Answers.Body: <p>I think you cannot accurately calculate the probability a given position has been previously played by someone, somewhere. But you can make a rough estimation with a big game database.</p>
  
  <p>To calculate this probability you need a really big database -I'd say it should contain some million games-. And you should have a good representation of games played by players of different levels and historical periods. Then using a database manager (like Scid), and search how many games in your database contain that position. Dividing the number of games containing the position by the total number of games, you have a rough estimation of the probability it has been previously played.</p>
  
  <p>This is a rough estimation because low-level players are not very well represented in the databases, because there is less information of games played in the past and because non-annotated games (blitz, friendly games) do not appear in the database.</p>
  
Answers.ContentLicense: CC BY-SA 3.0
Answers.CreationDate: 2015-09-17T18:04:25.107Z
Answers.LastActivityDate: 2015-09-17T18:04:25.107Z
Answers.UserDisplayName: lodebari
Answers.Body: <p>How much of the legal position space has been explored by humans or machines would be the question to ask first, or one would need to specify in which probability space you are asking your question.</p>
  <p>With opening theory repertoires aficionados, there is the question of how well distributed have past games been in terms of positions explored.</p>
  <p>So I you are asking about some non temporal context and forgetting about historical biases, would be different than using the current distribution over position space of all databases.</p>
  <p>Not an answer.  Maybe it should be a comment.</p>
  
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Answers.CreationDate: 2021-09-02T06:47:37.660Z
Answers.LastActivityDate: 2021-09-02T06:47:37.660Z
Answers.UserDisplayName: dbdb
Body: <p>When reading annotated games from GMs, I sometimes find annotations such as "This was tried by XXX in 1975 vs YYY". Such annotations are sometimes found very deeply in the game, sometimes past move 20.</p>
  
  <p>Depending on the move number, what is the probability that my position has been previously played by someone, somewhere?</p>
  
Comments.ContentLicense: CC BY-SA 3.0
Comments.CreationDate: 2015-09-13T09:06:23.873Z
Comments.Text: Opening theory consists mostly of "positions that have been played before", so it depends on how theoretical your opening repertoire is.
Comments.UserDisplayName: Dag Oskar Madsen
Comments.ContentLicense: CC BY-SA 3.0
Comments.CreationDate: 2015-09-13T12:35:31.020Z
Comments.Text: I do not know how many positions are possible. The possibility that a position comes up is 1 over this amount (if you look at it in a statistical way). The position after 1. e4 is however 5% and in if you look at all the games ever played it will be even more.
Comments.UserDisplayName: Marco
Comments.ContentLicense: CC BY-SA 3.0
Comments.CreationDate: 2015-09-13T16:56:26.083Z
Comments.Text: the answer to your question is entirely dependent on you chess ability, opening knowledgeopenings you play,style, etc. It would be nice if you added this on, though this question seems though to answer.
Comments.UserDisplayName: CognisMantis
Comments.ContentLicense: CC BY-SA 3.0
Comments.CreationDate: 2016-01-17T05:18:17.907Z
Comments.Text: In the other direction, many *endgame* positions have occurred numerous times, often reached by very different routes.
Comments.UserDisplayName: Noam D. Elkies
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2019-10-04T20:11:18.233Z
Comments.Text: Fascinating question, because simple to ask, hard to answer. The number of positions is known exactly for up to white's 6th move, https://oeis.org/A083276. And you could approximate beyond that. The harder question is "how many positions have ever been played by anyone anywhere ever?". Given that we're already at move 6 well beyond the total number of people who have ever lived, https://www.prb.org/howmanypeoplehaveeverlivedonearth/, ...
Comments.UserDisplayName: Jeff Y
Tags: <statistics><game-complexity>
Title: What is the probability that a position has been played before?
ThreadText: # What is the probability that a position has been played before?
  
  (Asked by: username_0 on 2015-09-13)
  
  When reading annotated games from GMs, I sometimes find annotations such as "This was tried by XXX in 1975 vs YYY". Such annotations are sometimes found very deeply in the game, sometimes past move 20.
  
  Depending on the move number, what is the probability that my position has been previously played by someone, somewhere?
  
  **Tags:** statistics, game-complexity
  
  > **Comments:**
  > **username_1**: Opening theory consists mostly of "positions that have been played before", so it depends on how theoretical your opening repertoire is.  
  > **username_2**: I do not know how many positions are possible. The possibility that a position comes up is 1 over this amount (if you look at it in a statistical way). The position after 1. e4 is however 5% and in if you look at all the games ever played it will be even more.  
  > **username_3**: the answer to your question is entirely dependent on you chess ability, opening knowledgeopenings you play,style, etc. It would be nice if you added this on, though this question seems though to answer.  
  > **username_4**: In the other direction, many *endgame* positions have occurred numerous times, often reached by very different routes.  
  > **username_5**: Fascinating question, because simple to ask, hard to answer. The number of positions is known exactly for up to white's 6th move, https://oeis.org/A083276. And you could approximate beyond that. The harder question is "how many positions have ever been played by anyone anywhere ever?". Given that we're already at move 6 well beyond the total number of people who have ever lived, https://www.prb.org/howmanypeoplehaveeverlivedonearth/, ...  
  
  ---
  
  ## 2 answers
  
  ### Answer by username_6 on 2015-09-17. Score: 2
  
  I think you cannot accurately calculate the probability a given position has been previously played by someone, somewhere. But you can make a rough estimation with a big game database.
  
  To calculate this probability you need a really big database -I'd say it should contain some million games-. And you should have a good representation of games played by players of different levels and historical periods. Then using a database manager (like Scid), and search how many games in your database contain that position. Dividing the number of games containing the position by the total number of games, you have a rough estimation of the probability it has been previously played.
  
  This is a rough estimation because low-level players are not very well represented in the databases, because there is less information of games played in the past and because non-annotated games (blitz, friendly games) do not appear in the database.
  
  
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  ### Answer by username_7 on 2021-09-02. Score: 1
  
  How much of the legal position space has been explored by humans or machines would be the question to ask first, or one would need to specify in which probability space you are asking your question.
  
  With opening theory repertoires aficionados, there is the question of how well distributed have past games been in terms of positions explored.
  
  So I you are asking about some non temporal context and forgetting about historical biases, would be different than using the current distribution over position space of all databases.
  
  Not an answer. Maybe it should be a comment.
  
  
  ---
  
  