Sf6 [B]). 1…Se4 2.c4 [C], but 1…Sh7! Key: 1.Sg3! (2.c4 [C]). 1…Rc5 2.Rd4 [A]. The three white moves marked [A], [B], and [C] recur in the virtual and actual play as threats and variation mates, in a pattern called the cyclic pseudo le Grand theme. Furthermore, in all three variations White’s mating move cuts off a white line of guard to a flight-square, after it’s blocked by a black piece.

2. Milan Vukcevich (1937-2003)

Composing: GM, FIDE Album points: 162.67
Game: FM, Best World Rank: 70
Solving: Master-level
Photo: ‘My Chess Compositions’ book cover

The Yugo-American Milan Vukcevich was a top-class problemist, brilliant player, and distinguished scientist rolled into one. Unusual among composers highly-skilled at the game, he created few endgame studies, and his diverse FIDE Album entries comprise directmates, selfmates, helpmates, and unorthodox types. He was also a strong solver who came third in the 1981 World Chess Solving Championship. In practical play, Vukcevich represented Yugoslavia in the 1960 Chess Olympiad where he won a bronze medal, and his best tournament results were equal first in the 1969 U.S. Open Championship (shared with Benko and Bisguier) and third place in the 1975 closed U.S. Championship. There’s little doubt he could have scaled even greater heights as a player if not for his chosen career as a professor and theoretical scientist, one who was nominated for a Nobel Prize in chemistry.

Milan Vukcevich
StrateGems 1998
1st Prize
Mate in 3

Key: 1.Qh7! (threat: 2.Rh1+ Kxg2 3.Qe4). 1…Qxh7 2.Kc3 (3.B~) Qxh2 3.Be4, 2…Qd3+ 3.Bxd3, 2…Qc2+ 3.Bxc2, 2…Qxb1 3.Rxb1, 2…Kf1 3.Bd3. 1…Bxh7+ 2.Kb3 (3.B~) Bd3 3.Bxd3, 2…Bc2+ 3.Bxc2, 2…Bxb1 3.Rxb1, 2…Kf1 3.Bd3. 1…Sxh7 2.Kd3 ~ 3.Bc2. 1…Sg6 2.Kc3 (3.B~) Kf1 3.Bd3. 1…g6 2.Rh1+ Kxg2 3.Qb7. 1…Kf1 2.Rh1+ Ke2 3.Qd3. This famous work features a three-fold queen-sacrifice key that also invites two black checks, followed by quiet white king moves and battery mates.

1. Genrikh Kasparyan (1910-1995)

Composing: GM, FIDE Album points: 175.83
Game: IM, Best World Rank: 31
Photo: ARVES

Considered by many to be the greatest study composer of all time, the Armenian Genrikh Kasparyan was one of four people honoured with the grandmaster title for composition when it was instituted in 1972. His body of work, consisting of about 600 studies, is marked by great depth of analysis and subtlety of play. His favourite themes include domination, positional draw, mate, stalemate, and systematic manoeuvre. He was an International Judge for composition, and he also authored many endgame anthologies that are now regarded as classics. In competitive chess, Kasparyan became an International Master in 1950 when the title was introduced. He won the Armenian Championship ten times, including twice with Petrosian as the joint-winner, and qualified for the finals of the USSR Championships four times.

Genrikh Kasparyan
64 1935
White to play and draw

Not 1.Qe4+? Kb8! 2.Qxe7 Qg6+ 3.Kxh4 Qh6+ 4.Kg4/Kg3 f1(Q), and Black wins. 1.Qc8!+ Ka7 2.Qc7+ Ka6 (2…Ka8 3.Qc8+ perpetual check) 3.Qxe7 Qg6+ (3…f1(Q) 4.Qb7+/Qa7+ Kxb7/Kxa7 stalemate, else perpetual check, e.g. 4.Qb7+ Ka5 5.Qb4+ Ka6 6.Qb7+) 4.Kxh4 Qh6+ (4…f1(Q) 5.Qb7+/Qa7+ Kxb7/Kxa7 stalemate, else perpetual check) 5.Kg3 f1(Q) 6.Qe2+! Qxe2 stalemate. Three different stalemate positions occur, the final one of which involves exploiting the black king’s placement on a6.

5 Aug. 2018 – ‘Chess Problems Out of the Box’ by Werner Keym

The German expert Werner Keym has brought out a wonderful new book entitled Chess Problems Out of the Box. An updated and expanded English edition of an earlier volume in German, this is a collection of 500 orthodox but out-of-the-ordinary problems by over 200 composers. Its first sections deal with the special moves in chess, namely castling, en passant capture, and pawn promotion, as they occur thematically in directmates, endgame studies, helpmates, and selfmates. A number of unconventional ideas and devices are then covered, such as asymmetry, board rotation, and the addition of pieces. The remainder of the problems – about half of the book’s total – involves retrograde analysis, either as the focus of a composition or a subsidiary feature. Practically all types of retros are represented here: last move determination, legality of castling and en passant capture, retractors, proof games, dead reckoning, illegal clusters, and many more.

The author has made a brilliant selection of problems for this anthology. For each theme that is examined, he provides a variety of first-rate examples that could be, say, a letztform (ideal setting), a maximum task, a first realisation, or a particularly attractive demonstration. Thus we see directmates in which the four castling moves all take place, endgame studies that bring about Allumwandlung, helpmates that (nearly!) accomplish the 100 Dollar theme (black and white excelsior knight-promotions), and so forth. While many famous classics are cited, the vast majority of the selected works are new to me, including the two samples below.

György Páros
FIDE Review 1958
Special Prize
Helpmate in 3
Twin (b/c/d) Sb5 to d3/f3/h5

The first is a beautiful rendering of black Allumwandlung in a helpmate. Depending on where the white knight begins in this quadruplet, Black promotes to a different type of piece and uses it to block each of the king’s four diagonal-flights. Meanwhile, the white bishop guards four pairs of flights cyclically and the white knight controls the fourth flight as it mates from different squares. 1.h1(B) Bd3 2.Bc6 Bg6 3.Bd7 Sc7, (b) 1.h1(Q) Bg2 2.Qh5 Be4 3.Qf7 Sc5, (c) 1.h1(S) Bb5 2.Sg3 Bc6 3.Sf5 Sg5, (d) 1.h1(R) Bb5 2.Rhd1 Be8 3.R1d5 Sg7. Readers are encouraged to solve the next problem before reading further!

Werner Keym
Weser-Kurier 1968
Mate in 2

The book’s wide-ranging coverage of retros, with clear explanations of the various sub-types, also makes it an excellent introduction to the genre, an area in which Keym is an authority. He is a fine composer too, and many of his own works are presented here. The miniature above is a delightful example in which the pleasantly open position disguises the retro content. Ostensibly this two-move problem is solved by 1.Rb6!? Kxc4 2.Qd4, but that’s an invalid solution because Black has no possible last move in the diagram! The black king couldn’t have come from any of its adjacent empty squares, where it would have been in an illegal double-check. Therefore White must have made the last move, and it’s Black to play now: …Kxe6 1.Rc7! Kd5 2.Qf5, and …Kxc4 1.Qd4+! Kxb3 2.Re3, 2…Kb5 2.Rb6. This retro idea, categorised under unconventional first move, is suitably described as a “nasty trick”!

Chess Problems Out of the Box (2018, Nightrider Unlimited) is available for €10 (paperback), €28 (hardback) + postage. For more details on the publication (including a free excerpt) and information on how to order, go to the book’s page on the publisher’s site.

8 Sep. 2018 – Adventures with endgame tablebases

In an earlier Walkabout column (12 Mar. 2018) I looked at the engine Stockfish from a problemist’s perspective. Another major advance in computer chess has been the development of endgame tablebases, which in some ways are even more amazing than super-strong engines. Tablebases are essentially databases of endgame positions that have been exhaustively analysed so that their outcomes (win/loss/draw) with best play by both sides are known with certainty. Moreover, in these positions the result of every possible move has been determined precisely, and thus each winning or losing move is provided with a “depth-to-mate” number, i.e. how many turns before mate is forced. What this means is that for any tablebase position, we know its complete “truth” and how perfect play would proceed.

Early tablebases could only deal with settings of specific materials, e.g. K+Q vs K+R, but as computer performances improved, we saw the creation of general tablebases that could handle any combination of pieces up to a certain total number of units. A milestone was reached in 2012 when a Russian team used a supercomputer to generate the Lomonosov tablebases, which cover all possible endgames with seven units or fewer (barring the trivial cases of six pieces vs king). Consequently, the game of chess is more-or-less solved for such miniature positions! Here are some online resources for accessing these marvels of modern technology: (1) Nalimov EGTB – 6 pieces maximum (free); (2) Lomonosov Tablebases – 7 pieces maximum (annual subscription fee required, but free for fewer pieces); (3) Android app for Lomonosov – 7 pieces maximum (free and highly recommended).

Tablebases analysis and resultant discoveries about the endgame have had a profound effect on many facets of the game; see the Wikipedia entry on the subject for details. Here I will consider how tablebases affect chess composition, and delve into three positions that illustrate what has been made feasible in problems and endgame studies. These positions employ the same material of Q+S vs R+B+S, and although I didn’t realise it at the time, this is identical to the pieces used in some length-record settings uncovered by tablebases, where to force mate requires over 500 (!) moves. My initial aim was merely to give Lomonosov some random homebase positions (all units on their array squares) to test and see if any of them would yield interesting play. The most remarkable case that I came across, with a depth-to-mate number of 90, is diagrammed below. [Syzygy TB Link]

If we treat this position as a directmate problem that requires the quickest mate to be found, a surprisingly large number of white moves in the solution are uniquely forced. In deciding on the main variation, I tried to maximise the number of such precise moves, and in the given line 77 of the 90 white moves are unique and they are marked with an '!'. Since “only” 13 white moves have duals, these alternatives are specified as well whenever they occur. As in most lengthy tablebase solutions, the play is not really human-comprehensible. But out of all these perfect moves, the stand-outs are three instances where the white king retreats from e2 to d1 for no apparent reason. If this were a composed problem without any duals, these recurring Kd1! (at moves 22, 32, and 41) would have been a marvellous theme!

Lomonosov tablebases position
Mate in 90

1.Qa4+! Kf7 2.Qb3+! Kg7 3.Qg3+! Kf7 4.Sd2! Be7 5.Qf3+! Sf6 6.Qb3+! Kf8 7.Qb8+! Kg7 8.Qg3+! Kf7 9.Sf3! Rh5 10.Sg5+! Kg7 11.Sh3+ (11.Se6+) Kf7 12.Sf4! Rh6 13.Qb3+! Ke8 14.Qe6 (14.Ke2) Kf8 15.Qc8+! Se8 16.Qf5+! Bf6 17.Ke2! Sd6 18.Qg4! Be7 19.Sg6+! Kf7 20.Se5+! Kf6 21.Sd7+ (21.Qf4+) Kf7 22.Kd1! Incredible! For instance, 22.Kd3? is one move slower, while 22.Kf3? takes another 195 moves to mate! 22…Rh1+ 23.Kc2! Rh2+ 24.Kd3! Rh6 25.Qf4+ (25.Qf3+) Kg7 26.Qg3+! Rg6 27.Qe5+! Kf7 28.Qd5+! Kg7 29.Qd4+! Kg8 30.Se5! Rg3+ 31.Ke2 (31.Kc2) Rg2+ 32.Kd1! Again! 32…Rg5 33.Qd5+! Kh7 34.Qe6! Rg1+ 35.Ke2! Rg2+ 36.Kf1 (36.Kf3) Rg7 37.Qh3+! Kg8 38.Ke2! Bf8 39.Qb3+! Kh8 40.Qe3 (40.Qf3) Kg8 41.Kd1! Yet again! Here some white king moves permit Black to draw, e.g. 41.Kf1? To see why, check the next diagram! 41…Be7 42.Sc6 (42.Qb3+) Bf8 43.Sd8! Be7 44.Qb3+! Kh7 45.Qd3+! Kg8 46.Qd5+! Kh8 47.Se6! Rf7 48.Qe5+ (48.Qh5+) Kg8 49.Qg3+! Kh8 50.Qg6! Rf1+ 51.Kd2! Rf2+ 52.Ke1 (52.Ke3) Rf7 53.Ke2! Rh7 54.Sf4! Bf8 55.Qg5! Sf7 56.Qf5 (56.Qd5) Kg8 57.Se6! Rh2+ 58.Kf1! Another mysterious retreat; now 58.Kd1? is slower by two moves. 58…Rh1+ 59.Kg2! Rh7 60.Qg4+ (60.Qg6+) Kh8 61.Qg3! Rg7 A strange-looking defence but it is the best. 62.Sxg7! Bxg7 63.Qh3+! Bh6 64.Kg3! Kg7 65.Kg4! Kf6 66.Qf3+! Ke6 67.Qb3+! Kf6 68.Qb6+! Ke7 69.Kf5! Sd6+ 70.Kg6! Bf4 71.Qd4! Bh2 72.Qh4+! Ke6 73.Qxh2! Kd5 74.Qg2+ (74.Qd2+/Qg3/Kg5) Ke5 75.Qc6! Se4 76.Qc4! Sd6 77.Qc5+! Ke6 78.Qd4! Se8 79.Qc4+! Kd6 80.Kf5! Sg7+ 81.Ke4! Se6 82.Qd5+! Ke7 83.Ke5! Sf8 84.Qd6+! Kf7 85.Qf6+! Kg8 86.Kf5! Sh7 87.Qe7! Sf8 88.Kg5! Sh7+ 89.Kh6! Sf6 90.Qg7!

In endgame studies, best play by both sides is assumed and since tablebases contain such perfect play information, they become a powerful resource for obtaining correct study positions. Some composers have written special programs to “mine” tablebases and generate studies that meet the criteria of soundness (dual-free variations) and interest (certain themes displayed). This method of composition is contentious for obvious reasons, but regardless, you can see some striking results of this approach in the problemist Árpád Rusz’s blog. Sometimes it’s even possible to “discover” a study by chance simply by examining the tablebase analysis of a random position. In the solution of the Mate-in-90 problem above, it’s mentioned that 41.Kf1? allows Black to draw. It turns out that the way in which Black forces a draw here is both precise and special – sufficiently so to work as a study. Here is the position in question, reflected and with the colours reversed: [Syzygy TB Link]

Peter Wong
OzProblems.com 2018
White to play and draw

Black generally has a win with this material (as implied by the forced mate in the homebase diagram), but if the knights were exchanged, the remaining Q vs R+B is normally a book draw. The sacrificial opening 1.Sc5! is thus aimed at bringing about a knight swap via the fork, e.g. 1…Qd5 2.Sxe4 Qxe4 =. Black has two options that avoid an immediate exchange. (1) Accept the sacrifice with 1…Sxc5, but this diverts the black knight to the queen-side with the result that it cannot interfere with a perpetual check: 2.Rf2+ Kg7 3.Rg2+ Kh6 4.Rh2+ Kg5 5.Rg2+ Kf6 6.Rf2+, etc. If the king goes to the e-file, two sub-variations arise: (a) 6…Ke7 7.Re2 Se4 8.Bg2. With the knight about to be lost, Black’s only chance is 8…Qb6+ 9.Kh1! (9.Kf1/Kh2? would lose, e.g. 9.Kf1? Qf6+! 10.Kg1 Qd4+ 11.Kf1 Qa1+ 12.Re1 Qf6+ 13.Ke2 Qf2+) Qh6+ 10.Kg1 Qc1+ 11.Kh2 Qc7+ 12.Kh1 and Black can make no progress despite the material advantage, i.e. a positional draw. (b) 6…Ke5 7.Re2 Se4 8.Bg2 Qb6+, and now in contrast to (a), 9.Kh1? would lose to 9…Kf4! 10.Rxe4+ Kg3 11.Bf1 Qh6+, but 9.Kf1 or 9.Kh2 draws – this dual is a pity – 9…Qb1+ 10.Re1 Qd3+ 11.Re2 Qd1+ 12.Re1 another positional draw. (2) The alternative 1…Qb6 seems to win the white knight without allowing perpetual check, as the piece is both pinned and doubly attacked, but 2.Rf2+! (unpinning the knight with check, e.g. 2…Ke7 3.Sxe4) induces 2…Sxf2 3.Sd7+ Ke7 4.Sxb6. I like how if Black doesn’t take the offered knight on the first move, White promptly sacrifices the rook instead!

How does this tablebase-produced study compare with existing compositions that involve the same material? The Chess Endgame Study Database, which enables searches based on the exact material used, brings up five studies with matching pieces. An examination of these varied endgames reinforces my view that the setting above is of publishable quality. However, among these examples there is an exceptional study that shows a similar kind of idea; though not an anticipation, it’s clearly the superior work thanks to its more intensive treatment of the theme, and I quote it below.

Naturally, we can set up this position on Lomonosov and check its analysis against the author’s solution. And this brings us to another salient feature of tablebases – their ability to confirm the soundness or otherwise of every miniature study ever composed. While engines like Stockfish are strong enough to solve most studies, they do so without necessarily providing certainty to the accuracy of the intended play. Tablebases can do these verification tasks perfectly and instantaneously, within the 7-piece limit. For testing directmate problems, programs like Popeye are still preferable because of the convenience of the solution files they produce, though again tablebases have a speed advantage when solving miniatures with lengthy solutions. In the case of the Matouš study here, it is proved to be sound and completely dual-free. [Syzygy TB Link]

Mario Matouš
Tidskrift för Schack 1981
1st Prize
White to play and draw

Black has numerous threats in the diagram, including 1…Qxb2, 1…Qf2+, and 1…Sxe2 2.Rxe2 Qxh4+, so White has to start with forcing checks: 1.Rb8+ Kh7 (1…Kg7? 2.Sf5+) 2.Rb7+ Kg8 (2…Kh6? 3.Sf5+) 3.Sf5! Qf2+ (best because Black wants to avoid exchanging the knights, e.g. 3…Qc5 4.Rg7+ Kf8 5.Rxg1 Qxf5 =) 4.Kh1. Now Black has three plausible captures, and in the resulting distinct variations White’s methods of securing a draw are remarkably harmonious. (1) 4…Qxe2 5.Se7+! (5.Kxg1? Qg4+, the black knight is immune to capture because of deadly queen checks, not just here but for the rest of the variation!) 5…Kf7 6.Sd5+ Kf8 (6…Ke8 7.Re7+, 6…Ke6/Kg6 7.Sf4+) 7.Rb8+ Kg7 8.Rb7+ Kh6 9.Rb6+ Kg5 (9…Kh5 10.Sf4+) 10.Rg6+! Kf5 (10…Kxg6 11.Sf4+) 11.Rf6+ Kg4 (11..Ke5 12.Re6+! Kxe6 13.Sf4+) 12.Rg6+ Kh4 (12…Kh3 13.Sf4+) 13.Rh6+ Kg3 14.Rg6+ Kf3 (14…Kf2 15.Rg2+) 15.Rf6+ perpetual check. (2) 4…Qxf5 5.Bc4+! (again White can’t touch the knight: 5.Kxg1? Qe4! 6.Rb8+ Kg7 7.Bf1 Qg4+ 8.Bg2 Qd4+ 9.Kh1 Qd1+ 10.Kh2 Qd6+) 5…Kh8 (5…Kf8 6.Rf7+) 6.Rb8+ Kg7 7.Rb7+ Kg6 (7…Kf6 8.Rf7+) 8.Rb6+ Kh7 (8…Kg5/Kh5 9.Rb5) 9.Rb7+ Kh6 10.Rb6+ perpetual check. (3) 4…Sxe2 5.Sh6+! Kh8 (5…Kf8 6.Rf7+) 6.Sf7+ Kg7 7.Se5+ Kg8 (7…Kh6/Kf6 8.Sg4+) 8.Rb8+ Kh7 9.Rb7+ perpetual check.

Three different perpetual checks are arranged with great precision and economy in this wonderful study. I was delighted to find that it was selected for the FIDE Album, the anthology of the world’s best chess compositions. And as readers may have noticed, this First Prize winner was published back in 1981, well before computers were able to assist with the creation of any chess problems or studies. That’s a victory for human ingenuity, yes?

22 Oct. 2018 – More adventures with endgame tablebases

Endgame tablebases are software that provides perfect play information with total accuracy for any position with up to seven pieces. They can determine (1) the outcome – win, loss, or draw – of every legal move in such positions based on optimal play by both sides, and (2) the precise number of moves required to force a mate for each winning or losing move. I gave a brief overview of tablebases in the previous Walkabout (8 Sep. 2018) and considered how they have been utilised in the field of chess composition. Here I will present three remarkable positions that came about with the aid of this tool. The first two are examples of mutual zugzwang, a paradoxical situation where neither player wants to be the side to move. The third is an offbeat endgame study that cleverly exploits not only tablebase data but also a problem convention relating to the 50-move draw rule.

In a mutual zugzwang (MZ) position, whoever has the move would prefer to pass on the turn because every possible move of each side contains a significant weakness, one that would result in a worse outcome than if the other player is to move. This curious type of situation is considered interesting in endgame theory, and tablebases have been used to systematically uncover examples. Recently the composer Árpád Rusz (mentioned in the last column) devised a program to generate hundreds of thousands of 7-piece MZ positions, categorised according to materials such as KPPP vs KPP and KRPP vs KRP. He has kindly shared on his site these massive lists of positions, from which I select two unusual cases. Both are attractively open settings with fairly mobile pieces and passed pawns, so the double-zugzwang is especially surprising. They also illustrate the less common full-point MZ. Whereas in a typical MZ one of the players would win if it’s the other’s turn but still draw if given the move, in a full-point MZ whoever is to move would lose the game.

MZ is a popular theme in endgame compositions, but of course not all MZ positions are suitable for adapting into studies. The diagram below shows a borderline case where White’s play at some stages is too imprecise to work as a proper study, but redeeming features include a delightful key-move and a natural try that make the MZ theme hard to miss, plus a fitting finish. [Syzygy TB Link]

Mutual zugzwang study (?)
White to play and win

White’s only winning move is 1.h3!!, producing the MZ position. Now not only is Black in zugzwang, but if it’s White’s turn again [Syzygy TB Link], then 2.h4 (or any other move) would lose, and that implies 1.h4? would fail too and hence function as a thematic try. The double-step is refuted by 1…Kd5! 2.Kc3 (2.h5 Ke6 3.h6 Kf6 4.h7 Kg7 5.Kc3 Kxh7 6.Kb4 Kg6 7.Kxa4 Kg5 8.Kb4 Kg4 9.Kc3 Kf3 10.Kd2 Kf2 and White must lose the pawn) 2…Ke6 3.Kb4 Kf5 4.Kxa4 Kg4 5.Kb4 Kxh4 6.Kc4 Kg3 7.Kd5 Kf3 8.Kxe5 Kxe3 and Black wins.

The advantage of 1.h3!! is that by attacking g4, it will cost the black king an extra tempo to capture the h-pawn. 1…Kd5 (1…a3 2.h4 a2 3.Kb2 Kd3 4.h5 Kxe3 5.h6 Kd2 6.h7 e3 7.h8(Q) wins) 2.Kc3 (2.Kb2 and then 3.Ka3 also works) 2…Ke6 3.Kb4 Kf5 4.Kxa4 Kg5 5.Kb4 (the white king can approach in other ways as well) 5…Kh4 6.Kc4 Kg3!? Sets a trap for White: 7.Kd5? Kf3! 8.h4 (8.Kxe5? loses to 8…Kxe3 because Black’s e-pawn will promote with check) 8…Kxe3 9.h5 Kd3 10.h6 e3 11.h7 e2 12.h8(Q) e1(Q) draws. 7.h4! Kxh4 (7…Kf3 8.h5 wins) 8.Kd5 Kg3 9.Kxe5! (9.Kxe4? Kf2 draws) 9…Kf3 10.Kd4! We end with a well-known full-point MZ position – whichever side is to move will lose their pawn and the game.

Despite both players having a rook in the next position, neither side (if given the turn) has a waiting move that could avoid fatal self-damage. The rooks are mostly tied to their ranks as they are stopping their opponents’ pawns from promoting. White’s connected passed pawns seem very strong, but to balance that, Black has opportunities for effecting a back-rank mate.

Mutual zugzwang position
White to play: Black wins
Black to play: White wins

White to play: Black forces a win. [Syzygy TB Link] White’s most interesting defence is 1.Ke1. The more tempting 1.g7, by closing the long diagonal, loses to 1…Rb1! because 2.h8(Q) no longer deals with the threat of 2…Rxc1+ 3.Kxc1 a1(Q) mate (or 2.Ke1 Rxc1+ though 2…Ke3 is an even faster win for Black). Any first move by the white rook is defeated easily, e.g. 1.Ra1 Rb1+ 2.Rxb1 axb1(Q) mate. The weakness of 1.Ke1 is that the white king no longer protects the rook, inviting 1…Rb1! Now White has two alternatives with subtle differences, even though they soon transpose into each other. (1) 2.h8(Q) Rxc1+! Not 2…a1(Q)? 3.Qxa1! Rxa1 4.Rxa1 wins. 3.Kf2 a1(Q) and Black has a Q+R vs Q book win, which the g-pawn is not sufficiently advanced to thwart. (2) 2.Kf2 Rxc1! Not 2…a1(Q)? 3.Rxb1! Qxb1 (if the black queen checks, White still draws, e.g. 3…Qf6+ 4.Ke1! Qxg6 – threatens mate and the h7-pawn – 5.Rb3+!) 4.h8(Q) draws. 3.h8(Q) a1(Q) transposing to the same Q+R vs Q win as (1).

Black to play: White forces a win. [Syzygy TB Link] Black has no standout move that compels White to play precisely for long, but 1…Rf8 could be viewed as the thematic line… If Black tries 1…Rb1 – such an effective response when White moves first – then White wins with 2.h8(Q) a1(Q) (2…Rxc1+ 3.Kxc1) 3.Qxa1 (3.Qh3+ also wins) Rxa1 4.Rxa1. The second alternative 1…Rc8 is a nice sacrifice that cannot be accepted (2.Rxc8? a1(Q)+ 3.Rc1 and Black mates in three with 3…Qb2/Qd4): 2.Ra1! Rb8 (threatening 3…Rb1+) and 3.Kc1 wins as the back-rank threats have dissipated and the connected pawns become decisive. After 1…Rf8, the mating threat on f1 forces 2.Ke1 and now 2…Re8+ is answered by 3.Kf2/Kf1, again winning for White because the king is out of danger. Here White must avoid 3.Kd1? when Black wins with the unique 3…Rb8!!, which brings back the diagram position with White to play and in zugzwang!

These MZ positions are extracted from the recently completed 7-piece Syzygy endgame tablebases, a free alternative to the Lomonosov tablebases. Their main difference is the metrics used to determine when a position is “won.” The more standard depth-to-mate (DTM) metric calculates the number of moves needed to achieve mate, disregarding the 50-move draw rule. Syzygy examines depth-to-zeroing (DTZ) instead: how quickly we can reach a “zeroing” move – a capture, a pawn move, or mate – that would reset the count for the 50-move rule (while maintaining the win). Now, since the 50-move draw rule doesn’t actually apply to chess compositions (see below), the DTZ metric holds no special advantage when used to analyse composed problems and studies. Indeed, for verifying directmate problems, where the quickest route to mate is stipulated, only DTM is suitable. For checking studies, which require a win or a draw to be found without imposing a move limit, the specific DTM or DTZ numbers are not that relevant, but both tablebase types are useful in revealing the win/loss/draw outcome of each possible move.

Oddly enough, our very next example contradicts what I just said about the unimportance of DTM and DTZ figures in studies! To grasp this unusual piece of work, first we have to consider how the 50-move draw rule is treated in compositions. On the World Federation for Chess Composition site, the Codex for Chess Composition states in Article 17: “Unless expressly stipulated, the 50 moves-rule does not apply to the solution of chess compositions except for retro-problems.” It makes sense for problems and studies – with their aesthetic intent and idealised play – to ignore such a rule, one based on an arbitrary number. The exception is made for retros to cover a sub-genre of problems in which it can be proved by retro-analysis that a large number of moves have taken place without a capture or a pawn move, such that the 50-move rule comes into play and it becomes part of the problem’s theme. Such retro problems involve intricate retractions and heavy positions, and seem far removed from the miniature studies we’ve been looking at, the sort where tablebase analysis is practicable. Yet by making allowance for these traditional retros, Article 17 has an unexpected consequence in certain situations, one brought to light by the composer of the following study.

Andrew Buchanan
Problem Database website 2017

By convention, the “Draw” stipulation means White is to play and force a draw, but how can that be the goal here when White has multiple mate-in-one moves? It turns out, upon further inspection, that Black couldn’t have made the last move to reach the diagram position. That’s because if the black king had just moved from a7 or b7 to b8, the piece would have been in an impossible double-check by the white pieces; and if the black queen had just come from any of the empty squares, a7, b7, c6, or d5, the piece would have been checking White while it’s Black’s turn – again an impossibility. That means, for the position to have arisen legally, White must have made the last move and it’s Black to play now. Black’s best move is 1…Qxa6 (anything else would allow White to at least draw easily). Now we have a KQ vs KBB ending, which is generally a win for the queen side. Indeed, if you were to set up this position on the Lomonosov tablebases (or the Nalimov ones), you’d find that the DTM is 69, i.e. Black has a forced mate in 69 moves against White’s best defence. So how can White achieve a draw?

Well, the study has required us to use retro-analysis to determine that it’s Black to play in the diagram. Therefore it also counts as a retro problem, and according to Article 17, the 50-move rule comes into effect! The DTM69 here is over 50 but it doesn’t actually tell us if Black could force a win under the 50-move rule, as that condition calls for a different winning strategy. This is the zeroing strategy mentioned above, where a player aims for a capture or a pawn move and thus reset the move count. We can see the exact results of this approach, viz. the DTZ numbers, by consulting the Syzygy tablebases. Here’s a link to the Syzygy site with the position already set up. Note that Syzygy also provides DTM data for positions with five pieces or fewer, but a little confusingly, they use single-move numbers (for both metrics), unlike Lomonosov and Nalimov which use the more familiar pair-move format; that’s why Syzygy indicates DTM137 for this position rather than DTM69. Now for the DTZ results, only one white move has a number higher than 100: Bc7+ with DTZ117. Thus after this bishop move, Black will need more than 50 moves to force a winning capture, but before the latter could be made, White can claim a draw under the 50-move rule as per Article 17. Therefore 2.Bc7+! is the unique drawing move. What a witty and imaginative composition! For more examples of this idea, check out its author’s Endgames to make your head hurt.

27 Nov. 2018 – Carlsen-Caruana WCC Game 6 – The actual forced-mate sequence that was missed

Game 6 of the 2018 World Chess Championship is perhaps most notable for an incredible winning sequence that was found by a computer named Sesse, but missed by the players. As widely reported, the Norwegian computer running the Stockfish engine announced a mate in 30 moves for Black after 68.Bc4, and even Carlsen was asked about it in the post-game press conference. Many GMs have since explained this very impressive winning manoeuvre starting with 68…Bh4!!, but they all finish their analysis with 84…Kxh7, because that capture leaves Black in a clearly won position. Like a lot of players, I was interested in seeing the full forced-mate sequence, but it wasn’t easy to find online. And strangely, some sources claim that it’s a mate in 36 moves rather than 30, while others that provide a specific mating line suggest that it takes even longer, such as the M42 given in a Chess.com news article, and a M63 from a Reddit post that apparently shows a Sesse screenshot. So what is the actual forced mate and how many moves does it involve? The answer is… none of the above!

I first noticed something was amiss when looking at the just-mentioned M42 in the Chess.com article. It commences with Sesse’s 17-move study-like play that wins the h-pawn with 84…Kxh7, but note that this capture reduces the position to 7 pieces, meaning from here we can use endgame tablebases to determine the shortest mating line with best play by both sides. (If you’re not familiar with tablebases, which effectively play perfect chess in light positions, check out my introductory column, Adventures with endgame tablebases.) And the Lomonosov tablebases indicate that it takes another 41 moves for Black to force mate, after the pawn capture. Checking some random moves in the M42 sequence – as well as those in the Reddit post M63 – against Lomonosov’s perfect analysis confirms that they include many sub-optimal choices. Now if the tablebases prove that after the first 17 moves, Black needs 41 more to mate, that’s a total of 58 moves. So how could Sesse have announced a mate in 30 or 36? Perhaps it started with another manoeuvre that’s quicker, but then all of the GMs would have been discussing a weaker line, which doesn’t make sense.

After more digging around online, I eventually found the full variations for the purported M30 and M36. Both were posted by a user on Chessgames.com, and confirmed by other sites. Here’s an image for each; the first is from a live coverage of the game on Chessdom.com, and the second is a Sesse screenshot posted on Imgur.com.

Both lines indeed begin with the familiar series of 17 moves, so the GMs were correct, but if they had examined Sesse’s ensuing play in these variations, they would have noticed something quite bizarre. In the M30, White’s play isn’t merely sub-optimal, but outright suicidal! After leaving the bishop en prise, White obligingly marches the king to a corner to make it easy for Black to mate, as if this were some sort of helpmate problem. The M36 isn’t as obviously erroneous, but consider the position after 98.Kh2 (=31.Kh2 below), for instance: the Stockfish on Chess.com finds various mates-in-3 for Black here, but Sesse took 6 moves to mate.

Carlsen vs Caruana
World Chess Championship 2018
Game 6
Position after 68.Bc4
Sesse “M30” and “M36” variations

1…Bh4!! 2.Bd5 Se2 3.Bf3 Sg1!! 4.Bg4 Kg8! 5.Kh6 Bg3 6.Kg6 Be5 7.Kh6 Bf4+ 8.Kg6 Bg5 9.h6 Kh8! 10.h7 Bh4 11.Kh6 Be1 12.Kg6 Bc3 13.Kh6 Bd2+ 14.Kg6 Bg5 15.Bh5 Sh3 16.Bg4 Sf4+ 17.Kf7 Kxh7
“M30”: 18.Bd1 Kh6 19.Kf8 Sd5 20.Kg8 Se7+ 21.Kh8 Sxf5 22.Kg8 Se3 23.Kf7 Sxd1 24.Ke6 f5 25.Kd5 f4 26.Kc4 f3 27.Kb3 f2 28.Ka2 f1(Q) 29.Ka1 Qe2 30.Kb1 Qb2.
“M36”: 18.Bd1 Kh6 19.Kf8 Bh4 20.Kf7 Kg5 21.Kg7 Kxf5 22.Kh6 Ke5 23.Kg7 f5 24.Kh6 Be1 25.Kg5 Sh3+ 26.Kh5 f4 27.Kg4 Sg1 28.Kg5 f3 29.Kg4 f2 30.Kg3 f1(Q)+ 31.Kh2 Qh3+ 32.Kxg1 Bf2+ 33.Kxf2 Kf4 34.Ke1 Ke3 35.Be2 Qf5 36.Kd1 Qb1.

How could the same Sesse/Stockfish that discovered the brilliant 68…Bh4!! and 70…Sg1!! make these terrible moves in its analysis? Sesse is even linked to the Lomonosov tablebases, according to their site. I’m no engine expert and could only hazard a guess that it relates to some incorrect or incomplete tablebases lookup. Tablebases provide two kinds of information: (1) the win-draw-loss outcome of a position and (2) the quickest route to a forced win/loss for any decisive move. Because the two types of data could be stored independently, perhaps Sesse had access to (1) and knew that 84…Kxh7 would result in a won position, but not (2) and so chose non-optimal moves based on a formula best known to itself.

Until this software issue is fixed, the Sesse team should really avoid announcing mate in X moves, and chess journalists should take the computer’s pronouncements of such with a grain of salt. But while there was actually no forced mate in 30 or 36 moves in Game 6, there was one in 58 moves as mentioned, and Sesse could have declared such a daunting mate if it was able to consult the tablebases properly. For the record, here is the correct mating sequence that combines Sesse/Stockfish’s winning manoeuvre with Lomonosov’s perfect finish.

Carlsen vs Caruana
World Chess Championship 2018
Game 6
Position after 68.Bc4
Sesse variation and Lomonosov DTM41

1…Bh4!! 2.Bd5 Se2 3.Bf3 Sg1!! 4.Bg4 Kg8! 5.Kh6 Bg3 6.Kg6 Be5 7.Kh6 Bf4+ 8.Kg6 Bg5 9.h6 Kh8! 10.h7 Bh4 11.Kh6 Be1 12.Kg6 Bc3 13.Kh6 Bd2+ 14.Kg6 Bg5 15.Bh5 Sh3 16.Bg4 Sf4+ 17.Kf7 Kxh7
Lomonosov M41: 18.Bf3 Bh4 19.Bh1 Kh6 20.Bf3 Kg5 21.Be4 Se2 22.Bd3 Sd4 23.Bb1 Sxf5 24.Ke6 Sd4+ 25.Kd5 Bf2 26.Ba2 f5 27.Ke5 f4 28.Bd5 f3 29.Bb7 Bg1 30.Bxf3 Sxf3+ 31.Ke4 Kg4 32.Kd5 Kf4 33.Kd6 Se5 34.Kd5 Bb6 35.Ke6 Ke4 36.Kd6 Kd4 37.Ke6 Bc7 38.Kf6 Sd7+ 39.Ke6 Sc5+ 40.Kf6 Ke4 41.Kg5 Bd6 42.Kh5 Kf4 43.Kh4 Se4 44.Kh3 Kf3 45.Kh4 Bg3+ 46.Kh5 Kf4 47.Kg6 Bh4 48.Kh5 Be7 49.Kh6 Kf5 50.Kg7 Sd6 51.Kh6 Se8 52.Kh5 Sg7+ 53.Kh6 Kf6 54.Kh7 Sf5 55.Kg8 Kg6 56.Kh8 Bd6 57.Kg8 Sh6+ 58.Kh8 Be5.

24 Dec. 2018 – Even more adventures with endgame tablebases

Endgame tablebases are remarkable software that effectively plays perfect chess in any position with up to seven pieces. As such they are an invaluable analytical tool and in two previous Walkabouts (Adventures and More Adventures), I demonstrated some of their capabilities. Besides analysing existing endgames, tablebases could also assist in the creation of new positions with intriguing and even study-like play, and last time we looked at two examples of mutual zugzwang (MZ) extracted from the Syzygy tablebases. For this final part of the series, I have picked three more special cases of these paradoxical situations, again from the massive MZ files produced by Árpád Rusz. The first instance lends itself to conversion to an actual endgame study with some neat and precise variations. The other two diagrams are almost unbelievable in exemplifying double zugzwang, because in these positions both sides are able to promote a pawn safely, meaning each player would prefer it if the other side were to queen first!

In a mutual zugzwang position, each player would be worse off if given the turn, because every legal move of each side entails some exploitable weakness. The MZs presented here (unlike those in the last instalment) are not full-point ones but of the more standard type: if White is to move, Black would be able to draw, yet if Black is to move, White would have a forced win. In the analysis provided, unique drawing and winning moves, by Black and White respectively, are given with an exclamation mark. Further, the diagrams are accompanied by links to the Syzygy tablebases that will open with the positions already set up; hence you can easily follow the main variations on that site and also explore any lines not covered. Such Syzygy links have been added to the two earlier Adventures columns as well.

In the first diagram, White seems to have the advantage despite being a pawn down, because of the advanced a-pawn supported by the king. But an immediate attack with 1.Kb7? or 1.a7? only draws, largely due to the centred black king which has flexible defences. Black’s connected passed pawns are of course dangerous too and after, say, 1.Sf4? h4!, White even loses with any continuation except for the drawing 2.Kb7 or 2.a7. [Syzygy TB Link]

Mutual zugzwang study
White to play and win

The correct opening 1.Sh4! places the knight in a less exposed spot and brings about the MZ position. Imagine if it’s White to move again [Syzygy TB Link], then surprisingly no win is possible: either 2.Kb7 Kc5! 3.Kxa8 (3.a7 Sb6) 3…Kb6! 4.a7 Kc7! or 2.a7 Ke5! 3.Kb7 Kd6! 4.Kxa8 Kc7! would trap the king and leave White unable to progress, as the knight is stuck holding off the black pawns. Or if White tries 2.Sf5+ then 2…Ke5! gains a vital tempo by threatening the knight, e.g. 3.Sh4 (3.Sg3? loses to 3…h4!) 3…g3 4.Kb7 Kf4! 5.Kxa8 Kg4! 6.Sg2 h4 7.Kb7 h3! draws.

With Black to play after 1.Sh4!, the king on d4 is forced by zugzwang to abandon its position where it has quick access to both c7 (via e5) and b6 (via c5), two crucial squares for defence as seen above. (1) 1…Ke5 2.Kb7! Kd6 3.Kxa8! Kc7 4.Ka7! g3 5.Sg2! h4!? By sacrificing the pawn, Black creates stalemating chances. 6.Sxh4! Kc8 7.Kb6 Kb8 8.Sg2. Not 8.a7+? Ka8 9.Sg2 =. 8…Ka8 9.Se3 (9.Sf4 is a minor dual that wins similarly.) 9…Kb8 10.a7+ Ka8 11.Sd5 g2 12.Sc7 mate. (2) 1…Kc4 2.a7! Kb4 3.Kb7! Kc5 4.Kxa8! Kb6 5.Kb8! wins. (3) 1…g3 2.Sf5+! Ke5 3.Sxg3! h4 and now a white dual follows with two “exact” ways of stopping the h-pawn: (a) 4.Se2 h3 5.Sg1! h2 6.Sf3+! or (b) 4.Sh1 h3 5.Sf2! h2 6.Sg4+! The three thematic try moves – Kb7, a7, and Sf5+ – in the MZ position suitably reappear as White’s initial moves in the three main variations.

I will finish this three-part series with two complex positions that may not be fully comprehensible, but which are fascinatingly counter-intuitive. Each setting contains five passed pawns, most of which seem free to push forward. That includes two pawns of different colours that are ready to promote, and either could do so without fear of losing the new queen to any simple tactics. Yet the outcome for each side would be better if the other were to move and could promote first. These MZ situations thus represent a sort of antithesis to the pawn race!

What’s happening here is that when the two players promote in turn, that leads to another MZ in which both queens (as well as every other piece) would prefer to stay put. The queens are already ideally placed because they control various critical squares in different directions. Now whichever queen is compelled to move first, it cannot maintain its “focus” on all of these squares, and this loss of control is immediately punished by the other side. The numerous squares that must be covered by the queens, for both offensive and defensive purposes, account for the complexity of the play. Nonetheless, in the given variations we see general principles at work that are quite understandable for such queen and pawn endings. Black, who is a pawn down, typically aims for perpetual check and sometimes draws by winning one of the two white pawns. White’s chief weapon against perpetual check is to force a queen exchange that will leave a won pawn ending. However, the deciding factor in such a simplified pawn ending is not so much White’s extra material but how advanced the remaining pawns are, and if White is not careful, Black could even win with a better placed pawn.

In the first case below, after the two promotion moves, both queens are focusing on two key squares, e8 and b4. Either queen could give a strong check on e8 if it’s left unguarded, while the white queen has another check on b4 that’s prevented by the black promotee. Another important square is c5, defended by the white queen and black king against each other.

Mutual zugzwang position
White to play: Black draws
Black to play: White wins

White to play: Black forces a draw. [Syzygy TB Link] 1.f8(Q) e1(Q) (1) 2.Qf6. Although this queen move gives up access to b4/e8, it produces new threats on the 6th rank, besides other compensations. But let’s consider the alternatives first:
(2) 2.Qd6 Qe8+! 3.Kc7 Qf7+! 4.Kd8 Qg8+! 5.Kc7 Qf7+ perpetual check, or White could even lose if the queens are exchanged, because the c4-pawn is unhindered, e.g. 6.Qd7+? Qxd7+! 7.Kxd7 c3! 8.d6 c2! 9.Ke8 c1(Q)! 10.d7 Qc6 wins.
(3) 2.Qf7 Kc5 (2…c3 also draws) 3.Qd7. This move keeps guarding d5 and e8 and threatens 4.Qc6+, but after 3…Qe4, White has to play precisely for the next five moves to avoid losing (in contrast, 3…Qe5? loses to 4.Qc6+!). 4.Qc6+!? Kd4 5.a4!? c3 6.a5!? c2 7.a6!? Qf5+ 8.Kb7!? Qxd5 9.Qxd5+ Kxd5 10.a7 c1(Q) 11.a8(Q) =.
(4) 2.Kb7 Qa5 (2…Qb1 also draws) 3.Qe8+ Kc5 4.Qc6+ Kd4 5.d6 c3! 6.d7 c2!! 7.Qd6+ (7.Qxc2 Qb5+! 8.Kc7 Qa5+! 9.Kc8 Qa8+ 10.Kc7 Qa7+ 11.Kd6 Qxa3+! 12.Ke6 Qe3+! 13.Kf7 Qf4+! 14.Kd8 Qe5+! 15.Kd8 Qa5+! 16.Qc7 Qa8+! 17.Ke7 Qe4+! perpetual check) 7…Ke4!! 8.Qe7+ Kf3!! 9.d8(Q) Qxd8 10.Qxd8 c1(Q) =. This terrific sequence – can you work out why 7…Ke4!! and 8…Kf3!! are forced? – is unfortunately devalued by the 2…Qb1 dual.
(5) 2.d6 Qe6+ (2…Qe4/Qh1 also draw) 3.Kc7 c3! 4.Qb8+ Kc4! 5.Qb4+ Kd3! 6.d7 Qe5+! 7.Kc8 Qf5! 8.Kc7 Qe5+! 9.Qd6+ Qxd6+! 10.Kxd6 c2! 11.d8=Q c1=Q! 12.Ke5+ Ke2!! =.

After 2.Qf6, White’s main threat is 3.Qc6+. 2…Qe8+! Not 2…c3? 3.Qc6+! Ka5 4.d6 c2!? 5.d7 (5.Qxc2? Qe6+ 6.d7 Qc6+ 7.Qxc6 =) 5…c1(Q) 6.d8(Q) mate. 3.Kc7 (3.Kb7? actually loses to 3…Qd7+! 4.Kb8 Qxd5). Now White threatens M2 with 4.Qb6+, and thanks to the queen’s placement on f6, Black is out of useful checks. However, Black still has one way to draw: 3…c3!!, a decoying sacrifice. Not 3…Qe3? 4.Qc6+! Ka5 5.Qa8+ Kb5 6.Qb7+ Kc5 7.Qb6+, or 3…Kc5? 4.Qc6+ Qxc6+ 5.dxc6 c3 6.Kb7 c2 7.c7 c1(Q) 8.c8(Q)+, or 3…Ka4? 4.d6! Qe3 5.d7! wins. 4.Qxc3 or 4.Qb6+ Kc4! 5.d6 c2 =, or 4.d6 Qc6+ 5.Kb8 c2 =. 4…Qe7+ 5.Kc8 Qe8+ 6.Kb7 or 6.Kc7 Qe7+ perpetual check. 6…Qd7+ 7.Qc7 Qxd5+! draws as White’s last pawn is too far back to pose a threat.

Black to play: White forces a win. [Syzygy TB Link] 1…e1(Q) 2.f8(Q) (1) 2…Ka4. The king aims for an escape to b3, and the queen on e1 is also allowed to maintain its focus. Other plausible moves by Black are:
(2) 2…Qa5 3.Qe8+! Kc5 4.Qc6+! Kd4 5.d6! c3 6.d7 Qf5 7.Kb7 Qf7 8.Ka6 Qf1+ 9.Ka7 Qf8 10.Qb6+ wins.
(3) 2…Qc3 3.Qe8+! Ka5 4.d6! Qf3 5.Qe5+! Ka6 (5…Ka4 6.Qc5! wins) 6.d7! Qc6+ 7.Kd8 c3 8.Ke7! c2 9.d8(Q)! c1(Q) 10.Qea5+! Kb7 11.Qda8 mate.
(4) 2…Qe4 3.Qb4+! Ka6 4.Kc7 Qh7+ 5.Kc6! Qg6+ 6.d6! Qe4+ 7.Kc7! (7.Kc5? Qf5+! = or 7.Kd7? Qb7+! =) 7…Qh7+ 8.d7 Qh2+ 9.Qd6+ wins.
(5) 2…c3 3.Qb4+! Ka6 4.Qa4+ Kb6 5.Qc6+ Ka5 6.d6 Qe6+ 7.Kc7 Qf7+ 8.d7 c2!? 9.Qb6+ (9.Qxc2? Qc4+! 10.Qxc4 =) 9…Ka4 10.Qb4 mate.

Black has multiple threats after 2…Ka4, including 3…Qa5 = and 3…Kb3 =, but c5 is left unguarded and b4 has become a potential mating square. 3.Qc5! Not 3.d6? c3 4.d7 c2! 5.Qf4+ Kxa3 6.d8(Q) c1(Q)+ =. 3…Qe8+ or 3…Kb3 4.Qb5+ Kxa3 (4…Kc3 5.Qb4+) 5.Qxc4! wins. Now White must choose carefully between 4.Kb7!! and 4.Kc7? The latter fails to 4…Qb5! 5.Qxb5+ Kxb5! 6.d6 c3! 7.d7 c2! 8.d8(Q) c1(Q)+! = when Black promotes with check. 4…Qb5+ or 4…Qd7+ 5.Ka6 Kb3 6.Qb4+! Ka2 7.Qxc4+ Kxa3 8.Qc5+ Ka2 9.Qa5+ Kb3 10.Qb5+, or 4…Kb3 5.Qb4+! Kc2 6.Qxc4+! wins. 5.Qxb5+! Kxb5 6.d6! c3 7.d7! c2 8.d8(Q)! c1(Q) and White has two neat ways to pick off the black queen. 9.Qb6+ (or 9.Qe8+ Ka5 10.Qa8+! Kb5 11.Qa6+ Kc5 12.Qc6+!) 9…Kc4 or 9…Ka4 10.Qb4 mate. 10.Qc6+ wins.

The final position is even more intricate. After both sides have promoted, the white queen guards h8 and e5, two invading points for the black queen. The latter is ironically well-placed in the corner, because it further threatens checks from the a-file when the black king moves. For instance, suppose Black is to move and plays 2…Kb6 (threatening 3…Qa8+/Qa6+), White’s only winning reply is 3.Qd8+!, taking advantage of the check to gain a tempo. But that means d8 is another key square that the white queen has to keep focusing on. If White starts instead and chooses, say, 2.Qe2+, then d8 is no longer accessible and Black draws uniquely with 2…Kb6!

Mutual zugzwang position
White to play: Black draws
Black to play: White wins

White to play: Black forces a draw. [Syzygy TB Link] 1.e8(Q) a1(Q) (1) 2.Qh5. This move poses Black the most difficulties (and even defeats 2…Kb6 in a new way). Here are the alternatives:
(2) 2.Qd7 Qh8+! 3.Kc7 (or 3.Qd8 Qe5! transposes to the next line) 3…Qe5+! 4.Qd6 Qg7+ perpetual check.
(3) 2.Qd8 Qe5! 3.b5+!? Qxb5! (3…Kxb5? 4.Kb7! Qe4 5.Qb6+! Ka4 6.Kb8! f3 7.c7! Qf4 8.Qc6+ Kb3 9.Ka8! f2 10.c8(Q) f1(Q) 11.Qc2+ Kb4 12.Q8c5 mate) 4.c7 f3 5.Qf6+ Qb6 6.Qxf3 Qe6+! 7.Kb8 Qb6+! 8.Kc8 Qe6+! 9.Kd8 Qd6+ perpetual check.
(4) 2.Qe2+ Kb6! 3.Qf2+ Ka6! (3…Kxc6? 4.Qc5 mate) 4.Qxf4 (or 4.c7 Qh8+! =) 4…Qh8+! 5.Kd7 Qg7+ 6.Kd6 Qg6+! 7.Kd5 (7.Kc5 Qh5+! =) 7…Qd3+! 8.Qd4 (8.Kc5 Qb5+! 9.Kd6 Qb8+ 10.c7 Qb6+! 11.Kd7 Qb5+! 12.Ke7 Kb7! =) 8…Qb5+ 9.Kd6 (9.Qc5 Qd3+! perpetual check) 9…Qxc6+! 10.Kxc6 =.
(5) 2.c7 Ka7 (2…Kb6 also draws) 3.b5 Qb2! 4.Qh5 Qb4!! 5.Qf5 f3! 6.Qxf3 Qxb5! 7.Qe3+ Ka6! 8.Qa3+ Kb6! 9.Qd6+ Ka7! (9…Ka5? 10.Qe6 wins) 10.Kd8 Qg5+! perpetual check.
(6) 2.Kb8 Kb6! (threatens M2 with 3…Qa7+!) 3.Qd8+!? (unique move for White to salvage a draw) Kxc6! 4.Qc7+ Kd5! = (4…Kb5? 5.Qc5+! Ka4 6.Qa5+ wins).

In the main variation, 2.Qh5 carries these advantages: the queen maintains its defence of h8 and e5, and targets the mating square a5; further, White now threatens 3.c7/Kb8/Qh7. But Black handles all of these complications with 2…Qa4!, threatening 3…Qxc6+. Not 2…Kb6? 3.Qc5+! Ka6 4.b5+ Ka5 5.Qa7+, or 2…Qa3? 3.Qh7 Qxb4 4.Qb7+! Ka5 5.Qa7+Kb5 6.c7 Qf8+ 7.Kb7! Qf7 8.Kb8 wins. 3.Qc5 or 3.c7 Qxb4! 4.Qh6+ Ka7! 5.Kd7 Qb5+ 6.Qc6 Qf5+! perpetual check. 3…Qb5! Not 3…f3? 4.Kc7! Qb5 5.Qd4!! wins by threatening 6.Qa1+. 4.Qd6 or 4.Kc7 Qxc5! 5.bxc5 Ka7! 6.Kd7 f3! 7.c7 f2! 8.c8(Q) f1(Q)! 9.Qc7+ Ka8! 10.Qa5+ Kb8! (10…Kb7? 11.c6+! wins) 11.Qb6+ Ka8 12.Kc7 Qf7+ perpetual check, or 4.Qxb5+ Kxb5! 5.c7 f3! 6.Kd7 f2! 7.c8(Q) f1(Q)! 8.Qb7+ Ka4! = (8…Kc4? 9.Qa6+! wins). 4…f3!! Pushing the pawn is the only way to counter White’s triple threats of 5.c7+/Qd7/Kc7. Not 4…Qf5+? 5.Kb8! Qb5+ 6.Ka8! f3 7.c7+, or 4…Qb6? 5.Qd3+ Qb5 6.Qd7 f3 7.Qb7+! wins. 5.c7+ Ka7!, threatens 6…Qe8+. Not 5…Qb6? 6.Qxb6+ Kxb6 7.Kb8! f2 8.c8(Q)! f1(Q) 9.Qb7 mate. 6.Qd4+ or 6.Kd8 Qg5+! perpetual check. 6…Ka6! Not 6…Ka8? 7.Qa1+! wins. 7.Qe4, White guards e8 and threatens M2 with 8.Qa8+. Or 7.Qa1+ Kb6! 8.Qa5+ Qxa5! 9.bxa5+ Kxa5 10.Kd7 f2! =. 7…Ka7! 8.Qe3+ Ka6! 9.Qa3+ or 9.Kd8 Qd5+! 10.Ke7 Kb7! =. 9…Kb6! 10.Qe3+ or 10.Kb8? loses to 10…Kc6+! 10…Ka6! 11.Qe6+ Ka7! Positional draw as the white queen is tied to defending e8 and cannot dislodge the aggressively-placed black king.

Black to play: White forces a win. [Syzygy TB Link] 1…a1(Q) 2.e8(Q) (1) 2…Qb2. Surprisingly this is the queen defence that requires the most precision from White, because it rules out 3.b5+, a white dual in some variations.
(2) 2…Qd4 3.c7 (3.b5+ also wins) 3…Ka7 (3…Qxb4 transposes to the main line) 4.Qa4+! Kb6 5.Qa5+ Kc6 6.Qc5+ wins.
(3) 2…Qf6 3.c7 (3.b5+/Qe2+ also win) 3…Kb6 4.Kb8 Qd6 5.Qc8 Qc6 (both queens have a potential mate on b7, and White’s next two moves are needed to avoid actually losing) 6.b5! Qd5 (6…Kxb5 7.Qb7+ wins) 7.Qa6+! Kc5 8.c8(Q)+ wins.
(4) 2…Qa4 3.Qe4 (3.Kd7/Qd7 also win) 3…Qb5 4.c7 (threatens M2 with 5.Qa8+) 4…Ka7 5.Qd4+! Ka6 6.Qa1+ Kb6 7.Qa5+ Qxa5 8.bxa5+! Kxa5 9.Kd7 wins. This is almost identical to a sub-variation of the White-to-play main line above. The sole difference is the placement of the f-pawn, f3 vs f4, and for Black that’s the difference between a draw and a loss!
(5) 2…Kb6 3.Qd8+! Ka6 (3…Kxc6 4.Qd7+! Kb6 5.Qb7 mate) 4.Kb8 Qe5+ 5.Ka8! f3 6.Qc8+! Kb5 7.Qb7+ Kc4 8.c7! Qa1+ 9.Kb8 Qe5 10.Qxf3 Qb5+ 11.Qb7 Qe5 12.Ka7 Qe3+ 13.Qb6 Qe7 14.Qc5+ wins.
(6) 2…Kb5 3.Qh5+! Kxb4 4.Qf5 Qa8+ 5.Kd7! (5.Kc7? Qa5+! =) 5…Qa7+ 6.c7 Qd4+ 7.Ke8 Qe3+ (7…Qh8+ 8.Qf8+ wins) 8.Kf8 wins.
(7) 2…f3 3.c7 (3.Qh5 also wins) 3…Kb6 4.Qe3+ Ka6 (4…Kb5 5.Qc5+ Ka4 6.Qa5+) 5.Kb8 Qh8+ 6.c8(Q)+ wins.

The black queen preserves its options on the long diagonal with 2…Qb2, and the move also threatens 3…Qxb4. But since the piece can no longer attack on the a-file, …Kb6 has become a weak move that doesn’t refute 3.c7! Now White threatens quick mates with 4.Qc6+/Qa4+, and the best response is still 3…Qxb4, or 3…Kb6 4.Qf8 Qe5 5.Qc5+! wins. 4.Qc6+! Not 4.Qe6+? Ka7! 5.Kd7 Qd4+ 6.Qd6 Qg7+! perpetual check. 4…Ka7 5.Kd7! Qd4+ 6.Ke6!! The intrepid white king finds a way to deal with the menacing black queen… Not 6.Qd6? Qg7+! 7.Kc6 Qc3+ 8.Qc5+ Qxc5!+ 10.Kxc5 Kb7! = or 6.Ke7? Qe5+ 7.Kf7 Qf5+ perpetual check. 6…Qe3+ 7.Kf6 Qd4+ 8.Kf7 and ironically Black’s f4-pawn has helped to create a safe haven for the white king against further checks. 8…f3 9.c8(Q)! wins.