Tie-breaks: Chess terminology

Tie-breaks

Definition

"Tie-breaks" are methods used to rank players or teams that finish with the same score. In chess this takes two main forms: mathematical tie-breaks (formulas applied to final standings) and playoff tie-breaks (extra games at faster time controls to produce a winner).

Where and how tie-breaks are used

• Swiss-system tournaments: Most common use of mathematical tie-breaks (e.g., Buchholz, Sonneborn–Berger) to order players with equal points.
• Round-robins: Either formulas (e.g., head-to-head, Sonneborn–Berger, most wins) or playoff matches if regulations specify.
• Knockouts (e.g., FIDE World Cup): Playoff tie-breaks with rapid/blitz/Armageddon games if classical mini-matches are drawn.
• World Championship matches: If tied after classical games, rapid (and potentially blitz/Armageddon) playoffs decide the title.
• Team events (Olympiads, leagues): Team-specific tie-breaks (e.g., match points, game points, team Sonneborn–Berger).

Common mathematical tie-break systems

• Direct encounter (head-to-head): Among tied players, the one who scored better in their games against each other ranks higher. Most intuitive in small ties; tricky in large circular ties.
• Sonneborn–Berger (SB): Sum of the final scores of opponents you beat, plus half the final scores of opponents you drew. Rewards wins against strong final scorers. Often used in round-robins; also as a secondary tie-break in Swiss events. See also Sonneborn–Berger.
• Buchholz: Sum of your opponents' final scores. A proxy for the strength of your opposition. Variants include Buchholz Cut-1 (drop your lowest opponent score) or Cut-2 to reduce pairing luck. In some federations, "Solkoff" is a Buchholz variant. See also Buchholz.
• Median-Buchholz (Modified Median): Drop the highest and lowest opponent scores before summing. Common in US Chess Swiss events to smooth out extremes.
• Cumulative (Progressive): Add your running score after each round (after R1, R1+R2, …). Rewards early wins and sustained performance.
• Most wins: The player with more decisive games ranks higher. Encourages fighting chess; famously used at the 2013 Candidates.
• Koya system: Counts points scored against the top half of the field. Emphasizes results versus stronger opposition.
• Rating performance/TPR: Ranks tied players by calculated performance rating; typically a deeper tiebreak in regulations.
• Team event variants:
  • Match points (win=2, draw=1) as the primary score, then tie-breaks like team SB or game points.
  • Game points (sum of individual board results) as a tie-break or, in some events, as the primary score.

Playoff formats (extra games)

When an outright winner is required, events may use playoffs instead of (or in addition to) formulas. Time controls vary by regulation but typically proceed from faster to faster:

• Rapid mini-matches (e.g., 25+10 or 15+10)
• Blitz mini-matches (e.g., 5+3 or 3+2) if still tied
• Armageddon: One game where White gets more time but must win; Black has draw odds. Procedures for color selection vary (coin toss, higher seed’s choice, or bidding systems). See Armageddon, Rapid, and Blitz.

Examples of events that regularly use playoffs: FIDE World Cup, World Rapid/Blitz, some national championships, and World Championship matches if tied after the classical portion.

Strategic significance

• Swiss events: Your opponents’ final results affect Buchholz/SB. Beating players who go on to score highly is beneficial; an early loss to someone who collapses can hurt.
• Round-robins: If "most wins" is a tiebreak, players may press harder with White and avoid quick draws. If head-to-head is primary, the direct clash(s) among contenders are paramount.
• Playoff readiness: Strong rapid/blitz skills become critical in modern elite events since many titles are decided in tie-breaks.
• Last-round decisions: Understanding your tiebreak status can guide whether to play for a win or accept a draw.
• Team events: Lineup strategy and board order can be influenced by which team tie-break is primary (match points vs game points).

Examples

Example 1: Sonneborn–Berger in a mini round-robin
Four players A, B, C, D play each other once. Final scores: A=2.0, C=2.0, B=1.0, D=1.0. Results among the leaders:

• A beat B and D; lost to C. SB(A) = score(B) + score(D) = 1.0 + 1.0 = 2.0.
• C beat A and D; lost to B. SB(C) = score(A) + score(D) = 2.0 + 1.0 = 3.0.
• Thus C ranks ahead of A on SB, despite equal points.

Example 2: Buchholz and Median-Buchholz in a Swiss
Player X scores 6/9. Their opponents finish with: 7, 6.5, 6, 5.5, 5, 5, 4.5, 4, 3 points.

• Buchholz(X) = 7 + 6.5 + 6 + 5.5 + 5 + 5 + 4.5 + 4 + 3 = 46.5.
• Buchholz Cut-1(X) drops the lowest (3) → 43.5; Cut-2 drops 3 and 4 → 39.5.
• Median-Buchholz would typically drop both the highest (7) and lowest (3), giving 36.5.
• If Player Y also scored 6/9 but has Buchholz 45.0, X ranks above Y on tie-break.

Example 3: Cumulative (Progressive Score)
Suppose your round-by-round scores are: 1.0, 2.0, 2.5, 3.0, 3.5, 4.0, 5.0, 5.5, 6.0 (final). Cumulative = 1.0 + 2.0 + 2.5 + 3.0 + 3.5 + 4.0 + 5.0 + 5.5 + 6.0 = 32.5. A rival who started slowly (e.g., 0.5 after two rounds) but finished on 6.0 will likely have a lower cumulative and thus rank behind you on this tie-break.

Example 4: Famous tie-break decisions

• World Championship 2016, Carlsen vs. Karjakin (New York): Tied 6–6 in classical; Carlsen won the rapid tie-break 3–1, finishing with the memorable 50. Qh6+ Kg8 51. Qg7#.
• World Championship 2018, Carlsen vs. Caruana (London): All 12 classical games drawn; Carlsen won the rapid tie-break 3–0.
• 2013 Candidates (London): Carlsen and Kramnik tied for first; the title shot went to Carlsen on the "most wins" tie-break, with no playoff games.
• 2019 FIDE World Cup (Khanty-Mansiysk): Radjabov defeated Ding Liren in playoffs after their classical games were drawn.

Practical tips for players

• Read the event regulations: Know the exact tie-break order and whether playoffs are used.
• In Swiss events, resist "safe early draws": your Buchholz/SB often improves if you keep facing (and beating) strong opponents.
• Track tie-breaks before the last round: If you trail on tie-breaks, a win may be essential; if you lead, a draw might suffice.
• Prepare for faster time controls: Practice rapid and blitz; study typical endgames under time pressure; have an Armageddon color preference strategy.
• Team captains: Align board orders and match strategy with the primary tie-break (match points vs game points).

Interesting facts and anecdotes

• Tie-break formulas like Sonneborn–Berger and Buchholz arose to reduce the need for lengthy playoff matches in congested schedules—especially important in large Swiss events.
• Modern elite chess often crowns champions via playoff tie-breaks. Carlsen won the World Championship twice this way (2016, 2018).
• Armageddon formats are debated: they guarantee a decision but raise questions about fairness and color advantage. Some events experiment with bidding systems to balance draw odds.
• In some events (e.g., 2013 Candidates), "most wins" can incentivize risk-taking throughout the tournament, shaping overall strategy and opening choices.
• Team tie-breaks can lead to suspense after the final round, as podium places hinge on other teams’ ongoing results that affect SB and game points.