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There are three possible outcomes of a game of chess: white wins, black wins, or the players draw.

Typically, we consider a win better than a draw, so when we say "white can force a draw" from a given position, usually we mean "white can force a draw or better (a win)". For the purposes of this question, consider the three possible results of a game as entirely separate possibilities. For example, in this question, a position is given where

  • white cannot force a win nor a draw (remember, exactly a draw),
  • black cannot force a win, nor a draw, nor a loss, but
  • white can force a loss.

(This is interesting because "neither player can force a win nor [exactly] a draw".) Is something more extreme possible? Is there a position where

  • white cannot force a win, nor a draw, nor a loss, and
  • black cannot force a win, nor a draw, nor a loss?

For example, this would mean that if white attempts to force a white loss, then they cannot because black can force that either white wins or the players draw (but without actually being able to choose which).

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  • 1
    What is your question?
    – Michael West
    Nov 7, 2022 at 17:52
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    @MichaelWest: The question ends with a question mark ("?") and begins with "Is there a position where".
    – A. Rex
    Nov 7, 2022 at 17:55
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    I don't think it's true that black can force a loss in the linked example. Rather, black can force a loss if white chooses not to force a loss.
    – Will Sawin
    Nov 7, 2022 at 17:59
  • @WillSawin: Good point! Obviously it cannot be the case that both players can force (inconsistent) outcomes. I have edited the question accordingly.
    – A. Rex
    Nov 7, 2022 at 18:06
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    "when we say "white can force a draw" from a given position, usually we mean "white can force a draw or better (a win)" No, I would say that indicating one side can force a draw is usually an indication that the other side is estimated to be better / winning. ie: "Black would otherwise have a checkmate available, but white can force a draw."
    – Grade 'Eh' Bacon
    Nov 8, 2022 at 14:20

2 Answers 2

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Such a position must be a draw with best play. Here's one where either player can make a winning threat that can only be parried by giving checkmate:

[Title "Neither player can force an exact outcome"]
[FEN "2n4k/2P3pP/6P1/8/8/6p1/2p3Pp/2N4K w - - 0 0"]

1. Nd3 Nd6 2. Ne5?!?

Best play is for White and Black to keep moving their Knights back to c1 and c8 respectively. But either player can prevent a drawn outcome by threatening mate in at most two moves with Ne5 or ...Ne4, forcing the opponent to either mate in 1 (by promoting to Q or R) or get mated.

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    After 1.Ne2 Nd6 2.Nxg3 it's not so clear anymore what happens next? If black promotes now, they lose the h pawn too, and maybe white can force a draw in that endgame.
    – blues
    Nov 8, 2022 at 10:22
  • 1 Nxg3? c1Q+ 2 Kxh2 Qxc7 is an easy Black win, e.g. 3 Kh3 Nc4 and Ne5 soon capturing the Pg6 and liberating the Kh8; Black is up more than enough material to win this even if Nxg6 had to be a Knight sacrifice (which it doesn't).
    – Noam D. Elkies
    Nov 8, 2022 at 11:46
  • So maybe white can force a loss this way?
    – blues
    Nov 8, 2022 at 12:07
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    No, "forcing a loss" means selfmate. Once Black has reduced White to helplessness there's nothing forcing Black to actually checkmate --- they can mark time forever or even force K vs. K.
    – Noam D. Elkies
    Nov 8, 2022 at 14:02
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Is there a position where white cannot force a win, nor a draw, nor a loss, and black cannot force a win, nor a draw, nor a loss?

Of course there is. It's a position we are all very familiar with. Here it is:

[fen ""]
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  • 17
    Do you have a proof that this satisfies the OP's conditions?
    – Dustin G. Mixon
    Nov 7, 2022 at 21:59
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    I admire your enthusiasm to the game of chess as one meant to be played, rather than mathematically analyzed. 😃 But perhaps you'll also indulge the mathematicians among us? For what it's worth, I do think it's plausible that the initial position satisfies the constraints of my question, but it would be implausible to mathematically prove this (as the previously commenter addresses), in line with your own comments about 32-piece tablebases.
    – A. Rex
    Nov 7, 2022 at 22:04
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    I find it completely implausible that this position meets the conditions. Having players able to force wn/loss but no draw takes a special position.
    – Ross Millikan
    Nov 8, 2022 at 5:29
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    @RossMillikan Read the question. It is not what you said.
    – Brian Towers ♦
    Nov 8, 2022 at 11:14
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    This answer does not justify or explain its claim.
    – Peter Olson
    Nov 8, 2022 at 15:09

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