Answers.Body: <p>As you noted, <code>w_i</code> is not calculated by the search tree. It is simply the number of wins out of the total simulations performed at that node (if this is the method used to score the node). This scoring mechanism is also known as <a href="https://github.com/LeelaChessZero/lc0/wiki/Technical-Explanation-of-Leela-Chess-Zero" rel="nofollow noreferrer">playout</a>.</p>
  
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2019-07-16T04:11:31.027Z
Answers.LastActivityDate: 2019-07-16T04:11:31.027Z
Answers.UserDisplayName: prusswan
Body: <p>How do we know <em>w_i</em> which is not possible to calculate using the <a href="https://medium.com/@quasimik/monte-carlo-tree-search-applied-to-letterpress-34f41c86e238" rel="nofollow noreferrer">tree search</a> only?</p>
  
  <p>From the <a href="https://slides.com/crem/lc0#/9" rel="nofollow noreferrer">lc0 slide</a>, <em>w_i</em> is equal to summation of subtree of <em>V</em> ? How is this equivalent to winning ?</p>
  
  <p><a href="https://i.sstatic.net/aLNja.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/aLNja.png" alt="tree"></a></p>
  
  <p><a href="https://i.sstatic.net/lFPTK.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/lFPTK.png" alt="UCB formula"></a></p>
  
  <p><a href="https://i.sstatic.net/tQ3Ls.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/tQ3Ls.png" alt="leela formula"></a></p>
  
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2019-07-15T07:21:42.143Z
Comments.Text: Beautiful chess question! Please don't expect to post a ton of formulas and graphs about something completely unrelated to chess without even explaining its context but still expect us to understand it
Comments.UserDisplayName: David
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2019-07-16T03:58:36.797Z
Comments.Text: @David this is perfect example of why novice users dominate this SE and attempt to close non-trivial questions
Comments.UserDisplayName: prusswan
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2019-07-16T07:22:37.517Z
Comments.Text: @prusswan I don't want to close this question because it's non-trivial, I want to close it because it has nothing to do with chess. There is like a million Stack Exchange sites about math, statistics, machine learning, artificial intelligence, programming and all of those nerd things, so I see no reason to have yet another one
Comments.UserDisplayName: David
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2019-07-16T11:30:20.370Z
Comments.Text: Highly technical questions about leela might find more understanding on leela discord than here.
Comments.UserDisplayName: hoacin
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2019-07-16T15:41:33.360Z
Comments.Text: I don't think this question needs to be closed. However, it needs a small introduction to give some context (about leela, her general algorithm, the part where $\omega_i$ appears...) so that people can have an idea what this is all about even if they cannot answer themselves.
Comments.UserDisplayName: Evargalo
Tags: <programming><mathematics><leela>
Title: Leela Chess PUCT Mechanism
ThreadText: # Leela Chess PUCT Mechanism
  
  (Asked by: username_0 on 2019-07-13)
  
  How do we know *w\_i* which is not possible to calculate using the [tree search](https://medium.com/@quasimik/monte-carlo-tree-search-applied-to-letterpress-34f41c86e238) only?
  
  From the [lc0 slide](https://slides.com/crem/lc0#/9), *w\_i* is equal to summation of subtree of *V* ? How is this equivalent to winning ?
  
  [![tree](https://i.sstatic.net/aLNja.png)](https://i.sstatic.net/aLNja.png)
  
  [![UCB formula](https://i.sstatic.net/lFPTK.png)](https://i.sstatic.net/lFPTK.png)
  
  [![leela formula](https://i.sstatic.net/tQ3Ls.png)](https://i.sstatic.net/tQ3Ls.png)
  
  **Tags:** programming, mathematics, leela
  
  > **Comments:**
  > **username_1**: Beautiful chess question! Please don't expect to post a ton of formulas and graphs about something completely unrelated to chess without even explaining its context but still expect us to understand it  
  > **username_2**: @username_1 this is perfect example of why novice users dominate this SE and attempt to close non-trivial questions  
  > **username_1**: @username_2 I don't want to close this question because it's non-trivial, I want to close it because it has nothing to do with chess. There is like a million Stack Exchange sites about math, statistics, machine learning, artificial intelligence, programming and all of those nerd things, so I see no reason to have yet another one  
  > **username_3**: Highly technical questions about leela might find more understanding on leela discord than here.  
  > **username_4**: I don't think this question needs to be closed. However, it needs a small introduction to give some context (about leela, her general algorithm, the part where $\omega_i$ appears...) so that people can have an idea what this is all about even if they cannot answer themselves.  
  
  ---
  
  ## 1 answers
  
  ### Answer by username_2 on 2019-07-16. Score: 4
  
  As you noted, `w_i` is not calculated by the search tree. It is simply the number of wins out of the total simulations performed at that node (if this is the method used to score the node). This scoring mechanism is also known as [playout](https://github.com/LeelaChessZero/lc0/wiki/Technical-Explanation-of-Leela-Chess-Zero).
  
  
  ---
  
  