Body: <p>For position you never played, book probability is perfectly fine for me. The question starts when you already played position x-times. I'm looking for function that will update book probabilities with your style. Obviously if you play 1.d4 in 97 games out of 100 games, probability of playing 1.e4 runs close to 0%. On the other hand, if you played some late position just once, it's nowhere close to 100% you will repeat the move. I could probably make some  workaround myself, but this looks like problem data scientists must have already solved, as it is applicable to virtually any discipline where you want to predict someone's behavior.</p>
  
  <p><strong>Edit: I think there should be one parameter &lt;0;1> measuring how seriously we take book probabilities and how seriously we take players games. With one extreme being ignoring book and one being ignoring player's games.</strong></p>
  
Comments.ContentLicense: CC BY-SA 3.0
Comments.CreationDate: 2017-07-21T07:24:15.877Z
Comments.Text: If you're using database games of your opponent, then he is probably using yours as well. So if _you_ always play the same thing against 1.e4 and score very badly with it, the chances that he'll choose that go up a lot. It's more game theory than statistics.
Comments.UserDisplayName: RemcoGerlich
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Comments.CreationDate: 2017-07-21T07:54:08.783Z
Comments.Text: @RemcoGerlich There are some limitations of results I will get, but I think they will be very usefull anyway. I understand your point, but I find players not exploitive enough. Ruy Lopez players won't exploit you in poisoned pawn Najdorf, even if you lost it every single time. That's not happening. At least my approach will be sound enough to evaluate our own behavior, so I keep waiting for an answer. I can compare our behavior to opponent's and find probable exploits, but first I need something to start with and it is behavior biased by observation of games.
Comments.UserDisplayName: hoacin
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Comments.CreationDate: 2017-07-21T07:58:08.253Z
Comments.Text: But then, is it not simply a matter of taking a database of the player's games, and see how often they played with move? E.g. if they played 1.d4 97 times out of 100, why isn't the probablility of 1.d4 just 97%?
Comments.UserDisplayName: RemcoGerlich
Comments.ContentLicense: CC BY-SA 3.0
Comments.CreationDate: 2017-07-21T08:52:47.947Z
Comments.Text: @RemcoGerlich Why would those millions of games be useless once in position we played at least once? Ok for 1.d4 you won't make mistake with that, but in 6th move of Najdorf, imagine one game played, would you really like 100% probability for move from the game? I see no reason why 0 games would use those millions of games to predict and 1+ games would just throw them away. Good prediction should use them. Word prediction will be also much more effective if you used texts of millions of people and only then update recommendations with your writing style. Our actions are not that unique.
Comments.UserDisplayName: hoacin
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Comments.CreationDate: 2017-07-21T09:02:34.430Z
Comments.Text: @RemcoGerlich The easiest refutation of your approach is one game sample. Is our opponent expected to repeat the same game with 100% certainty?
Comments.UserDisplayName: hoacin
Comments.ContentLicense: CC BY-SA 3.0
Comments.CreationDate: 2017-07-21T09:05:14.317Z
Comments.Text: Thanks, now I understand your question -- and realize that it probably needs a lot of independent research to answer...
Comments.UserDisplayName: RemcoGerlich
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Comments.CreationDate: 2017-07-21T09:12:07.710Z
Comments.Text: Two things: 1) It depends on the intrinsics of the position -- if there's only one legal move, or if 10,000 games in the database all played the same move there, then this player will also play that, even if it's his first time. 2) If you have some model with some parameters, you may be able to estimate them using a large database of games, trying to predict the move someone played in a position using all the previous times he played it. So there is a way to do it.
Comments.UserDisplayName: RemcoGerlich
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Comments.CreationDate: 2017-07-21T09:31:55.693Z
Comments.Text: @RemcoGerlich I think I feel quite comfortable using all book probabilities like if the sample to get them was infinity (reacting to 10000 same moves by various players). That should make things easier. I only look for methods to update these probabilities with n-games sample. Seems like one of the easier problems to data scientists, hopefully someone will help.
Comments.UserDisplayName: hoacin
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Comments.CreationDate: 2017-07-21T14:07:30.323Z
Comments.Text: Perhaps you might consider applying anything that you come up with to rock, paper, scissors.Or, if not, explain why not?
Comments.UserDisplayName: Philip Roe
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Comments.CreationDate: 2017-07-21T14:36:27.100Z
Comments.Text: @PhilipRoe Somehow I don't see connection between my question and some game theory concept you maybe point to.
Comments.UserDisplayName: hoacin
Comments.ContentLicense: CC BY-SA 3.0
Comments.CreationDate: 2017-07-21T14:43:26.737Z
Comments.Text: @hoacin The comment was intended to be humorous but with a serious point. Suppose that there exists some objective algorithm that predicts my opening play, at whatever level of detail, accurately enough to be useful. Then that same algorithm is also available to me and I know what you are expecting, and also the confidence with which you expect it. So Ill (probably) do something else.
  
  This is nothing more than the standard game-theory proof that a strategy for rock,paper, scissors does not exist, and that the best choice is a random choice, because if I know that you follow some algorithm,
Comments.UserDisplayName: Philip Roe
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Comments.CreationDate: 2017-07-21T14:55:24.750Z
Comments.Text: then I can use it against you.
  
  In chess, of course, the space of options is much larger, but the onus is on you to show that the argument does not apply in principle.
Comments.UserDisplayName: Philip Roe
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Comments.CreationDate: 2017-07-21T15:35:03.390Z
Comments.Text: @PhilipRoe I didn't even write here what I want the numbers for :) Forcing opponent to random choice, killing his preparation, that's dream scenario for me.
Comments.UserDisplayName: hoacin
Comments.ContentLicense: CC BY-SA 3.0
Comments.CreationDate: 2017-07-22T11:32:44.393Z
Comments.Text: @hoacin Ah, that makes it more interesting. You want to nullify his preparation by predicting what it will be. So that knowing this, he will actually choose at random?
  
  But your information is limited to his playing history and the statistics in data bases. There is a lot that you do not have access to. How does he read the tournament situation (needs a win?). Was his previous game long and tiring? What did he talk about over dinner with his friend?
Comments.UserDisplayName: Philip Roe
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Comments.CreationDate: 2017-07-22T12:05:45.263Z
Comments.Text: @PhilipRoe This discussion seems pretty off topic here.
Comments.UserDisplayName: hoacin
Comments.ContentLicense: CC BY-SA 3.0
Comments.CreationDate: 2017-07-23T20:32:41.953Z
Comments.Text: @hoacin
  MMM. Kind of the point I was making. Off-topic issues seems very important to your stated objective. Over and out.
Comments.UserDisplayName: Philip Roe
Tags: <opening><programming><mathematics>
Title: Estimating probability of player playing move in the opening
ThreadText: # Estimating probability of player playing move in the opening
  
  (Asked by: username_0 on 2017-07-21)
  
  For position you never played, book probability is perfectly fine for me. The question starts when you already played position x-times. I'm looking for function that will update book probabilities with your style. Obviously if you play 1.d4 in 97 games out of 100 games, probability of playing 1.e4 runs close to 0%. On the other hand, if you played some late position just once, it's nowhere close to 100% you will repeat the move. I could probably make some workaround myself, but this looks like problem data scientists must have already solved, as it is applicable to virtually any discipline where you want to predict someone's behavior.
  
  **Edit: I think there should be one parameter <0;1> measuring how seriously we take book probabilities and how seriously we take players games. With one extreme being ignoring book and one being ignoring player's games.**
  
  **Tags:** opening, programming, mathematics
  
  > **Comments:**
  > **username_1**: If you're using database games of your opponent, then he is probably using yours as well. So if _you_ always play the same thing against 1.e4 and score very badly with it, the chances that he'll choose that go up a lot. It's more game theory than statistics.  
  > **username_0**: @username_1 There are some limitations of results I will get, but I think they will be very usefull anyway. I understand your point, but I find players not exploitive enough. Ruy Lopez players won't exploit you in poisoned pawn Najdorf, even if you lost it every single time. That's not happening. At least my approach will be sound enough to evaluate our own behavior, so I keep waiting for an answer. I can compare our behavior to opponent's and find probable exploits, but first I need something to start with and it is behavior biased by observation of games.  
  > **username_1**: But then, is it not simply a matter of taking a database of the player's games, and see how often they played with move? E.g. if they played 1.d4 97 times out of 100, why isn't the probablility of 1.d4 just 97%?  
  > **username_0**: @username_1 Why would those millions of games be useless once in position we played at least once? Ok for 1.d4 you won't make mistake with that, but in 6th move of Najdorf, imagine one game played, would you really like 100% probability for move from the game? I see no reason why 0 games would use those millions of games to predict and 1+ games would just throw them away. Good prediction should use them. Word prediction will be also much more effective if you used texts of millions of people and only then update recommendations with your writing style. Our actions are not that unique.  
  > **username_0**: @username_1 The easiest refutation of your approach is one game sample. Is our opponent expected to repeat the same game with 100% certainty?  
  > **username_1**: Thanks, now I understand your question -- and realize that it probably needs a lot of independent research to answer...  
  > **username_1**: Two things: 1) It depends on the intrinsics of the position -- if there's only one legal move, or if 10,000 games in the database all played the same move there, then this player will also play that, even if it's his first time. 2) If you have some model with some parameters, you may be able to estimate them using a large database of games, trying to predict the move someone played in a position using all the previous times he played it. So there is a way to do it.  
  > **username_0**: @username_1 I think I feel quite comfortable using all book probabilities like if the sample to get them was infinity (reacting to 10000 same moves by various players). That should make things easier. I only look for methods to update these probabilities with n-games sample. Seems like one of the easier problems to data scientists, hopefully someone will help.  
  > **username_2**: Perhaps you might consider applying anything that you come up with to rock, paper, scissors.Or, if not, explain why not?  
  > **username_0**: @PhilipRoe Somehow I don't see connection between my question and some game theory concept you maybe point to.  
  > **username_2**: @username_0 The comment was intended to be humorous but with a serious point. Suppose that there exists some objective algorithm that predicts my opening play, at whatever level of detail, accurately enough to be useful. Then that same algorithm is also available to me and I know what you are expecting, and also the confidence with which you expect it. So Ill (probably) do something else.  This is nothing more than the standard game-theory proof that a strategy for rock,paper, scissors does not exist, and that the best choice is a random choice, because if I know that you follow some algorithm,  
  > **username_2**: then I can use it against you.  In chess, of course, the space of options is much larger, but the onus is on you to show that the argument does not apply in principle.  
  > **username_0**: @PhilipRoe I didn't even write here what I want the numbers for :) Forcing opponent to random choice, killing his preparation, that's dream scenario for me.  
  > **username_2**: @username_0 Ah, that makes it more interesting. You want to nullify his preparation by predicting what it will be. So that knowing this, he will actually choose at random?  But your information is limited to his playing history and the statistics in data bases. There is a lot that you do not have access to. How does he read the tournament situation (needs a win?). Was his previous game long and tiring? What did he talk about over dinner with his friend?  
  > **username_0**: @PhilipRoe This discussion seems pretty off topic here.  
  > **username_2**: @username_0 MMM. Kind of the point I was making. Off-topic issues seems very important to your stated objective. Over and out.  
  
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