Answers.Body: <p>The question is somewhat interesting, so I gathered some data to see if the player who first has White has an advantage.</p>
  <p>The Chess World Cup is an ideal tournament to test this hypothesis. This tournament consists entirely of two-game matches. After a 1-1 tie, two-game rapid and blitz matches are played, but I did not include those in the analysis. Below, I analyze the inaugural 2005 World Chess Cup.</p>
  <p>After scraping all 286 classical games from the <a href="https://cup2005.fide.com/results.asp-cat=3.htm" rel="noreferrer">FIDE website</a> and putting them in a useful format, I randomly split them into two groups. Half of the players had the White pieces in the first game, and half started with Black. A player can obtain 0, ½, 1, 1½, or 2 points (let's call it the player's <em>score</em>).</p>
  <p>A one-sided t-test for the mean showed no evidence for a difference between the average number of points obtained between the two groups (p = 0.402, df = 141). Furthermore, whereas the rating difference was highly significant in predicting a player's score (p = 0.000), who played White in the first game didn't matter (p = 0.735). (Technically, predicting the outcome of a match is a classification task, but OLS regression on the number of obtained points seems like a reasonable approximation.)</p>
  <p>There are two caveats. First, the games played at the World Cup are of a high level: for amateur games, the advantage may differ. Second, I have only considered classical games. So perhaps the results will not generalize to rapid and blitz tournaments, though I am unsure why they wouldn't.</p>
  
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Answers.CreationDate: 2021-07-22T06:35:17.220Z
Answers.Text: thank you for doing that analysis. "I randomly split them into two groups" Why did you do this? I don't see any need to do anything random.
Answers.UserDisplayName: Rosie F
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Answers.Text: I split the scores into two random groups to compare them with an independent two-sample t-test. Without this, the two groups would be dependent in a somewhat unusual way, as each match would appear twice in the data.
Answers.UserDisplayName: rpdejonge
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Answers.LastEditDate: 2021-07-21T12:14:00.450Z
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Body: <p>Many rapid and blitz tournaments use a multigame match system in the elimination rounds. What statistics are there on how frequently the player with White in the first game wins? Is there a statistical advantage to playing white in game 1 of a two-game match of chess?</p>
  <p>Assumptions:</p>
  <ul>
  <li>You play with the other color in the second game.</li>
  <li>The margin of victory does not matter. What counts is if you win, lose or draw the match.</li>
  </ul>
  
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2021-07-20T06:16:15.387Z
Comments.Text: Mhm,
  I wil prefer white Reason-
  1.Its up to you which color do you like.i like white therefore I prefer white and secondly you have an advantage over the player bcz white is very cool. Bruh!!
Comments.UserDisplayName: Atharv kumar
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Comments.CreationDate: 2021-07-20T08:21:53.320Z
Comments.Text: I try to answer the question you (possibly) *intended* to ask, abstracting from edits and maybe unfortunate formulation of details, from a strictly theoretical side. (I.e. feel free to accept an answer instead which takes the time to dig up practical stats.) I assume a common setting (all blitz tiebreaks in my town are done this way): You play a blitz match, first it's "win over two games", after a tie you blitz on and the first won game decides. Colors will be swapped on each match. By the independency and additivity of expectation value argument, it doesn't matter which is your first color *
Comments.UserDisplayName: Hauke Reddmann
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2021-07-20T09:54:18.513Z
Comments.Text: I doubt there are statistics on this effect on chess, but we have statistical analysis on the first go advantage in penalty shoot out. the data indicate that the team that shoots first has a 60% chance of winning the penalty shootout, which in this study is significant at less than a 2% level. Even more interesting is the finding that the team shooting second has a consistently lower shooting percentage and consistently longer odds of leading the shootout after each round. So there exists a significant and persistent advantage to the team the shoots first in a penalty kick shootout. From the p
Comments.UserDisplayName: jf328
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2021-07-21T07:33:05.337Z
Comments.Text: I think we can't give an answer that tells the OP what they need to know. The best I can do is suggest other matters the OP might want to consider.
  If game 1 is decisive, both of you know that game 1's loser needs to win game 2 in order to avoid losing the match, whereas game 1's winner need only avoid losing game 2 in order to win the match. Therefore, what colour you want in game 1 depends on how you rate your ability, as White (resp. Black), to win (resp. avoid loss). And also, if you know anything about your opponent's play, how you rate their ability to do the same.
Comments.UserDisplayName: Rosie F
Tags: <statistics>
Title: When playing a two-game match, is it better to have white in the first game?
ThreadText: # When playing a two-game match, is it better to have white in the first game?
  
  (Asked by: username_0 on 2021-07-19)
  
  Many rapid and blitz tournaments use a multigame match system in the elimination rounds. What statistics are there on how frequently the player with White in the first game wins? Is there a statistical advantage to playing white in game 1 of a two-game match of chess?
  
  Assumptions:
  
  * You play with the other color in the second game.
  * The margin of victory does not matter. What counts is if you win, lose or draw the match.
  
  **Tags:** statistics
  
  > **Comments:**
  > **username_1**: Mhm, I wil prefer white Reason- 1.Its up to you which color do you like.i like white therefore I prefer white and secondly you have an advantage over the player bcz white is very cool. Bruh!!  
  > **username_2**: I try to answer the question you (possibly) *intended* to ask, abstracting from edits and maybe unfortunate formulation of details, from a strictly theoretical side. (I.e. feel free to accept an answer instead which takes the time to dig up practical stats.) I assume a common setting (all blitz tiebreaks in my town are done this way): You play a blitz match, first it's "win over two games", after a tie you blitz on and the first won game decides. Colors will be swapped on each match. By the independency and additivity of expectation value argument, it doesn't matter which is your first color *  
  > **username_3**: I doubt there are statistics on this effect on chess, but we have statistical analysis on the first go advantage in penalty shoot out. the data indicate that the team that shoots first has a 60% chance of winning the penalty shootout, which in this study is significant at less than a 2% level. Even more interesting is the finding that the team shooting second has a consistently lower shooting percentage and consistently longer odds of leading the shootout after each round. So there exists a significant and persistent advantage to the team the shoots first in a penalty kick shootout. From the p  
  > **username_4**: I think we can't give an answer that tells the OP what they need to know. The best I can do is suggest other matters the OP might want to consider. If game 1 is decisive, both of you know that game 1's loser needs to win game 2 in order to avoid losing the match, whereas game 1's winner need only avoid losing game 2 in order to win the match. Therefore, what colour you want in game 1 depends on how you rate your ability, as White (resp. Black), to win (resp. avoid loss). And also, if you know anything about your opponent's play, how you rate their ability to do the same.  
  
  ---
  
  ## 1 answers
  
  ### Answer by username_5 on 2021-07-21. Score: 8
  
  The question is somewhat interesting, so I gathered some data to see if the player who first has White has an advantage.
  
  The Chess World Cup is an ideal tournament to test this hypothesis. This tournament consists entirely of two-game matches. After a 1-1 tie, two-game rapid and blitz matches are played, but I did not include those in the analysis. Below, I analyze the inaugural 2005 World Chess Cup.
  
  After scraping all 286 classical games from the [FIDE website](https://cup2005.fide.com/results.asp-cat=3.htm) and putting them in a useful format, I randomly split them into two groups. Half of the players had the White pieces in the first game, and half started with Black. A player can obtain 0, ½, 1, 1½, or 2 points (let's call it the player's *score*).
  
  A one-sided t-test for the mean showed no evidence for a difference between the average number of points obtained between the two groups (p = 0.402, df = 141). Furthermore, whereas the rating difference was highly significant in predicting a player's score (p = 0.000), who played White in the first game didn't matter (p = 0.735). (Technically, predicting the outcome of a match is a classification task, but OLS regression on the number of obtained points seems like a reasonable approximation.)
  
  There are two caveats. First, the games played at the World Cup are of a high level: for amateur games, the advantage may differ. Second, I have only considered classical games. So perhaps the results will not generalize to rapid and blitz tournaments, though I am unsure why they wouldn't.
  
  > **Comments:**
  > **username_4**: thank you for doing that analysis. "I randomly split them into two groups" Why did you do this? I don't see any need to do anything random.  
  > **username_5**: I split the scores into two random groups to compare them with an independent two-sample t-test. Without this, the two groups would be dependent in a somewhat unusual way, as each match would appear twice in the data.  
  
  ---
  
  