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 Problem of the Week

421. Arthur Mosely
Weekly Times 1919
2nd Prize
Mate in 2

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Archive | 2010 |...| 2018
Chess and problem rambles by PW

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.

22 Oct. 2018 – More adventures with endgame tablebases
8 Sep. 2018 – Adventures with endgame tablebases
5 Aug. 2018 – ‘Chess Problems Out of the Box’ by Werner Keym