Buchholz Cut 2 (BH-2): Swiss tiebreak
Buchholz Cut 2
Definition
Buchholz Cut 2 (often written as BH-2) is a Swiss-system chess tournament tiebreak that sums the final scores of a player’s opponents, excluding the two lowest-scoring opponents. It’s a refinement of the classic Buchholz system designed to reduce the impact of one or two especially weak results among your opposition on your tiebreak value.
How It’s Used in Chess
In many Swiss tournaments—both OTB and online—players often finish on the same total points. Organizers then apply a predefined Tiebreak system order such as:
- Total points
- Buchholz Cut 2 (BH-2)
- Buchholz Cut 1 (BH-1)
- Median-Buchholz or Sonneborn-Berger (depending on event policy)
Using Buchholz Cut 2 helps compare how tough each player’s field of opponents was without over-penalizing them for having one or two opponents who scored very poorly (perhaps due to withdrawals or a last-round collapse). It’s widely recognized by FIDE-rated events and is available in all major pairing programs. You’ll see it in weekend opens, scholastic events, and large festivals that use the Swiss system.
Calculation (Step by Step)
To compute a player’s Buchholz Cut 2:
- List all opponents the player actually faced.
- Record each opponent’s final score at the end of the tournament.
- Sort those opponent scores from highest to lowest (or vice versa).
- Exclude the two lowest opponent scores (the “cut 2”).
- Sum the remaining opponent scores. The result is the player’s BH-2.
Notes:
- Event regulations specify how to treat unplayed rounds (byes/forfeits). Organizers usually apply standard FIDE/ratings-server rules or software defaults. When in doubt, consult the event’s regulations.
- BH-2 differs from “Median-Buchholz,” which removes highest and lowest scores symmetrically. BH-2 only removes the two lowest.
Worked Example
Imagine a 7-round Swiss where Player X’s opponents finish with these final scores: 5.5, 4.5, 4.0, 3.0, 3.0, 2.0, 1.5.
- Standard Buchholz (no cuts): 5.5 + 4.5 + 4.0 + 3.0 + 3.0 + 2.0 + 1.5 = 23.5
- Buchholz Cut 2: remove the two lowest scores (2.0 and 1.5), then sum: 5.5 + 4.5 + 4.0 + 3.0 + 3.0 = 20.0
This BH-2 value better reflects Player X’s typical strength of opposition by trimming the two weakest results among their opponents.
Strategic and Practical Significance
- Fairer field-strength measure: BH-2 dampens distortions caused by opponents who underperform or withdraw.
- Tiebreak awareness: In tight races, players and coaches track BH-2 to assess prize prospects when a final-round draw offers a safe finish versus chasing a win for clear first.
- Comparison with other systems:
- Buchholz (no cut): Most sensitive to all opponents’ scores, including outliers.
- Buchholz Cut 1: Excludes the single lowest; moderate smoothing.
- Median-Buchholz: Excludes highest and lowest equally, focusing on the “middle” of your opposition.
- Sonneborn-Berger: Weights results by the opponents you beat/drew; more common in round robins, but used in some Swiss events too.
Historical Context
The Buchholz system is named after Bruno Buchholz, a German chess organizer who popularized the approach as a strength-of-schedule metric in Swiss tournaments. “Cut” variants like BH-1 and BH-2 emerged to address practical issues—late withdrawals, uneven pairings, and noise at the tails of the opposition list—providing more stable and perceived-fairer rankings in large open events.
Common Use-Cases and Organizer Tips
- Large opens and scholastic events: BH-2 is frequently placed early in the tiebreak order to reduce pairing noise.
- Publish the order: Clearly announce whether tiebreaks are Buchholz, BH-1, BH-2, Median-Buchholz, etc., to avoid confusion at prize-giving.
- Consistent software settings: Ensure your pairing software’s Buchholz parameters (handling byes/forfeits) match your regulations.
Misconceptions
- “BH-2 rewards luck.” In reality, eliminating the two lowest opponent scores reduces randomness and makes the metric more robust.
- “It’s the same as Median-Buchholz.” No—Median-Buchholz trims both the top and bottom equally; BH-2 cuts only from the bottom.
- “It ignores who you beat.” Correct—like all Buchholz variants, BH-2 measures the overall strength of your opposition, not which specific results you achieved against them.
Interesting Facts and Anecdotes
- Close podiums in Swiss opens are often decided by a fraction of a BH-2 point, especially when the leaders faced mostly the same pack but differed on two weaker opponents.
- Some federations prefer BH-2 over straight Buchholz in youth events because a single early pairing with a newcomer or a withdrawing player won’t unduly tank a child’s tiebreaks.
- On many platforms, BH-2 is shown alongside raw Buchholz and Median-Buchholz so players can cross-check fairness at a glance.
Related Terms and See Also
Quick Summary
Buchholz Cut 2 = sum of your opponents’ final scores, excluding the two lowest. It’s a widely used, fairer Swiss tiebreak that softens outliers, helping organizers rank tied players by the typical strength of their opposition.