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In game 6 of the World Championship 2021 between Magnus Carlsen and Ian Nepomniachtchi, before Qe6 the engine says +0.9 at around depth 30/99, but I heard supposedly it's a (theoretical) draw. I know there are some cases of fortresses that have evaluations with absolute value greater than 3.0, but this doesn't quite look like a fortress to me.

  1. Is it really a draw?

  2. Is/Are there another term/other terms for this position, assuming it's a draw?

    [FEN "4k3/8/8/4PR2/5P2/6NK/q7/8 b - - 0 1"]
    
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2 Answers 2

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There is no question. It is a theoretical draw (see tablebase).[1]

Obviously to mere mortals, playing on may hold practical chances for one side. GM Nakamura repeatedly said that Game 6 of WCC positions were extremely difficult to play for Black.

In this position, Black only has two moves that draw: ...Qb1 and ...Qc2 (without considering the 50 move rule).

As pointed out by @Glorfindel, perfect play after multiple Black moves would lead to win by White, but after the 50 move rule would have been invoked. With that considered, in the diagrammed position Black can play: ...Qa1, ...Qa7, ...Qa8, ...Qd2, ...Qd5, ...Qf2, ...Qa3, ...Qa4, ...Qb3, and yes, even Qe6, provided that Black continues to play perfectly.

Regarding the practical side, GM Hikaru Nakamura repeated said that many of the theoretically drawn positions in Game 6 of the 2021 World Chess Championship game were extremely difficult to play as Black. Other super GMs also said many lines in the tablebases had successively fewer and fewer move options for Black to maintain the draw. As a human, this means right move(s) may become almost impossible to find as the ideas become more difficult to spot.

[1] For positions with 7 or less pieces in total on the board (from both sides), the theoretical status is known. All legal moves have been explored with the outcomes recorded. Read more on endgame tablebases here.


Edit: The OP has asked if this position is a fortress.

Fortresses are often defined by multiple properties:

  • Useful pawn breakthroughs are not possible.
  • If the stronger side has pawns, they are firmly blocked.
  • The stronger side's king cannot penetrate, either because it is cut off or near the edge of the board.
  • Zugzwang positions cannot be forced, because the defender has waiting moves available.

Clearly the tablebase shows there is a way for Black to hold indefinitely. Whether that meets the fortress definition, I do not know.

Playing through multiple tablebase lines shows that White can maneuver to use King or Pawn moves to put Black into only move situations. From a practical (human) perspective, that seems pretty useful so maybe this isn't a fortress. If you are a computer playing Black, you aren't scared of such things (so maybe it is).

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  • thanks re Q1. as for Q2, is there any term for this kind of position? it's not fortress is it?
    – BCLC
    Dec 4, 2021 at 14:46
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    @BCLC I've updated my answer. Dec 4, 2021 at 15:08
  • ok not a fortress what is it? any term? or not really? maybe not necessarily a term to describe the position but perhaps terms to describe what's going on as to why it's a draw. looks something like a semi-perpetual
    – BCLC
    Dec 4, 2021 at 17:35
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    @BCLC: My suggestion for the definition: "A fortress is a position that is drawn, although the material advantage for one side is big enough to win from a neutral position." Thus e.g. KQ/KBN has exactly one fortress (the "Karstedt") - all else is won. In contrast KQ/KNN is no fortress - even neutral KQ/KNN is drawn. This example is none either, since it is also drawn in most cases. I simply would call it "insufficient material" - White is a half pawn up. Dec 5, 2021 at 11:59
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The other answers have answered the first question. For the second, these positions where one person is winning but is foiled by the 50-move rule are known as "cursed wins".

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  • thanks Allure. afaik pawns don't count towards 50 move rule sooo: ahh so is it also a little like a zugzwang but just for the pawns because the tablebase shows a way for the pawns to not move for some reason and so white just keeps trying to defend against the actual or potential queen checks with rook or knight hoping to advance pawns but can never advance (without being captured)? or what?
    – BCLC
    Dec 4, 2021 at 18:21
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    @BCLC Speaking precisely, White can never play a zeroing move (i.e. one that resets the 50-move counter) without losing the win. So it could be that White can advance pawns but they are captured, White can advance pawns but they allow a perpetual check, or White never gets the chance to advance pawns - they are all possible, I have not checked the line in detail.
    – Allure
    Dec 4, 2021 at 23:15
  • ok thanks Allure! btw do you disagree with ais523?
    – BCLC
    Dec 5, 2021 at 2:35
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    @BCLC On checking I think ais523 is correct, DTZ is measured in ply so it's not actually a cursed win.
    – Allure
    Dec 5, 2021 at 3:06

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