I don't disagree with any of this.

At the press conference, Magnus said that 45... f4 had been a 'very, very weak moment' that spoiled the game for him - he thought he was easily winning by infiltrating on the light queenside squares with the king. He was underestimating Sergey's chance of making a fortress. Moreover, Magnus said he's 'not a big believer in fortresses in chess' , has experience of breaking them down.

There was a joke that Putin should make karjakin minster of defence

i) Most analysis engines showed black up between 1 & 2 pawns
ii) When the engines showed the board 30 moves ahead it looked very similar to the position when a draw was agreed.
iii) Most expert humans thought the position a draw.

Q. What explains the discrepancies?

If an engine shows the same value for the top 3 lines (e.g. -1.61 for all the 3), there's a high chance that, in fact, there's a drawing fortress. It's a well-known bug.

Engines evaluate positions at the end of a game tree basing on material advantage, open file possession, etc. In the fortress case, no matter the search depth, there will be almost the same position at each of the end leaves of the game tree and there will be no forced draw (no move repetition and no naked kings) as, from the engine's viewpoint, the side with the material advantage prefers to play on instead of repeating moves*. Engines don't check for the 50-move rule unless it's specified in the tablebase settings.

Here's a position from my own online game.



Stockfish correctly shows that Kxf5 is a losing move (White gets mated in 34) but it evaluates all the other king moves as -2.06 whereas it's obvious that Black can't break through then (either his king or his bishop has to shepherd the a-pawn, so he can't afford to sac the bishop for the f4 pawn).

Brag: my White opponent did take on f5, hoping to win
Beat: I should have finished him off much earlier instead of allowing him to pass the a-pawn.

* If an engine is told to avoid 50-move rule draws, then funny games can happen like Nakamura vs Rybka (there's an epic troll ending).

As to W.E. Rudolf's famous study (from La Strategie, 1912),



Stockfish 8 at depth 25/46 recommends c4+ (-9.77), exf6 (-9.92) and b3 (-9.97) as its top 3 picks, while the only drawing move is its 4th suggestion valued at -11.33, lol.

That was pretty cool.

Sick study. Someone should show it to Magnus since he doesn't believe in fortresses.

It's so well-known that I first saw it when I was around 10. Magnus surely saw it long ago already.

Why doesn't Stockfish "value" the correct play at -11.33 when elementary examination of a couple of plys (sorry for my imprecise argot) shows it at 0.00?

The only rule that can be invoked to declare a draw automatically in this study within a reasonable number of moves is the 50-move rule (theoretically, the threefold repetition rule is enough, as the number of possible positions is finite, but in practice, no search engine has a search depth big enough for the repetition to be forced).

As I explained above, Stockfish can't invoke the 50-move rule when there are more than 7 men left on the board (i.e. when it can't just query an endgame tablebase). All it sees is that, within its move search horizon, Black maintains a huge material advantage. The fact that Black can't deliver mate, take a piece or move a pawn within 60 plies (halves of a full move) doesn't force Stockfish to declare a draw. To invoke the 50-move rule, Stockfish would need to calculate 100 plies deep, whereas it takes a ton of time to compute 60 plies deep even in a position where White can only move the king, and I'd run out of temper if I had to wait for it to go 100 plies deep.

The chess fortress is a pattern that the human brain, with its spatial vision and creative logic, still spots better than the blind alpha-beta pruning computer AI.

Ah, thanks! So it's too difficult to implement a 'no pawns can move & no pawns can be captured and no king can be forced in to check' type thing? Would there be too many similar but not identical 50 rule move endings to program to allow Stockfish to search for 'shortcuts' to identify 50 rule move endings?

The idea of 'a library of standard fortress positions' is a fruitful one that chess engine programmers yet need to implement.

Meanwhile, Magnus has chosen 3. Bc4 and we're seeing a Giuoco Pianissimo in game 5!

Game 5 could be heading towards a dynamic endgame after move 19.

Carlsen has a 4-2 kingside pawn advantage (with a passed e-pawn). Karjakin has a 4-2 queenside pawn advantage (with a passed d-pawn)

That's an exciting imbalance, it's too bad I need to get my sleeping schedule in order.

Following Magnus's 20. Rf3, I was wondering why Sergey went into the opposite colour bishop endgame so easily, but Stockfish somehow says Sergey's bishop pair was going to RIP anyway due to concrete considerations. The proposed main line is:

20... Bg6 21. Rxf7 Bxf7 22. e6 Bg6 23. Qd2 a5 24. Nxb7 Qxb4 25. Nxa5



25... Qxa5!? 26. Qxa5 Bxf2+ 27. Kxf2 Rxa5 28. Re3 Rxa4 29. e7 Rf4+ 30. Kg3 Rf1.



Stockfish evaluates this position as offering only a tiny advantage for Black. Go figure.

Edit: anyway, as played (20... Bxc5), as Svidler has mentioned, Black's queenside pawn chain is dead. He's lacking the dark-square bishop to put b7-b6 in. Alone, the d-pawn isn't dangerous at all. Only White can play for a win from now on. This is becoming another round of suffering for Sergey.

It's amazing how quickly Magnus let his position deteriorate, and the 43. Qxd4 played by him now (instead of 43. Bxd4) might be the nail in his king's coffin if Sergey finds (43... Rh8 44. Qe4 Qh6 45. Kf1 Qh1+ 46. Ke2) 46... Bd5. Wow.

Why is black considered slightly ahead?

Wow, if that's all karjakin can do make magnus suffer there I don't see how he ever wins this match. Can he be awarded Armageddon or does the champ automatically get to pick black for that game?

I shouldn't think so.

Magnus not a happy bunny in the press conference very salty.

I think he is playing 'poorly' for him. Normally he would have closed out one of those games he was pressing and doesn't make errors as in the last game.

Feels a tiny tiny bit like kaspy v kramnik where he got super frustrated (though for different reasons magnus seems more annoyed with himself than anything).

Would love to see a couple of solid whites from karjakin where he puts sustained pressure on magnus.

I don't think magnus has ever faced that in a match and would be interesting to see how he copes with the challenge

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behaved like an idiot in the press conference. i remember anand did too when he lost some games last time.

The difference is that Vishy was salty after losses, which is more natural than being such after a series of draws vs a contender who's merely 70 rating points lower.

But even if Magnus loses the title now, it will be quite easy for him to return to the throne in 2018, in the Botvinnik fashion, though I'd certainly like to see someone else win the Candidates.

I'm not sure it would be "quite easy" for him to return if he loses. He will be a favorite to win the candidates tournament but I'd say that is pretty high variance and I'd imagine he wouldn't be an overwhelming favorite, just the favorite.