Answers.Body: <blockquote>
  <p>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?</p>
  </blockquote>
  <p>Of course there is. It's a position we are all very familiar with. Here it is:</p>
  <pre><code>[fen &quot;&quot;]
  </code></pre>
  
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Answers.CreationDate: 2022-11-07T21:59:29.970Z
Answers.Text: Do you have a proof that this satisfies the OP's conditions?
Answers.UserDisplayName: Dustin G. Mixon
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Answers.CreationDate: 2022-11-07T22:04:29.050Z
Answers.Text: 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.
Answers.UserDisplayName: A. Rex
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Answers.CreationDate: 2022-11-08T05:29:21.623Z
Answers.Text: 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.
Answers.UserDisplayName: Ross Millikan
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Answers.CreationDate: 2022-11-08T11:14:55.160Z
Answers.Text: @RossMillikan Read the question. It is not what you said.
Answers.UserDisplayName: Brian Towers
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Answers.CreationDate: 2022-11-08T15:09:08.530Z
Answers.Text: This answer does not justify or explain its claim.
Answers.UserDisplayName: Peter Olson
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Answers.CreationDate: 2022-11-08T22:52:45.007Z
Answers.Text: I like this solution as it's the first one I thought of too.  However, I do believe that it is not known whether or not this position has a forced result for either side (although with perfect play my understanding is that it is generally believed to be a draw).
Answers.UserDisplayName: Michael
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Answers.CreationDate: 2022-11-07T21:56:37.287Z
Answers.LastActivityDate: 2022-11-07T21:56:37.287Z
Answers.UserDisplayName: Brian Towers
Answers.Body: <p>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:</p>
  <pre><code>[Title &quot;Neither player can force an exact outcome&quot;]
  [FEN &quot;2n4k/2P3pP/6P1/8/8/6p1/2p3Pp/2N4K w - - 0 0&quot;]
  
  1. Nd3 Nd6 2. Ne5?!?
  </code></pre>
  <p>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.</p>
  
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2022-11-08T10:22:42.587Z
Answers.Text: 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.
Answers.UserDisplayName: blues
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Answers.CreationDate: 2022-11-08T11:46:30.680Z
Answers.Text: 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).
Answers.UserDisplayName: Noam D. Elkies
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2022-11-08T12:07:34.033Z
Answers.Text: So maybe white can force a loss this way?
Answers.UserDisplayName: blues
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Answers.CreationDate: 2022-11-08T14:02:33.120Z
Answers.Text: 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.
Answers.UserDisplayName: Noam D. Elkies
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2022-11-08T02:37:26.730Z
Answers.LastActivityDate: 2022-11-08T02:37:26.730Z
Answers.UserDisplayName: Noam D. Elkies
Body: <p>There are three possible outcomes of a game of chess: white wins, black wins, or the players draw.</p>
  <p>Typically, we consider a win better than a draw, so when we say &quot;white can force a draw&quot; from a given position, usually we mean &quot;white can force a draw <em>or better</em> (a win)&quot;.  For the purposes of this question, consider the three possible results of a game as entirely separate possibilities.  For example, in <a href="https://chess.stackexchange.com/questions/40623/position-where-neither-player-can-force-a-win-and-neither-player-can-force-a-dra">this question</a>, a position is given where</p>
  <ul>
  <li>white cannot force a win nor a draw (remember, <em>exactly</em> a draw),</li>
  <li>black cannot force a win, nor a draw, nor a loss, but</li>
  <li>white can force a loss.</li>
  </ul>
  <p>(This is interesting because &quot;neither player can force a win nor [exactly] a draw&quot;.)  Is something more extreme possible?  Is there a position where</p>
  <ul>
  <li>white cannot force a win, nor a draw, nor a loss, and</li>
  <li>black cannot force a win, nor a draw, nor a loss?</li>
  </ul>
  <p>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).</p>
  
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2022-11-07T17:52:01.047Z
Comments.Text: What is your question?
Comments.UserDisplayName: Michael West
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2022-11-07T17:55:31.900Z
Comments.Text: @MichaelWest: The question ends with a question mark ("?") and begins with "Is there a position where".
Comments.UserDisplayName: A. Rex
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2022-11-07T17:59:38.777Z
Comments.Text: 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.
Comments.UserDisplayName: Will Sawin
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2022-11-07T18:06:43.133Z
Comments.Text: @WillSawin: Good point!  Obviously it cannot be the case that both players can force (inconsistent) outcomes.  I have edited the question accordingly.
Comments.UserDisplayName: A. Rex
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2022-11-08T14:20:25.000Z
Comments.Text: "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."
Comments.UserDisplayName: Grade 'Eh' Bacon
Tags: <problems>
Title: Position where neither player can force an *exact* outcome
ThreadText: # Position where neither player can force an *exact* outcome
  
  (Asked by: username_0 on 2022-11-07)
  
  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](https://chess.stackexchange.com/questions/40623/position-where-neither-player-can-force-a-win-and-neither-player-can-force-a-dra), 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).
  
  **Tags:** problems
  
  > **Comments:**
  > **username_1**: What is your question?  
  > **username_0**: @username_8West: The question ends with a question mark ("?") and begins with "Is there a position where".  
  > **username_2**: 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.  
  > **username_0**: @WillSawin: Good point!  Obviously it cannot be the case that both players can force (inconsistent) outcomes.  I have edited the question accordingly.  
  > **username_3**: "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."  
  
  ---
  
  ## 2 answers
  
  ### Answer by username_9 on 2022-11-08. Score: 11 | Accepted answer
  
  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.
  
  > **Comments:**
  > **username_10**: 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.  
  > **username_9**: 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).  
  > **username_10**: So maybe white can force a loss this way?  
  > **username_9**: 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.  
  
  ---
  
  ### Answer by username_4 on 2022-11-07. Score: 2
  
  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 ""]
  
  > **Comments:**
  > **username_5**: Do you have a proof that this satisfies the OP's conditions?  
  > **username_0**: 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.  
  > **username_6**: 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.  
  > **username_4**: @RossMillikan Read the question. It is not what you said.  
  > **username_7**: This answer does not justify or explain its claim.  
  > **username_8**: I like this solution as it's the first one I thought of too.  However, I do believe that it is not known whether or not this position has a forced result for either side (although with perfect play my understanding is that it is generally believed to be a draw).  
  
  ---
  
  