Answers.Body: <p>Here's a position with all pieces where either side to play loses.</p>
  <p>Seeing why it's a loss takes some analysis.  With Black moving first, White's best plan is to open up the Bishop on f1 pinning the pawn, then Qxa4 checkmate.  This happens in most but not all lines.  Shredder evaluates the main line as +22, because either Nxc5 or cxb8=Q with leave White up a queen.</p>
  <pre><code>[Title &quot;Zugzwang with full board&quot;]
  [FEN &quot;nbb5/nqrp4/krpP3p/1pP3pP/pP3pP1/P3pPRK/4PRQN/5BBN b - - 1 0&quot;]
  [startflipped &quot;&quot;]
  
  1... fxg3 (1... exf2 2. Bxf2 fxg3 3. e4 gxh2 4. f4 gxf4 5. Bh4 f3 6. Qc2 f2 7. Qxa4#) 2. Nxg3 exf2 3. f4 gxf4 4. Ne4 f3 (4... fxg1=Q 5. Qxg1 f3 6. g5 hxg5 7. exf3 g4+ 8. Kg3 gxf3 9. Bd3 f2 10. Qd1 f1=N+ 11. Kf4 Ng3 12. Qxa4#) 5. Qxf2 fxe2 6. cxb6 exf1=Q+ 7. Nxf1 c5 8. bxc7  
  </code></pre>
  
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2021-01-30T00:22:58.257Z
Answers.LastActivityDate: 2021-01-30T01:54:43.493Z
Answers.LastEditDate: 2021-01-30T01:54:43.493Z
Answers.UserDisplayName: jmamos
Answers.Body: <p>The second player mates by their 4th move at the latest, with completely unique play.</p>
  <pre><code>[Title &quot;mate in 4 playing second&quot;]
  [FEN &quot;nnb5/bqrp3p/krpP3P/1pP3p1/1P3pP1/p3pPRK/P3PRQB/5BNN b - - 1 0&quot;]
  [startflipped &quot;&quot;]
  
  1... fxg3 (1... exf2 2. Qxf2 fxg3 3. Qe3 g2,gxh2 4. Qxa3#) 2. Qxg3 exf2 3. f4 fxg1=N+ (3... fxg1=Q,R,B,gxf4 4. Qxa3#) 4. Bxg1 gxf4 5. Qxa3#
  </code></pre>
  <p>Most of the time in chess it's an advantage to go first. In combinatorial game theory terms, this is called &quot;hot&quot;. Zugzwang positions, where it's a disadvantage to have the move, are termed &quot;cold&quot;. In billiards &amp; snooker, this state is called &quot;being snookered&quot;. A similar effect used to occur under archaic golf rules: see <a href="https://en.wikipedia.org/wiki/Stymie" rel="nofollow noreferrer">&quot;stymied&quot;</a>.</p>
  <p>Chess is mostly a hot game, but can get colder as the game progresses. Yet this paradoxical position, almost in the opening still, is very cold indeed, as neither side can move except to open up the position for the other player to win.</p>
  <p>As someone mentioned in a comment, we can't exclude the remote possibility that the chess starting position itself is a full point zugzwang! See <a href="https://mathoverflow.net/questions/107385/a-chess-question-of-w-t-tutte/226893#226893">a chess question of W.T. Tutte</a>.</p>
  <p>The example without the knights in the question had a stronger property: it's a selfmate in 1. So not only does the first player always lose against best play: they <em>must</em> lose. I don't know if that can be done with any of the knights present.</p>
  
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Answers.Text: I am glad to see discussion of combinatorial game theoretic notions here. I would like to remark that chess is mostly a hot game indeed, and it doesn't get colder as the game progresses. Rather, a small number of branches of the game tree are cold. Also, it is extremely unlikely that the starting position in chess is full point zugzwang (evidence from strong chess engines evenif we discard the circumstancial evidence).
Answers.UserDisplayName: Cyriac Antony
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Answers.CreationDate: 2023-07-01T16:34:38.693Z
Answers.Text: I completely agree, @CyriacAntony. To me, the oddity is that the start position for such a hot game has not been proven mathematically not to be a win for Black.
Answers.UserDisplayName: Laska
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Answers.Text: Correction to the last paragraph: It's not selfmate because 1 bxa6+ Kc6 or 1 . . . gxh3+ 2 Kf3 avoids the mate and in fact gives stalemate.
Answers.UserDisplayName: Noam D. Elkies
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Answers.CreationDate: 2021-01-30T03:55:43.100Z
Answers.LastActivityDate: 2021-07-16T07:34:20.673Z
Answers.LastEditDate: 2021-07-16T07:34:20.673Z
Answers.UserDisplayName: Laska
Answers.Body: <p>If you literally mean <em>all pieces</em>, the simple answer would be <strong>no</strong>, there are simply too many free pieces to move that you cannot enforce a real zugzwang scenario there.</p>
  <p>Note that, if all pieces are still on the board, it means there hasn't been any promotion yet either. Without capturing, the pawns cannot change their files, and continuing on the same file they'll toss on the opponent's pawn.</p>
  <p><em>The side to move is checkmated in 1</em> is legitimate, but if you add the zugzwang condition that (let's assume the side to move is not under check to make it a legal scenario) without moving that same player would have survived the position, but only because of the necessity to move, they will get checkmated in 1; then we end up in the same disclaimer above: there are simply too many (16!) pieces around to enforce a full zugzwang.</p>
  <p>Actually, if being realistic is not a requirement, you can reach a zugzwang scenario with all pieces on board with the real meaning: if not moving were an option, that would be the best move. With mate in 1, that's pretty much impossible to achieve. Also without being realistic, I don't see the point of setting up a zugzwang position, because the idea of such a position is that things were more or less equal up to now, but the next move will cause damage. Whereas in a scenario like this, the opponent already had many trivial chances to win material advantage. Anyway, for the sake of completeness, I'm posting such a position. Anything that doesn't resemble this will mean that one side has too many free pieces, hence that won't work.</p>
  <pre><code>[FEN &quot;&quot;]
  [startply &quot;40&quot;]
  
  
  1. b3 a5 2. d3 a4 3. f3 a3 4. h3 g5 5. Nc3 g4 6. Nb1 g3 7. Nc3 e5 8. Nb1 e4 9. Nc3 e3 10. Nb1 h5 11. Nc3 h4 12. Nb1 f5 13. Nc3 f4 14. Nb1 d5 15. Nc3 b5 16. Nb1 c5 17. Nc3 c4 18. Nb1 b4 19. Nc3 d4 20. Nb1 c3
  </code></pre>
  
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Answers.CreationDate: 2020-05-30T23:48:59.743Z
Answers.Text: It's not immediately clear that White actually loses this: 
  after 1 Bxa3 bxa3 2 Qc1 Black still has some work to do.  I guess
  triple on the a-file, play Nb4 and Be6, and break through with Bxb3.
Answers.UserDisplayName: Noam D. Elkies
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2015-04-14T07:13:09.537Z
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Answers.LastEditDate: 2021-01-30T02:16:23.170Z
Answers.UserDisplayName: downhand
Body: <p>I have two questions.</p>
  
  <p>1) Is there a position with all pieces on board such that the side to move loses?</p>
  
  <p>2) Is there a position with all pieces on board such that the side to move is checkmated in 1?</p>
  
  <p>Regarding question two, here is one example position that I’ve made where the side to move is checkmated immediately, but the knights are still missing.</p>
  
  <pre><code>[FEN ""]
  [startply "54"]
  
  1. Nc3 Nf6 2. Na4 Nh5 3. Nc5 Nf4 4. d4 e5 5. h4 a5 6. Bxf4 Bxc5 7. a4 h5 8.Ra3 Rh6 9. Nf3 Nc6 10. Ng5 Nb4 11. Qd2 Qxg5 12. Qxb4 Qf6 13. Qc3 Qa6 14. Qh3 Rb8 15. Rg1 Qa8 16. Qh1 Ba7 17. Rh3 c5 18. Bh2 Ra6 19. f4 Kd8  20.Kf2 Kc7 21. g3 b6 22. d5 Kb7 23. Kg2 f5 24. b4 e4 25. b5 g5 26. c4 e3 27. d6 g4
  </code></pre>
  
  <p>Maybe, someone can improve this.</p>
  
Comments.ContentLicense: CC BY-SA 3.0
Comments.CreationDate: 2015-04-14T07:22:48.237Z
Comments.Text: Actually, for all we know, the starting position of chess could be such a position.  Though, admittedly, this seems rather unlikely.
Comments.UserDisplayName: Jester
Comments.ContentLicense: CC BY-SA 3.0
Comments.CreationDate: 2015-04-14T12:13:37.920Z
Comments.Text: Perhaps one could find something by locking up most of the pieces so they can't move - i.e. embed a simpler zugzwang into a bigger board.  The set up would be highly implausible though
Comments.UserDisplayName: Corvus
Comments.ContentLicense: CC BY-SA 3.0
Comments.CreationDate: 2015-04-22T21:21:05.407Z
Comments.Text: It is not relevant if the position is reachable with plausible moves. But I admit that it is very hard, perhaps impossible, to find a position with this proprty.
Comments.UserDisplayName: Peter
Tags: <checkmate><problems><zugzwang>
Title: Full board with full point mutual zugzwang
ThreadText: # Full board with full point mutual zugzwang
  
  (Asked by: username_0 on 2015-04-12)
  
  I have two questions.
  
  1) Is there a position with all pieces on board such that the side to move loses?
  
  2) Is there a position with all pieces on board such that the side to move is checkmated in 1?
  
  Regarding question two, here is one example position that I’ve made where the side to move is checkmated immediately, but the knights are still missing.
  
  ```
  [FEN ""]
  [startply "54"]
  
  1. Nc3 Nf6 2. Na4 Nh5 3. Nc5 Nf4 4. d4 e5 5. h4 a5 6. Bxf4 Bxc5 7. a4 h5 8.Ra3 Rh6 9. Nf3 Nc6 10. Ng5 Nb4 11. Qd2 Qxg5 12. Qxb4 Qf6 13. Qc3 Qa6 14. Qh3 Rb8 15. Rg1 Qa8 16. Qh1 Ba7 17. Rh3 c5 18. Bh2 Ra6 19. f4 Kd8  20.Kf2 Kc7 21. g3 b6 22. d5 Kb7 23. Kg2 f5 24. b4 e4 25. b5 g5 26. c4 e3 27. d6 g4
  
  ```
  
  Maybe, someone can improve this.
  
  **Tags:** checkmate, problems, zugzwang
  
  > **Comments:**
  > **username_1**: Actually, for all we know, the starting position of chess could be such a position.  Though, admittedly, this seems rather unlikely.  
  > **username_2**: Perhaps one could find something by locking up most of the pieces so they can't move - i.e. embed a simpler zugzwang into a bigger board.  The set up would be highly implausible though  
  > **username_0**: It is not relevant if the position is reachable with plausible moves. But I admit that it is very hard, perhaps impossible, to find a position with this proprty.  
  
  ---
  
  ## 3 answers
  
  ### Answer by username_3 on 2021-01-30. Score: 9
  
  Here's a position with all pieces where either side to play loses.
  
  Seeing why it's a loss takes some analysis. With Black moving first, White's best plan is to open up the Bishop on f1 pinning the pawn, then Qxa4 checkmate. This happens in most but not all lines. Shredder evaluates the main line as +22, because either Nxc5 or cxb8=Q with leave White up a queen.
  
  ```
  [Title "Zugzwang with full board"]
  [FEN "nbb5/nqrp4/krpP3p/1pP3pP/pP3pP1/P3pPRK/4PRQN/5BBN b - - 1 0"]
  [startflipped ""]
  
  1... fxg3 (1... exf2 2. Bxf2 fxg3 3. e4 gxh2 4. f4 gxf4 5. Bh4 f3 6. Qc2 f2 7. Qxa4#) 2. Nxg3 exf2 3. f4 gxf4 4. Ne4 f3 (4... fxg1=Q 5. Qxg1 f3 6. g5 hxg5 7. exf3 g4+ 8. Kg3 gxf3 9. Bd3 f2 10. Qd1 f1=N+ 11. Kf4 Ng3 12. Qxa4#) 5. Qxf2 fxe2 6. cxb6 exf1=Q+ 7. Nxf1 c5 8. bxc7  
  
  ```
  
  
  ---
  
  ### Answer by username_4 on 2021-01-30. Score: 4
  
  The second player mates by their 4th move at the latest, with completely unique play.
  
  ```
  [Title "mate in 4 playing second"]
  [FEN "nnb5/bqrp3p/krpP3P/1pP3p1/1P3pP1/p3pPRK/P3PRQB/5BNN b - - 1 0"]
  [startflipped ""]
  
  1... fxg3 (1... exf2 2. Qxf2 fxg3 3. Qe3 g2,gxh2 4. Qxa3#) 2. Qxg3 exf2 3. f4 fxg1=N+ (3... fxg1=Q,R,B,gxf4 4. Qxa3#) 4. Bxg1 gxf4 5. Qxa3#
  
  ```
  
  Most of the time in chess it's an advantage to go first. In combinatorial game theory terms, this is called "hot". Zugzwang positions, where it's a disadvantage to have the move, are termed "cold". In billiards & snooker, this state is called "being snookered". A similar effect used to occur under archaic golf rules: see ["stymied"](https://en.wikipedia.org/wiki/Stymie).
  
  Chess is mostly a hot game, but can get colder as the game progresses. Yet this paradoxical position, almost in the opening still, is very cold indeed, as neither side can move except to open up the position for the other player to win.
  
  As someone mentioned in a comment, we can't exclude the remote possibility that the chess starting position itself is a full point zugzwang! See [a chess question of W.T. Tutte](https://mathoverflow.net/questions/107385/a-chess-question-of-w-t-tutte/226893#226893).
  
  The example without the knights in the question had a stronger property: it's a selfmate in 1. So not only does the first player always lose against best play: they *must* lose. I don't know if that can be done with any of the knights present.
  
  > **Comments:**
  > **username_5**: I am glad to see discussion of combinatorial game theoretic notions here. I would like to remark that chess is mostly a hot game indeed, and it doesn't get colder as the game progresses. Rather, a small number of branches of the game tree are cold. Also, it is extremely unlikely that the starting position in chess is full point zugzwang (evidence from strong chess engines evenif we discard the circumstancial evidence).  
  > **username_4**: I completely agree, @username_5. To me, the oddity is that the start position for such a hot game has not been proven mathematically not to be a win for Black.  
  > **username_6**: Correction to the last paragraph: It's not selfmate because 1 bxa6+ Kc6 or 1 . . . gxh3+ 2 Kf3 avoids the mate and in fact gives stalemate.  
  
  ---
  
  ### Answer by username_7 on 2015-04-14. Score: 3
  
  If you literally mean *all pieces*, the simple answer would be **no**, there are simply too many free pieces to move that you cannot enforce a real zugzwang scenario there.
  
  Note that, if all pieces are still on the board, it means there hasn't been any promotion yet either. Without capturing, the pawns cannot change their files, and continuing on the same file they'll toss on the opponent's pawn.
  
  *The side to move is checkmated in 1* is legitimate, but if you add the zugzwang condition that (let's assume the side to move is not under check to make it a legal scenario) without moving that same player would have survived the position, but only because of the necessity to move, they will get checkmated in 1; then we end up in the same disclaimer above: there are simply too many (16!) pieces around to enforce a full zugzwang.
  
  Actually, if being realistic is not a requirement, you can reach a zugzwang scenario with all pieces on board with the real meaning: if not moving were an option, that would be the best move. With mate in 1, that's pretty much impossible to achieve. Also without being realistic, I don't see the point of setting up a zugzwang position, because the idea of such a position is that things were more or less equal up to now, but the next move will cause damage. Whereas in a scenario like this, the opponent already had many trivial chances to win material advantage. Anyway, for the sake of completeness, I'm posting such a position. Anything that doesn't resemble this will mean that one side has too many free pieces, hence that won't work.
  
  ```
  [FEN ""]
  [startply "40"]
  
  1. b3 a5 2. d3 a4 3. f3 a3 4. h3 g5 5. Nc3 g4 6. Nb1 g3 7. Nc3 e5 8. Nb1 e4 9. Nc3 e3 10. Nb1 h5 11. Nc3 h4 12. Nb1 f5 13. Nc3 f4 14. Nb1 d5 15. Nc3 b5 16. Nb1 c5 17. Nc3 c4 18. Nb1 b4 19. Nc3 d4 20. Nb1 c3
  
  ```
  
  > **Comments:**
  > **username_6**: It's not immediately clear that White actually loses this:  after 1 Bxa3 bxa3 2 Qc1 Black still has some work to do.  I guess triple on the a-file, play Nb4 and Be6, and break through with Bxb3.  
  
  ---
  
  