Body: <p>A game leading to a given position is called a proof game. Of course any proof game can be prepended with 1.Nf3 Nf6 2.Ng1 Ng8, so we defined a shortest proof game as, duh, the shortest possible proof game. Especially interesting are unique shortest proof games. For example, 1.e4 e5 2.Nf3 is not unique - White could swap moves. In contrast, 1.e4 e5 2.Bc4 is unique.</p>
  <p>Rules of the fun game: First one creating a position without a unique shortest proof game loses. And that's it.</p>
  <p>Do you have ideas for strategies or even a forced win for one side? Checking might be a good idea to force the hand of the opponent; 1.e4 d5?! 2.Bb5+ and now Nc6 or c6 lose, but anything to d7 is OK. (EDIT: And don't let your opponent capture, since one-side noncommuting moves run out quite fast.)</p>
  <p>(For testers: Proof game checkers <a href="https://wismuth.com/jacobi/" rel="nofollow noreferrer">exist</a>.)</p>
  
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2022-10-23T01:03:42.563Z
Comments.Text: Can you also lose by being checkmated?
Comments.UserDisplayName: Noam D. Elkies
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2022-10-23T08:15:40.353Z
Comments.Text: @NoamD.Elkies: The problem forum where I found this game said nothing about that. I think any move ending the game (stalemate, 50 move rule, etc.) should be treated as an attempt to bail out :-) and thus lose.
Comments.UserDisplayName: Hauke Reddmann
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2022-10-23T11:22:53.737Z
Comments.Text: Very cool idea for a game!
  Just a remark, if the proof game requires castling, it cannot be prepended with your dance of knights.
Comments.UserDisplayName: Miguel Ambrona
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2022-10-23T21:45:12.967Z
Comments.Text: @MiguelAmbrona Why not?  Prepending 1 Nf3 Nh6 2 Ng1 Ng8 doesn't lose any castling rights.
Comments.UserDisplayName: Noam D. Elkies
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2022-10-24T08:54:43.213Z
Comments.Text: I want to play this game !
Comments.UserDisplayName: Evargalo
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2022-10-24T09:28:01.547Z
Comments.Text: @MiguelAmbrona: Prepending "null" sequences *could* be relevant in a 50 move situation. I doubt that this could become relevant, though.
Comments.UserDisplayName: Hauke Reddmann
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2022-10-24T21:36:22.767Z
Comments.Text: @NoamD.Elkies: Would it be possible to be checkmated without having lost already?
Comments.UserDisplayName: supercat
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2022-10-24T21:49:25.193Z
Comments.Text: @supercat Yes, there are many unique proof games ending in checkmate.  For example, 1 e4 f5 2 exf5 g5 3 Qh5#.
Comments.UserDisplayName: Noam D. Elkies
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2022-10-25T04:48:25.190Z
Comments.Text: @NoamD.Elkies: Nice example,  How many more exist?  What's the longest?
Comments.UserDisplayName: supercat
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2022-10-25T07:45:07.990Z
Comments.Text: @supercat: You can do a PDB search by going on https://pdb.dieschwalbe.de/index.jsp and enter K='unique proof game' AND SOL='#'. This is no surefire answer, as '#' might be omitted and not all UPGs are in the database. A fleeting search gave the P0002187 with whopping 38.5 moves! (418 games are shown, so even that might not be the record...)
Comments.UserDisplayName: Hauke Reddmann
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2022-10-25T15:15:47.593Z
Comments.Text: @HaukeReddmann: Wow, I never would have guessed.  I'd had sufficient difficulty coming up with any kind of mating strategy that I would have estimated the number of possible such games at under a dozen.  I wonder how much computing horsepower would be required to do a breadth-first search of all unique proof positions?
Comments.UserDisplayName: supercat
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2022-10-25T15:16:58.017Z
Comments.Text: @HaukeReddmann: BTW, do you know any nice way of converting the German-language notation games to use NBRQK so as to facilitate importing to other programs?
Comments.UserDisplayName: supercat
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2022-10-25T17:04:57.950Z
Comments.Text: @supercat: 59 moves were attempted lately...but unfortunately, cooked as fast as composed. Next question: For G/E conversion, depends what you want. For a casual convert, any PGN reader able to deal with both languages will do. For batch, if no comments are present, I write a Python converter in ten minutes (especially as I need the feature constantly, I just was too lazy up to now). With comments, if they are all cleanly in {}, 20 minutes :-)
Comments.UserDisplayName: Hauke Reddmann
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2022-10-25T17:06:54.883Z
Comments.Text: @supercat: Not what you want, but might come in handy: http://marianogappa.github.io/ostinato-examples/convert - maybe the author can be pestered :-) (The proggie can handle even oldschool notation, German symbols would be easy...)
Comments.UserDisplayName: Hauke Reddmann
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2022-10-25T17:24:38.160Z
Comments.Text: You are right, for some reason I assumed the rooks were moving too. My bad.
Comments.UserDisplayName: Miguel Ambrona
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2022-10-27T01:16:09.160Z
Comments.Text: @NoamD.Elkies (and HaukeReddmann): If the rules are that checkmate has the same result as in ordinary chess, then one interesting result is that 1. f3 is a losing move for white.  Black has a couple losing moves, but the best response of e5 forces Kf2 and black can continue so that the whole game is forced as follows: 1. f3? e5 2. Kf2 Qh4+ 3. Ke3 Qd4#!
Comments.UserDisplayName: A. Rex
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2022-10-27T15:31:11.857Z
Comments.Text: @A.Rex that's a nice variation, though it's not quite forced: 2 f4 is legal too.
Comments.UserDisplayName: Noam D. Elkies
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2022-10-27T16:41:48.180Z
Comments.Text: @NoamD.Elkies: Unfortunately, that is another dimension upon which the definition of the game in question can vary. I was operating under the version where 1. f3 e5 2. f4 is *not* a legal move for white because 1. f4 e5 is a shorter game resulting in the same *diagram*. Of course a different player has the move, so the position is "different", but on the other hand if someone published a "shortest proof game" puzzle for the diagram, surely the solution is the one in 2 ply. *However*, this just raises yet another definitional issue: is 2. f4 okay because the position has a *different* USPG?
Comments.UserDisplayName: A. Rex
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2022-10-27T17:27:11.097Z
Comments.Text: @A.Rex good point.  To me it feels most natural to require that after N ply the diagram have a unique proof game in N ply, even if there are games in N-1 or N-2 that also reach this position.  (Yes, that's possible -- there's a famous N=8 puzzle.)  Even then 1 f3? loses: 1 f3? e5 2 f4 Bc5 3 fxe5 (or f5) Qh4+ and the forced 4 g3 loses uniqueness.
Comments.UserDisplayName: Noam D. Elkies
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2024-06-19T13:18:44.810Z
Comments.Text: *In contrast, 1.e4 e5 2.Bc4 is unique.* It isn't: 1.e3 e6 2.Lc4 e5 3.e4 - or similar.
Comments.UserDisplayName: bakunin
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2024-06-20T06:38:00.063Z
Comments.Text: @bakunin: See my first paragraph - NO position has an unique proof game, thus the qualifier *shortest* proof game, and all other proof games, like yours, are longer for this position.
Comments.UserDisplayName: Hauke Reddmann
Tags: <problems><chess-variants>
Title: A fun game (for problem composers, mostly...)
ThreadText: # A fun game (for problem composers, mostly...)
  
  (Asked by: username_0 on 2022-10-22)
  
  A game leading to a given position is called a proof game. Of course any proof game can be prepended with 1.Nf3 Nf6 2.Ng1 Ng8, so we defined a shortest proof game as, duh, the shortest possible proof game. Especially interesting are unique shortest proof games. For example, 1.e4 e5 2.Nf3 is not unique - White could swap moves. In contrast, 1.e4 e5 2.Bc4 is unique.
  
  Rules of the fun game: First one creating a position without a unique shortest proof game loses. And that's it.
  
  Do you have ideas for strategies or even a forced win for one side? Checking might be a good idea to force the hand of the opponent; 1.e4 d5?! 2.Bb5+ and now Nc6 or c6 lose, but anything to d7 is OK. (EDIT: And don't let your opponent capture, since one-side noncommuting moves run out quite fast.)
  
  (For testers: Proof game checkers [exist](https://wismuth.com/jacobi/).)
  
  **Tags:** problems, chess-variants
  
  > **Comments:**
  > **username_1**: Can you also lose by being checkmated?  
  > **username_0**: @username_1: The problem forum where I found this game said nothing about that. I think any move ending the game (stalemate, 50 move rule, etc.) should be treated as an attempt to bail out :-) and thus lose.  
  > **username_2**: Very cool idea for a game! Just a remark, if the proof game requires castling, it cannot be prepended with your dance of knights.  
  > **username_1**: @username_2 Why not?  Prepending 1 Nf3 Nh6 2 Ng1 Ng8 doesn't lose any castling rights.  
  > **username_3**: I want to play this game !  
  > **username_0**: @username_2: Prepending "null" sequences *could* be relevant in a 50 move situation. I doubt that this could become relevant, though.  
  > **username_4**: @username_1: Would it be possible to be checkmated without having lost already?  
  > **username_1**: @username_4 Yes, there are many unique proof games ending in checkmate.  For example, 1 e4 f5 2 exf5 g5 3 Qh5#.  
  > **username_4**: @username_1: Nice example,  How many more exist?  What's the longest?  
  > **username_0**: @username_4: You can do a PDB search by going on https://pdb.dieschwalbe.de/index.jsp and enter K='unique proof game' AND SOL='#'. This is no surefire answer, as '#' might be omitted and not all UPGs are in the database. A fleeting search gave the P0002187 with whopping 38.5 moves! (418 games are shown, so even that might not be the record...)  
  > **username_4**: @username_0: Wow, I never would have guessed.  I'd had sufficient difficulty coming up with any kind of mating strategy that I would have estimated the number of possible such games at under a dozen.  I wonder how much computing horsepower would be required to do a breadth-first search of all unique proof positions?  
  > **username_4**: @username_0: BTW, do you know any nice way of converting the German-language notation games to use NBRQK so as to facilitate importing to other programs?  
  > **username_0**: @username_4: 59 moves were attempted lately...but unfortunately, cooked as fast as composed. Next question: For G/E conversion, depends what you want. For a casual convert, any PGN reader able to deal with both languages will do. For batch, if no comments are present, I write a Python converter in ten minutes (especially as I need the feature constantly, I just was too lazy up to now). With comments, if they are all cleanly in {}, 20 minutes :-)  
  > **username_0**: @username_4: Not what you want, but might come in handy: http://marianogappa.github.io/ostinato-examples/convert - maybe the author can be pestered :-) (The proggie can handle even oldschool notation, German symbols would be easy...)  
  > **username_2**: You are right, for some reason I assumed the rooks were moving too. My bad.  
  > **username_5**: @username_1 (and username_0): If the rules are that checkmate has the same result as in ordinary chess, then one interesting result is that 1. f3 is a losing move for white.  Black has a couple losing moves, but the best response of e5 forces Kf2 and black can continue so that the whole game is forced as follows: 1. f3? e5 2. Kf2 Qh4+ 3. Ke3 Qd4#!  
  > **username_1**: @username_5 that's a nice variation, though it's not quite forced: 2 f4 is legal too.  
  > **username_5**: @username_1: Unfortunately, that is another dimension upon which the definition of the game in question can vary. I was operating under the version where 1. f3 e5 2. f4 is *not* a legal move for white because 1. f4 e5 is a shorter game resulting in the same *diagram*. Of course a different player has the move, so the position is "different", but on the other hand if someone published a "shortest proof game" puzzle for the diagram, surely the solution is the one in 2 ply. *However*, this just raises yet another definitional issue: is 2. f4 okay because the position has a *different* USPG?  
  > **username_1**: @username_5 good point.  To me it feels most natural to require that after N ply the diagram have a unique proof game in N ply, even if there are games in N-1 or N-2 that also reach this position.  (Yes, that's possible -- there's a famous N=8 puzzle.)  Even then 1 f3? loses: 1 f3? e5 2 f4 Bc5 3 fxe5 (or f5) Qh4+ and the forced 4 g3 loses uniqueness.  
  > **username_6**: *In contrast, 1.e4 e5 2.Bc4 is unique.* It isn't: 1.e3 e6 2.Lc4 e5 3.e4 - or similar.  
  > **username_0**: @username_6: See my first paragraph - NO position has an unique proof game, thus the qualifier *shortest* proof game, and all other proof games, like yours, are longer for this position.  
  
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  ## 0 answers
  
  