16 Oct. 2019 – A heraldic endgame-tablebase composition

Last year my Adventures series of blogs examined endgame tablebases, software that provides perfect play information for any positions with up to seven pieces. I reviewed the remarkable capabilities of these programs – they play as God effectively – and gave some links to access them for free. We discussed in particular how they have impacted on the field of chess composition, including their applications for testing endgame studies and for generating new positions with striking play. In the second part of that series, I also quoted a special study that makes explicit use of tablebase data and exemplifies a novel form of composition. The author of that work, Andrew Buchanan, has sent me a brand-new problem of this type, which I am delighted to present here. The problem exhibits an intriguing aspect of heraldry as well and that will be disclosed by Andrew after its solution.

As in the earlier example, this study follows a chess problem convention relating to the 50-move draw rule. The official rules of problems are maintained by the World Federation for Chess Composition, and Article 17 of its Codex states: “Unless expressly stipulated, the 50 moves-rule does not apply to the solution of chess compositions except for retro-problems.” That means in any study position, if tablebases prove that a winning white move would require more than 50 turns to force a capture or a pawn move, there’s no draw claim and that white move is still a win. Except, that is, in the cases of problems involving retro-analysis (backward reasoning about the play leading up to the diagram).

A second important problem convention is relevant here, about the legality of castling moves when a king and a rook are on their initial squares. Article 16 of the Codex indicates: “Castling is permitted unless it can be proved that it is not permissible.” So the default assumption is that castling is legal, unless it can be shown by retro-analysis that the king or the rook must have moved previously in a hypothetical game. The situation in tablebases is quite the opposite: all castling moves are disregarded and effectively deemed illegal. That’s an understandable decision on the part of the programmers, given how unlikely in a practical game that the right to castle would remain in an ending position (besides any technical reasons). But, ideally, users should be able to select either option. A choice would not only suit composed problems but also make the tablebases genuinely complete, since chess with seven units isn’t strictly solved when positions with active castling rights are omitted.

In any case, with these considerations in mind (they are significant clues!), plus the actual tablebase results for the diagram, we are ready to tackle the study. Click this link to the Syzygy tablebases that will open with the correct position. White is a knight ahead here and that seems to be a decisive material advantage according to Syzygy, since almost every legal white move is marked as a win. But is that really true, or is there just one winning move?

	Andrew Buchanan Original
	White to play and win

Here is the solution as explained by the composer himself:

Apparently, any move by White wins, except for the blundering 1.Sa2?, which only draws. But let’s try White’s apparently quickest route to victory, 1.Sd3. Of course, the tablebase strategy is not necessarily to checkmate directly, but instead to find a capture, pawn move (or indeed mate itself!) to reach a simpler but still winning position which will reset the 50-move clock. DTZ shown in Syzygy stands for distance-to-zero in this sense.

Syzygy counts in single moves so 90 means 45 moves by White and 45 by Black. Any win or loss in more than 100 single moves is shaded to show that they would be draws if the 50-move rule applied, which by default it doesn’t.

So it looks as if White just wins, as 1.Sd3! achieves DTZ in 90 single moves? But Syzygy doesn't understand castling, and if you manually shift the two black pieces, and make sure that the “White to move” button is clicked, then you can see that after 1…0-0-0! White cannot win, with or without the 50-move rule. Black has two threats: to simply capture the knight on d3 or to skewer the white king, setting up a trade of rooks. Indeed 2.Sc1? even loses for White.

However, if you look at the position, you can see that Black’s last move must have been with king or rook. If the knight has just moved, it would have been illegally checking the white king. Therefore we can conclude that Black is not allowed to castle. 1.Sd3! does win.

And the point of the problem is that because retro reasoning is a critical element to the solution, this is a “retro problem” and the 50-move rule switches on, which does not normally apply to endgame studies. Thus all the other candidate first moves for White cannot win. For example, 1.Sc3? and 1.Se3?, which both have DTZ101, i.e. they are just too slow. So the first move is unique. If castling did not threaten to defeat the key, then it wouldn’t be relevant to go through the retro reasoning, so you couldn’t say it’s genuinely a retro problem.

This splendid piece of work is likely a unique find, considering the many twists and turns displayed in its logical solution. Somehow the composer has uncovered a tablebase set-up with these features: (1) White has multiple winning moves but only one below DTZ100, (2) this white move is refuted solely by black castling, (3) the castling move turns out to be illegal due to retro-analysis, and (4) the need for retro-analysis ensures that the white move below DTZ100 is the only viable win. The problem – a great example of a “tablebase retro-study” – demonstrates how this curious genre of composition is unlike anything else!

Andrew then mentioned how the composition was suggested by the logo of his old school, a heraldic shield that contains three chess figurines. Below he described how this led to a startling coincidence with the finished diagram position:

A few days ago I was emailing a problemist who happens to have attended the same school as me, the Royal Grammar School in Newcastle (UK). The school shield shows two white knights and a rook, and I mentioned I wanted to compose a problem featuring these units. I had no thought how I might achieve this, but amazingly this composition then popped up. The three black units kind of echo the three “charges” in the “chief” of the shield, to use what I hope is the right heraldic terminology. It is odd how similar the board and the shield are, given that as far as I can see I have no choice at all in the position.

So why does the shield show chess pieces? According to David Goldwater of RGS (whose friendly explanations of their historical research is gratefully acknowledged), quoting an earlier history, and using heraldic terminology redolent of Game of Thrones:

This shield of arms symbolises the name, founder and place of the school. The chief bears a leopard of England (lion passant guardant) between two of the lilies of France, referring to the title, royal when the royal arms as borne by the House of Tudor were France and England quarterly. The horses’ heads are taken from the canting [= visually punning] shield of Thomas Horsley, the founder of the school, which bore gules three horses’ heads erased argent. The triple-towered silver castle in base is part of the arms of the city and county of Newcastle upon Tyne, whose “most ancient armes” are three gules three castles triple towered argent.

So here you have it: the first heraldic chess problem, and perhaps the only one ever.