Answers.Body: <p>The longest game I've ever found in tournament play is Nikolic - Arsovic, played in Belgrade in 1989. You can watch it <a href="https://www.chessgames.com/perl/chessgame?gid=1268705" rel="nofollow noreferrer">here</a>. It ended in a draw after 269 moves in a rook+bishop-vs-rook endgame</p>
  
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Answers.CreationDate: 2019-11-08T09:43:41.197Z
Answers.Text: This is a good sanity check for any sort of result from logic, but this is not an answer to my question.
Answers.UserDisplayName: psitae
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Answers.Text: Then please clarify your question. What does "non-cooperative" mean?
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Answers.UserDisplayName: David
Answers.Body: <p>If, in some chess position, one side can win against any defence, then we may ask what the least n, where the winning side can guarantee to checkmate in n moves or fewer, against any defence.</p>
  
  <p>Analysis of seven-piece positions has brought to light some positions where n is as large as 549, for example <a href="http://tb7.chessok.com/articles/Top8DTM_eng" rel="nofollow noreferrer">this one in KQPKRBN</a>.</p>
  
  <p>Presumably if the number of units allowed on the board were increased, there'd be positions whose shortest wins are even longer.</p>
  
  <p>But for a game to reach such a position, one side must have already blundered a half-point (supposing that the initial position is a draw with best play). So long as neither player blunders into a position where the other player can force a win, how do you decide which possible moves are co-operative and which are not?</p>
  
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Body: <p>Typical arguments for the longest possible game of chess take a form something like this.</p>
  
  <p>1) Each player moves their knights back of forth 49 times
  2) Each player moves one pawn forward one square and repeats the knight shuffling.
  3) Once all pawns are on the 4th and 5th ranks, ....
  and so on. </p>
  
  <p>I,we found estimates around 9000. I'm interested in the longest possible game of chess, with the restriction that the players are actually trying to win, and not cooperating to make the longest possible game allowable by the rules. We might call this the longest realistic game of chess.</p>
  
  <p>Since the above argument totally breaks down, what are some new considerations that might allow us to lower the upper bound on the longest realistic game of chess?</p>
  
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2019-11-08T08:27:19.667Z
Comments.Text: It's hard to combine a rigorous requirement like longest _possible_ with the vague notion of "trying to win". Could you try to define what "trying to win" would be in a more formal way, or alternatively are you just looking for the record so far?
Comments.UserDisplayName: RemcoGerlich
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2019-11-08T09:42:07.547Z
Comments.Text: Trying to win is well defined. Try to find the best move in every position. Formally, best play is given by the minimax algorithm.
Comments.UserDisplayName: psitae
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2019-11-08T09:43:04.267Z
Comments.Text: I'm not looking for the record. I to reformulate the type of argument seen above where cooperation is not allowed. Sorry this wasn't clear.
Comments.UserDisplayName: psitae
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2019-11-08T10:00:07.947Z
Comments.Text: It is pretty clear that in many situations competently trying to win, will shorten the game compared to incompetently trying to win. But if you make the players too incompetent, in which way can you still meaningful say that they are trying to win? You end up with random moves and the longest random game is one that is indistinguishable from a collaborative effort.
Comments.UserDisplayName: BlindKungFuMaster
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2019-11-08T10:05:26.060Z
Comments.Text: The min-max algorithm depends on a value-function. The value-function tells you how "good" a position is. How good a position is, is not objective. It's relative to your opponent or your pool of opponents. "Best play" is not formally defined except maybe in winning positions where there is a shortest way to mate against best defense.
Comments.UserDisplayName: BlindKungFuMaster
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2019-11-08T10:51:48.750Z
Comments.Text: @psitae: "try" isn't well defined, and assuming only players who play the best move are trying isn't "realistic".
Comments.UserDisplayName: RemcoGerlich
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2019-11-09T00:44:17.640Z
Comments.Text: @RemcoGerlich you're right, we don't know how people make decisions. But I'm not asking for a solution to that problem
Comments.UserDisplayName: psitae
Tags: <theory><mathematics>
Title: Longest non-cooperative game of chess
ThreadText: # Longest non-cooperative game of chess
  
  (Asked by: username_0 on 2019-11-08)
  
  Typical arguments for the longest possible game of chess take a form something like this.
  
  1) Each player moves their knights back of forth 49 times
  2) Each player moves one pawn forward one square and repeats the knight shuffling.
  3) Once all pawns are on the 4th and 5th ranks, ....
  and so on.
  
  I,we found estimates around 9000. I'm interested in the longest possible game of chess, with the restriction that the players are actually trying to win, and not cooperating to make the longest possible game allowable by the rules. We might call this the longest realistic game of chess.
  
  Since the above argument totally breaks down, what are some new considerations that might allow us to lower the upper bound on the longest realistic game of chess?
  
  **Tags:** theory, mathematics
  
  > **Comments:**
  > **username_1**: It's hard to combine a rigorous requirement like longest _possible_ with the vague notion of "trying to win". Could you try to define what "trying to win" would be in a more formal way, or alternatively are you just looking for the record so far?  
  > **username_0**: Trying to win is well defined. Try to find the best move in every position. Formally, best play is given by the minimax algorithm.  
  > **username_0**: I'm not looking for the record. I to reformulate the type of argument seen above where cooperation is not allowed. Sorry this wasn't clear.  
  > **username_2**: It is pretty clear that in many situations competently trying to win, will shorten the game compared to incompetently trying to win. But if you make the players too incompetent, in which way can you still meaningful say that they are trying to win? You end up with random moves and the longest random game is one that is indistinguishable from a collaborative effort.  
  > **username_2**: The min-max algorithm depends on a value-function. The value-function tells you how "good" a position is. How good a position is, is not objective. It's relative to your opponent or your pool of opponents. "Best play" is not formally defined except maybe in winning positions where there is a shortest way to mate against best defense.  
  > **username_1**: @username_0: "try" isn't well defined, and assuming only players who play the best move are trying isn't "realistic".  
  > **username_0**: @username_1 you're right, we don't know how people make decisions. But I'm not asking for a solution to that problem  
  
  ---
  
  ## 2 answers
  
  ### Answer by username_3 on 2019-11-08. Score: 2
  
  The longest game I've ever found in tournament play is Nikolic - Arsovic, played in Belgrade in 1989. You can watch it [here](https://www.chessgames.com/perl/chessgame?gid=1268705). It ended in a draw after 269 moves in a rook+bishop-vs-rook endgame
  
  > **Comments:**
  > **username_0**: This is a good sanity check for any sort of result from logic, but this is not an answer to my question.  
  > **username_3**: Then please clarify your question. What does "non-cooperative" mean?  
  
  ---
  
  ### Answer by username_4 on 2019-11-08. Score: 1
  
  If, in some chess position, one side can win against any defence, then we may ask what the least n, where the winning side can guarantee to checkmate in n moves or fewer, against any defence.
  
  Analysis of seven-piece positions has brought to light some positions where n is as large as 549, for example [this one in KQPKRBN](http://tb7.chessok.com/articles/Top8DTM_eng).
  
  Presumably if the number of units allowed on the board were increased, there'd be positions whose shortest wins are even longer.
  
  But for a game to reach such a position, one side must have already blundered a half-point (supposing that the initial position is a draw with best play). So long as neither player blunders into a position where the other player can force a win, how do you decide which possible moves are co-operative and which are not?
  
  
  ---
  
  