Berger-Swiss Tournament System

Tournament Settings

Berger Rounds
Five initial rounds plus the selected extra rounds.

Pairing System

  • TPNs are assigned in initial descending rating order and never change. Equal ratings retain their input order.
  • After all exchanges, each Berger group is independently randomized. The resulting bottom Swiss group is placed in rating order, without randomization, and plays Swiss rounds from Round 1.
  • A withdrawal takes effect from the next unpaired round. During the initial phase, the affected Berger group and every subsequent Berger group normally form one Swiss field together with any existing Swiss field. Earlier unaffected Berger groups retain their schedules. Exception: if there is no existing Swiss field and only the last Berger group is affected, that group retains its remaining Berger schedule. Active players scheduled to face withdrawn players receive one-point pairing byes. Initial group numbers and memberships remain recorded permanently.
  • Swiss pairing order: descending score, descending WNT, then ascending TPN. Opponents are considered by smallest score difference first, then by color penalties and standings order. The normal search keeps the difference between White and Black game totals within two and avoids three consecutive games of the same color. Maximum score differences of zero, half a point, and one point are tried in that order. Color restrictions are relaxed if necessary. A further fallback permits larger score differences while still excluding rematches. Only if no complete pairing without rematches exists for any eligible bye recipient are rematches permitted.
  • Swiss colors: Both color assignments are considered. The program first prefers assignments that avoid extending a same-color run beyond two games, then considers color balance and alternation. If these considerations are equal, White goes to the player with fewer previous White games, or to the higher TPN if equal. Byes and forfeits add no played color.
  • A bye scores one tournament point and contributes no direct WNT. In Round 1, the lowest-rated player receives the bye if the field is odd. Later bye recipients must have the fewest previous byes among active players in the current Swiss field. A repeat bye is allowed only when every player in that field has already received at least one. Eligible recipients are considered from the bottom of the Swiss standings, subject to a complete pairing of the remaining players. Scheduled byes in a retained Berger group are an exception to Swiss bye selection and count toward subsequent Swiss bye eligibility. A higher-ranked eligible player may receive the bye if lower-ranked eligible recipients would require a rematch or a longer same-color run.
  • The current published round is not changed by a withdrawal. Enter its result normally, or select an explicit forfeit result if the game was not played. Forfeits award the selected points but add no direct WNT, played colors, or encounter.

About the Berger-Swiss System

Group construction and interchange

Positions used for interchange refer to the original rating order within each group, before randomization. After all exchanges, every Berger group is independently shuffled. The resulting bottom Swiss group is sorted in rating order without randomization. Permanent TPNs never change.

Withdrawals and early conversion to Swiss

Use Withdraw Player to announce a withdrawal after the currently published round. The current pairings and entered results remain unchanged. The player is excluded from the next unpaired round onward.

During the initial group phase, the affected Berger group and all subsequent Berger groups normally form one Swiss field together with any existing Swiss field. Earlier unaffected Berger groups retain their fixed schedules. For example, a withdrawal from Berger 2 converts Berger 2 and every later group, while leaving Berger 1 unchanged, unless the isolated-last-group exception below applies.

If there is no existing Swiss field and only the last Berger group is affected, that group retains its remaining Berger schedule. Active players scheduled to face withdrawn players receive one-point pairing byes, regardless of their previous bye counts. Games scheduled between two withdrawn players are omitted. These byes add no direct WNT or played color, but count toward later Swiss bye eligibility. If an earlier group subsequently converts, the last group joins the resulting Swiss field.

Group numbers refer to the established groups after interchange, not to current standings. Original group memberships are retained as historical records. A subsequent withdrawal from an earlier retained Berger group expands the Swiss field again.

Completed results, scores, opponent histories, color histories, and previous byes are carried forward. WNT continues to be recalculated. Withdrawn players remain in the standings, and their completed results are not annulled.

Withdrawals do not reset previous bye counts. If an odd Swiss field needs a bye, eligible recipients are the active players in that field with the fewest previous byes. A repeat bye is allowed only when every remaining Swiss player has already received at least one. If fewer than two active players remain for the next round, the tournament finishes after the current round is submitted.

Swiss pairing

Players are ordered by descending score, descending WNT, and ascending TPN. The highest remaining player is paired first. Within each search stage, candidate opponents are considered by smallest score difference, then color penalties, then standings order. Every choice must permit a complete pairing of the remaining field.

The search first excludes rematches and seeks a complete pairing without giving anyone a third consecutive game of the same color. At each color-run limit, eligible bye recipients are considered from the bottom of the Swiss standings. The first recipient who permits a complete pairing is selected before score differences and total color balance are optimized. Thus, a higher-ranked recipient is not selected merely to obtain smaller score differences or better total color balance.

For the selected recipient, the search first seeks pairings that keep each player's White and Black totals within two games. Maximum score differences of zero, half a point, one point, and unrestricted differences are tried in that order. If necessary, the total-balance restriction is relaxed and those score differences are tried again. If no eligible recipient permits a complete pairing at the current color-run limit, that limit is increased.

Rematches are permitted only after every no-rematch possibility has failed for every eligible bye recipient. In the rematch search, candidate opponents who have not met are preferred, followed by those with fewer previous meetings, then by score difference, color penalties, and standings order. This is a top-down preference, not a guarantee of the minimum total number of rematches. Rematches are marked in the pairing list.

Color allocation

Berger colors follow the fixed Berger table. For each prospective Swiss pairing, both color assignments are compared. Preference is given first to limiting runs of identical colors, then to reducing color-streak violations, maintaining total color balance, and alternating colors. If these considerations are equal, White goes to the player with fewer previous White games, or to the higher TPN if equal. Color counts and histories include the Berger phase. Longer color runs and total-balance exceptions may be permitted according to the Swiss search priorities described above.

Byes and forfeits add neither White nor Black games and do not interrupt a played-color streak. Unresolved postponed Berger games temporarily retain their scheduled colors as allocations.

Postponed Berger games

Select ‘p’ to mark a Berger game as postponed. In a submitted round, that game temporarily gives zero points to both players and contributes no direct WNT to either player. The scheduled Berger colors remain recorded as allocations.

Forfeits

Use 1-0 (Forfeit), 0-1 (Forfeit), or 0-0 (Double forfeit) when the scheduled game was not played. These results award the indicated tournament points but contribute no direct WNT and add no played colors or encounter. A forfeit win is not treated as a pairing bye by this custom system. No forfeit is assigned automatically when a player withdraws.

WNT

WNT = 100 × Σ [(Pᵢ / N) × (rᵢ + Pᵢ / (2N))] Pᵢ = opponent i's current tournament score rᵢ = result in the played game: 1, ½, or 0 N = number of submitted rounds The sum is over played games. Byes, forfeits, and unresolved postponed games are excluded.

WNT is recalculated from all submitted rounds. Repeated played encounters contribute separately. Results entered in an unsubmitted round are saved, but do not yet affect scores or tie-breaks. Permitted corrections to submitted Berger results immediately update scores and WNT.

WNT distinguishes players tied on tournament points by combining their results against opponents with those opponents' current tournament scores. Its formula contains both a result-weighted linear term and a quadratic term. A played loss contributes positively whenever the opponent has a positive tournament score, with a larger contribution against a higher-scoring opponent. Byes, forfeits, and unresolved postponed games contribute no direct WNT. A bye may lead to stronger subsequent opposition, but the system does not guarantee compensation for the missing played-game contribution.

Within equal-score groups, players with higher WNT are considered first. This gives priority to the combination of opposition scores and game results measured by WNT, rather than sorting directly by rating. Opponent selection remains subject to the complete-pairing search, color considerations, and rematch restrictions. Initial groups and permanent TPNs remain based on pre-tournament ratings.

Field sizes and byes

In an odd initial field, the lowest-rated player receives the first bye. Later bye recipients must have the fewest previous byes among active players in the current Swiss field. Among those eligible players, recipients are considered from the bottom of the current Swiss standings, requiring a complete pairing for everyone else. Repeat byes are allowed only when every player in that field has already received at least one. A Swiss field receives at most one pairing bye per round. Repeat Swiss byes are permitted only under the eligibility rule above. A retained Berger group may produce multiple scheduled byes in one round after multiple withdrawals. A higher-ranked eligible player may receive the bye if lower-ranked eligible recipients would require a rematch or a longer same-color run.

The setup round limit remains based on the original field size. It is a program policy, not a guarantee that all planned rounds remain possible after withdrawals.

The Berger-Swiss system was developed by Mats Winther in October 2026.

Sources

The embedded sample roster contains illustrative names and ratings, not a FIDE ranking snapshot. This is a custom Berger-Swiss implementation, including its withdrawal and forfeit policies, not a claim of FIDE approval.

Berger Pairings: Rounds 1–5

Withdraw Player

Current pairings and entered results are retained. No result or forfeit is assigned automatically. A confirmed withdrawal cannot be reversed in this interface.