Answers.Body: <p>On the website of <a href="http://www.cruxis.com/chess/houdini.htm" rel="noreferrer">Houdini</a>, one of the best chess engines (see for instance <a href="http://www.computerchess.org.uk/ccrl/404/" rel="noreferrer">CCRL</a> or <a href="http://www.husvankempen.de/nunn/40_4_Ratinglist/40_4_BestVersion/rangliste.html" rel="noreferrer">CEGT</a>), the author writes</p>
  
  <blockquote>
    <p>Houdini 4 uses calibrated evaluations in which engine scores correlate directly with the win expectancy in the position. A +1.00 pawn advantage gives a 80% chance of winning the game against an equal opponent at blitz time control. At +2.00 the engine will win 95% of the time, and at +3.00 about 99% of the time. If the advantage is +0.50, expect to win nearly 50% of the time.</p>
  </blockquote>
  
  <p>The <a href="https://chessprogramming.wikispaces.com/Pawn+Advantage%2C+Win+Percentage%2C+and+ELO" rel="noreferrer">Chess Programming Wiki</a> mentions a study where data from more than 400 000 computer games have been used to find a relation between pawn advantage (P) and winning percentage (W).</p>
  
  <blockquote>
    <p>W = 1 / (1+10^(-P/4))</p>
  </blockquote>
  
Answers.ContentLicense: CC BY-SA 3.0
Answers.CreationDate: 2016-08-29T21:32:54.197Z
Answers.Text: Amazing that only one pawn gives so much advantage.
Answers.UserDisplayName: Santropedro
Answers.ContentLicense: CC BY-SA 3.0
Answers.CreationDate: 2016-08-30T07:39:53.300Z
Answers.Text: True, the 80% winning percentage for P=1 in case of Houdini is quite high. Especially when compared to other engines: according to the formula, for P=1, W=0.64. But, as you correctly mention in your question, the score has a different purpose and it is not necessarily related to the winning percentage.
Answers.UserDisplayName: Maxwell86
Answers.ContentLicense: CC BY-SA 3.0
Answers.CreationDate: 2016-08-30T10:01:49.843Z
Answers.Text: P=4 and W = 91% seems rather low
Answers.UserDisplayName: jf328
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2020-11-23T06:35:31.487Z
Answers.Text: Also check "Peter Österlund’s Texel Tuning" in Andrew Grant, Evaluation & Tuning in Chess Engines", which you can locate under [Andrew Grant](https://www.chessprogramming.org/Andrew_Grant) wiki entry were you will get his [work](https://pdfhost.io/v/Q~Yrnl8kj_Tuningpdf.pdf) on relating the engine evaluation to the winning percentage.
Answers.UserDisplayName: djnavas
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Answers.CreationDate: 2016-08-29T19:33:36.843Z
Answers.LastActivityDate: 2016-08-29T20:05:50.997Z
Answers.LastEditDate: 2016-08-29T20:05:50.997Z
Answers.UserDisplayName: Maxwell86
Body: <p>I was wondering if there is a statistical or probabilistic (at least approximate) way of looking at a score of a chess position of a certain fixed engine, say "crafty version 5" for example. </p>
  
  <p>i.e. maybe +2 could be interpreted as "if the engine keeps on playing, 60% wins white, 30% black and 10% draw. I know this isn't the purpose of the score, but maybe it can be translated to approximate probabilities, maybe someone has done a statistical test with hundreds of games to see the correlation. And the amount of draw maybe depends on the "sharpness" of the position.</p>
  
Tags: <engines><statistics><evaluation>
Title: Does engine score correlate with winning chances?
ThreadText: # Does engine score correlate with winning chances?
  
  (Asked by: username_0 on 2016-08-29)
  
  I was wondering if there is a statistical or probabilistic (at least approximate) way of looking at a score of a chess position of a certain fixed engine, say "crafty version 5" for example.
  
  i.e. maybe +2 could be interpreted as "if the engine keeps on playing, 60% wins white, 30% black and 10% draw. I know this isn't the purpose of the score, but maybe it can be translated to approximate probabilities, maybe someone has done a statistical test with hundreds of games to see the correlation. And the amount of draw maybe depends on the "sharpness" of the position.
  
  **Tags:** engines, statistics, evaluation
  
  
  ---
  
  ## 1 answers
  
  ### Answer by username_1 on 2016-08-29. Score: 6 | Accepted answer
  
  On the website of [Houdini](http://www.cruxis.com/chess/houdini.htm), one of the best chess engines (see for instance [CCRL](http://www.computerchess.org.uk/ccrl/404/) or [CEGT](http://www.husvankempen.de/nunn/40_4_Ratinglist/40_4_BestVersion/rangliste.html)), the author writes
  
  > Houdini 4 uses calibrated evaluations in which engine scores correlate directly with the win expectancy in the position. A +1.00 pawn advantage gives a 80% chance of winning the game against an equal opponent at blitz time control. At +2.00 the engine will win 95% of the time, and at +3.00 about 99% of the time. If the advantage is +0.50, expect to win nearly 50% of the time.
  
  The [Chess Programming Wiki](https://chessprogramming.wikispaces.com/Pawn+Advantage%2C+Win+Percentage%2C+and+ELO) mentions a study where data from more than 400 000 computer games have been used to find a relation between pawn advantage (P) and winning percentage (W).
  
  > W = 1 / (1+10^(-P/4))
  
  > **Comments:**
  > **username_0**: Amazing that only one pawn gives so much advantage.  
  > **username_1**: True, the 80% winning percentage for P=1 in case of Houdini is quite high. Especially when compared to other engines: according to the formula, for P=1, W=0.64. But, as you correctly mention in your question, the score has a different purpose and it is not necessarily related to the winning percentage.  
  > **username_2**: P=4 and W = 91% seems rather low  
  > **username_3**: Also check "Peter Österlund’s Texel Tuning" in Andrew Grant, Evaluation & Tuning in Chess Engines", which you can locate under [Andrew Grant](https://www.chessprogramming.org/Andrew_Grant) wiki entry were you will get his [work](https://pdfhost.io/v/Q~Yrnl8kj_Tuningpdf.pdf) on relating the engine evaluation to the winning percentage.  
  
  ---
  
  