Minimum Number of Consecutive Rounds With Same Colour in a Chess Tournament

In a chess match, one player plays with white pieces while the other plays with black. It is generally known that players playing with the white pieces have a slight advantage [1]. To keep it fair, a tournament tries to have each player play an equal number of games with the white pieces as with the black pieces. However, in a single round-robin, this is not achievable. Each player would have some rounds where they play with white and some rounds with black. Further, they might have consecutive rounds where they play with the same colour. This creates a psychological challenge, particularly if a player has to play with black pieces in consecutive rounds late in a round-robin tournament. This article introduces a new metric that counts the total pairs of rounds when any player plays with the same color. Then, a construction of how each player should play with another player in every round of a single or double round-robin tournament that minimizes this sum is provided. This will help to ensure maximum fairness to the players in round-robin chess tournaments.