Buchholz Cut 1 (BH-1) tiebreak in Swiss chess
Buchholz Cut 1
Definition
Buchholz Cut 1 (often written as BH-1 or “Buchholz -1”) is a widely used chess tiebreak system for Swiss-system events. It is a variant of the classic Buchholz score that sums the final scores of a player’s opponents—but with the single lowest opponent score removed (“cut”). This reduces the distortion that can occur if one of your opponents scores very poorly or withdraws.
How it is used in chess tournaments
In Swiss tournaments, many players can finish with the same number of points. Organizers specify a tiebreak order in the regulations, and Buchholz Cut 1 is frequently near the top of that list. A typical order might be:
- Direct encounter (head-to-head)
- Buchholz Cut 1 (BH-1)
- Total Buchholz (BH)
- Sonneborn-Berger or number of wins
- Playoff games if still tied
Standings software (e.g., Swiss pairing programs) calculates BH-1 automatically. Arbiters include it in the official crosstable to rank tied scores without requiring additional games, saving time and keeping the event on schedule.
Why “Cut 1” matters
By removing your weakest opponent’s final score, Buchholz Cut 1 provides a more stable measure of the average strength of your opposition. This mitigates the “bad luck” of being paired against an opponent who has a rough event, a bye, or an early withdrawal. Compared to straight Buchholz, BH-1 is less volatile and often considered fairer for large, mixed-strength fields.
How to calculate Buchholz Cut 1
- List each opponent you faced and their final tournament score.
- Sum those opponent scores.
- Remove the single lowest opponent score (the “cut”).
- The result is your Buchholz Cut 1 tiebreak.
Notes and common conventions:
- Unplayed games by an opponent are commonly treated as draws (0.5) for Buchholz-type systems, but always follow the event’s published regulations.
- If you received a full-point bye or forfeit win, events may specify a fixed value (often 0 or 0.5) for that “virtual opponent”; again, check the tournament rules.
- “Cut 2” (BH-2) removes the two lowest opponent scores; “Median-Buchholz” removes one highest and one lowest.
Worked example (5-round Swiss)
Player A finishes with 4/5. Their opponents’ final scores are:
- Round 1 vs. Opponent X: 4.0/5
- Round 2 vs. Opponent Y: 3.5/5
- Round 3 vs. Opponent Z: 3.0/5
- Round 4 vs. Opponent W: 2.0/5
- Round 5 vs. Opponent V: 1.0/5
Total Buchholz = 4.0 + 3.5 + 3.0 + 2.0 + 1.0 = 13.5
Buchholz Cut 1 = 13.5 minus the lowest (1.0) = 12.5
Suppose Player B also scores 4/5, with opponent scores 4.0, 3.0, 3.0, 2.5, 2.0. Their Total Buchholz is 14.5; BH-1 = 14.5 − 2.0 = 12.5. If direct encounter doesn’t separate A and B, they remain tied on BH-1 and the next tiebreak (e.g., Total Buchholz or Sonneborn-Berger) is applied.
Strategic and practical significance
- Pairing luck: In a large Swiss, early pairings can vary widely. BH-1 smooths out extreme results from one very weak or struggling opponent.
- Root for your past opponents: Once your game ends, your Buchholz-based tiebreaks improve when your previous opponents continue to score well.
- Fairness vs. simplicity: BH-1 is easy to explain, quick to compute, and fairer than raw Buchholz in most fields.
Comparison to other tiebreaks
- Total Buchholz (BH): Sums all opponent scores with no cut; more sensitive to a single outlier.
- Median-Buchholz: Cuts the highest and lowest opponent scores; even more robust, sometimes used for very large opens.
- Sonneborn-Berger: Weights opponents by the result you scored against them; common in round-robins but also used in Swiss events.
- Head-to-head: If tied players met, this can rank ahead of Buchholz-type methods.
- Playoff: Rapid/blitz/Armageddon games are used in elite or title-deciding events when mathematical tiebreaks aren’t desired.
Historical note
The Buchholz system is named after Bruno Buchholz and has been used in chess since the early 20th century. The “Cut 1” refinement gained traction as Swiss tournaments grew in size and diversity, offering a simple statistical dampening of one anomalously low opponent score.
Arbiter and organizer tips
- Publish the full tiebreak order in advance and keep it consistent across sections.
- State clearly how byes, forfeits, and unplayed games are scored for Buchholz/BH-1.
- Use reliable pairing software and verify BH-1 totals before awarding prizes.
- In junior or mixed-strength fields, consider Median-Buchholz to reduce volatility further.
Common misconceptions
- “Buchholz is pure luck.” In reality, BH-1 rewards performance against opponents who themselves do well, a reasonable proxy for difficulty of schedule.
- “A late ‘Fish’ ruins my tie-breaks.” BH-1 mitigates a single weak opponent; consistent strength of your other opponents matters more. See: Fish.
Fun facts and anecdotes
- Elite opens sometimes see several players tied for first; BH-1 has decided prize order without extra games, avoiding time-consuming playoffs late at night.
- Players occasionally track “tiebreak rooting interests,” following how their earlier opponents are scoring in the final round to estimate their BH-1.
Related terms
Quick reference
- Name: Buchholz Cut 1 (BH-1, Buchholz -1)
- Core idea: Sum of opponents’ final scores minus the lowest one
- Best for: Ranking ties in Swiss events with minimal distortion
- Alternatives: Total Buchholz, Median-Buchholz, Sonneborn-Berger