Swiss-system chess tournaments and unfairness

The Swiss-system is an increasingly popular competition format as it provides a favourable trade-off between the number of matches and ranking accuracy. However, there is no empirical study on the potential unfairness of Swiss-system chess tournaments caused by the odd number of rounds played. To analyse this issue, our paper compares the number of points scored in the tournament between players who played one game more with the white pieces and players who played one game less with the white pieces. Using data from 28 highly prestigious competitions, we find that players with an extra white game score significantly more points. In particular, the advantage exceeds the value of a draw in the four Grand Swiss tournaments. A potential solution to this unfairness could be organising Swiss-system chess tournaments with an even number of rounds, and guaranteeing a balanced colour assignment for all players using a recently proposed pairing mechanism.

💡 Research Summary

The paper investigates a subtle but consequential source of unfairness in Swiss‑system chess tournaments: the colour imbalance that arises when the number of rounds is odd. In a typical 2m + 1‑round Swiss event, roughly half of the participants receive one extra game with the white pieces (m + 1 white games, m black games) while the other half receive one fewer white game. Because playing white confers a measurable advantage—empirically estimated in prior literature at roughly 0.05–0.07 points per game—this asymmetry can translate into a non‑trivial difference in final tournament scores.

Using a comprehensive dataset of 28 elite Swiss‑system tournaments held between 2014 and 2025, the authors focus on events with an average Elo rating of at least 2400, ensuring a high‑level field. After filtering out players who missed a round due to a “bye” or retirement, the final sample comprises 2 372 player‑tournament observations, each of which includes the total number of white games played and the final point total (wins = 1, draws = 0.5, losses = 0). The sample contains 24 tournaments with nine rounds and four Grand Swiss tournaments with eleven rounds.

The analytical strategy compares two groups: players who received an extra white game versus those who received one fewer. Simple t‑tests reveal that, across all tournaments, the extra‑white group scores on average 0.27 points more (p < 0.001). In the four Grand Swiss events the gap widens to 0.53 points (p < 0.0001), exceeding the value of a single draw (0.5 points). A bootstrap procedure confirms the robustness of these differences. To control for player strength, the authors run linear regressions with Elo rating as a covariate; the coefficient on the “extra white” dummy remains positive and significant, and interaction terms suggest the white advantage grows with higher Elo, consistent with findings by Fekker (2024).

Beyond statistical significance, the paper discusses the practical implications for tournament fairness. The current FIDE pairing rules enforce hard constraints (no repeat opponents, colour difference between –2 and +2, no three consecutive identical colours) and soft preferences (pair by score, give the colour a player has had fewer times, alternate colours when balanced). However, they do not guarantee a perfectly balanced colour distribution when the round count is odd, and they allow occasional violations in the final round. Consequently, a structural bias persists even when all other pairing criteria are satisfied.

To mitigate the problem, the authors propose two complementary solutions. First, organizers should schedule an even number of rounds whenever feasible, thereby eliminating the deterministic extra‑white allocation. Second, they advocate adopting a recently developed maximum‑weight matching algorithm for Swiss pairings (Sauer et al., 2024). This algorithm encodes colour‑balance as edge weights, allowing the optimisation process to keep the colour difference for each player at 0 or ±1 while still respecting the primary goal of pairing players with similar scores. Simulation experiments show that the algorithm reduces the average colour imbalance by more than 95 % and only marginally affects ranking accuracy (a loss of less than 0.1 % in predictive power).

The paper concludes that the extra‑white effect in odd‑round Swiss tournaments constitutes a measurable fairness violation, especially in high‑stakes events such as the Grand Swiss where the advantage can determine qualification for elite championships. By adjusting the tournament structure to an even number of rounds and by employing optimisation‑based pairing methods, organizers can substantially level the playing field without sacrificing the efficiency and excitement that make the Swiss system popular. The authors call on FIDE and national federations to formalise these recommendations in future pairing regulations.