Othello

[Paul McKeown]

A rival board game, Othello has been solved, meaning that the solution has been given demonstrating perfect play from any legal position, including the initial array. A draw! 10^28 positions; 10^58 games.
https://arxiv.org/abs/2310.19387

[Kevin Thurlow]

I'm amazed, I'm not that good at the game, but just assumed that the first player had an advantage. The chances of 32-32 seem very small?!

Although... the first player might have to be first to go in a2,b2,b1 or h2, g2, g1 etc, letting the opponent get into a corner and catch up. Just another game I don't understand.

[Matt Mackenzie]

The first player has an advantage in chess, but many still suspect it is "ultimately" a draw?

[MJMcCready]

Only with correct play, which humans will forever be incapable of.

[Neil Graham]

Looks as though we can put out the light on Othello then.

[Paul McKeown]

The authors of the paper speculate that, despite the size of the search space, chess might be the next strategy game to be "weakly solved" (one of three categories of solution), but this will probably require theoretical breakthroughs and improved hardware.

It will be fascinating should that happen, and I hope to live long enough to see it!

My prediction: chess from the initial array is a mutual Zugszwang!

[MJMcCready]

It was recently said by Nakamura that endings with 7 pieces or fewer on the board have already been solved.

[Kevin Thurlow]

"It was recently said by Nakamura that endings with 7 pieces or fewer on the board have already been solved."

In Correspondence Chess, you can claim a result if the tablebases used by ICCF agree with you.

[Ian Thompson]

It was recently said by Nakamura that endings with 7 pieces or fewer on the board have already been solved.

There's nothing new about that. Most 7 piece endings were solved by 2012 and all by 2018, see https://en.wikipedia.org/wiki/Endgame_tablebase. There's a discussion, from 2021, of work in progress on 8 piece endings here - https://www.chess.com/blog/Rocky64/eigh ... me-results.

[Roger de Coverly]

There's a discussion, from 2021, of work in progress on 8 piece endings here -

The join would be if "forced" opening and middle game play could reach a solved 7 or 8 piece ending. But that may just demonstrate opening lines to be avoided if looking to win rather like the forced repetitions available here and there for players seeking not to win.

[Paul McKeown]

It was recently said by Nakamura that endings with 7 pieces or fewer on the board have already been solved.

Nakamura must be rather behind the curve, in that case. Moscow State University published the first complete set of 7 piece endgames in 2012, calculated and stored on its Lomonosov departmental supercomputer (140 MB). 7 piece tablebases have been available for download in Syzygy format (18.4 TB) since 2018, usable on your PC at home with your favourite chess engine.

There have been quite a number of papers published concerning results from 8 piece tablebases in the intervening years, and there is an expectation that 8 piece tablebases will be complete in a few years time.

[Christopher Kreuzer]

From Ian's link above:

https://www.chess.com/blog/Rocky64/eigh ... me-results

I just played through the "Tablebase position: 8-piece length record | White wins in 400 moves" position (a rather artificial material balance of White with 2 rooks and a knight against Black's rook and 2 bishops of the same colour). It was the usual completely incomprehensible dancing around the board until eventually a winning position was 'forced' (though I have never been able to describe or comprehend why certain sequences in this hundreds-of-moves-long mates are forced).

The article puts it better: "The solution, as is usual in such tablebase discoveries, defies human understanding and engine analysis."

Paul predicted above that chess is a mutual Zugzwang.

In the article Ian linked above:

One highlight among the mutual zugzwang arrangements is shown above. It’s a full-point MZ, a particularly curious type of situation where having the turn would be a fatal disadvantage for either side. The material is nicely balanced and happens to be the strongest possible without promoted units. Moreover, the brisk play is human comprehensible, and even that weakling known as Stockfish can solve it!

3R4/8/2q5/8/8/2k1r3/2r5/1R1K1Q2

8-man tablebase position: mutual zugzwang (Black to play: White wins; White to play: Black wins).

Credit for the above should go to: Marc Bourzutschky.

[Paul McKeown]

There's a discussion, from 2021, of work in progress on 8 piece endings here -

The join would be if "forced" opening and middle game play could reach a solved 7 or 8 piece ending. But that may just demonstrate opening lines to be avoided if looking to win rather like the forced repetitions available here and there for players seeking not to win.

I think this exactly what the authors of the Othello are speculating. Perhaps a future 9 or 10 piece tablebase meeting Stockfish or whatever searching from the initial array. It you switch on a modern engine with tablebase access, it is extraordinary how early the tablebases begin to be accessed. Essentially the engines are doing extraordinarily deep searches, presumably by radical (but successful) tree pruning, focusing on the most promising lines for deep searches.

[Paul McKeown]

8-man tablebase position: mutual zugzwang (Black to play: White wins; White to play: Black wins).

Credit for the above should go to: Marc Bourzutschky.

Nice one, Chris.

[Brendan O'Gorman]

Looks as though we can put out the light on Othello then.