user28415: 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.


user28429: 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 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.

28415: <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>
 28429: <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>
