The event is over, two players are level on points and there is one trophy. What settles it is a tie-break - and it turns out there are about twenty of them, they carry different names in the FIDE handbook and in American practice, and the order of application is set by your own regulations. This page collects the whole set: what each measure actually measures, how it is computed, which system it belongs to, what to put in your regulations, and how real events do it.
Which is why a search for one of them keeps returning the other. Worth separating up front.
A number computed from the games already played, used to order players on equal points. In the crosstable it sits in the columns beside the score: BH, SB, TB1, TB2. That is what this page is about.
A match at a faster time control used to separate a tie in a decisive event: rapid, then blitz, then in the limit an Armageddon. Used where a title cannot be handed over on arithmetic.
Both live in the same regulations and often work together: the scores decide who even reaches the play-off, and then the games are played. That is exactly how the world rapid champion was decided in Warsaw - and it produced one of the loudest arguments about tie-breaks in recent memory, covered below.
In an event with a fixed number of rounds, players inevitably arrive at the same totals. The shorter the event and the more even the field, the more often: in a five-round club evening three players on the top line is entirely normal. If there is one prize, one qualifying spot or one medal, somebody has to be placed above the others - and it cannot be at the arbiter's discretion.
A tie-break is a rule announced in advance that settles the argument arithmetically. Every measure shares one principle: they compare players only within a group on equal points. No coefficient ever lifts a player above someone who scored more.
Grouped by meaning rather than alphabetically, because that is how you actually choose one. Article numbers follow the FIDE Play-Off and Tie-Break Regulations in the edition effective from 1 March 2026. The list is not exhaustive - the narrow team-event measures are left out.
The most direct principle of all: if the players contesting the place met each other, their own game settles it.
art. 6
points scored in the games between the tied players
You look at the result of the game between the players sharing the place. If several are tied and all of them met, those games form a mini-table of their own. Games not played at the board are excluded by default.
Where it applies: Universal. Always applicable in a round-robin; in a Swiss only if the tied players actually met.
In a Swiss everybody gets a different draw: one player is handed a brutal path, another an easy one. This group measures that path through the opponents' final results.
art. 8.1
BH = sum of the final scores of all opponents
Add up the final score of everyone the player met. The better the opposition did, the higher the number.
Where it applies: The Swiss system. In round-robins the regulations explicitly forbid it: everyone faces the same field, so the values coincide and separate nothing.
Full guide to Buchholzart. 8.2
AOB = the mean Buchholz of the player's opponents
A second-order measure: not how strong your opponents were, but how strong theirs were. Rarely used, and usually deep down the list.
Where it applies: Swiss events where the earlier tie-breaks came out level.
art. 10.1
ARO = sum of opponents' ratings ÷ number of games
Looks not at what the opponents scored but at the rating they carried before the event started. The value is rounded to a whole number.
Where it applies: Events where everybody has an official rating. This is the measure that decided the 2022 European Championship.
art. 10.2
TPR = average rating of opponents + rating difference from the score percentage
Shows the rating level the player effectively performed at in this event.
Where it applies: Rated events, and board prizes in team competitions.
Here the opponents' scores are weighted by your result against them: beating the leader counts for more than beating the tail-ender.
art. 9.1
SB = Σ (opponent's final score × points scored against them)
Written out, that is the sum of the scores of the opponents you beat plus half the scores of those you drew with. Opponents who beat you contribute nothing.
Where it applies: The primary tie-break of the round-robin. In a Swiss it serves as a secondary one.
Calculator and full explanationart. 9.2
KS = points scored against opponents who finished on 50% or more
Only the games against the solid half of the field are counted. It answers how the player did against equals and betters, ignoring points harvested from the bottom boards.
Where it applies: Round-robins. For a Swiss it has to be written into the regulations explicitly.
This group ignores the opposition and looks at your own tournament: when the points came, in which colour, and at what cost.
art. 7.5
PS = sum of the running totals after every round
After each round you note the running score, then add all those numbers up. Results of 1, ½, 1 give running totals of 1, 1½ and 2½, so the measure is 5. It favours the player who led from the start over the one who caught up at the end.
Where it applies: Swiss events, and very common in junior and scholastic chess.
art. 7.1
WIN = the number of rounds scored as a win
Counts every winning result, including those awarded without a game. A narrower variant, WON, counts only wins at the board.
Where it applies: Almost any format. Players understand it instantly and it rewards playing for a win.
art. 7.4
BWG = games won with the black pieces at the board
Recognises that winning with Black is objectively harder, so those wins weigh more. A related measure, BPG, simply counts games played with Black.
Where it applies: A follow-on when the total number of wins also came out level.
art. 7.7
STD = rounds where the player outscored the opponent, plus half the drawn rounds
New in the 2026 edition. It maps the classical scoring scale onto events that award points differently, such as three for a win and one for a draw.
Where it applies: Competitions with alternative scoring systems.
Last resorts. You hope never to reach them, but they still have to be in the regulations.
art. 7.8
TPN = the player's number from the initial draw
Formally arbitrary, but known in advance and beyond dispute. Added in the 2026 edition alongside the other new measures so that events reach a drawing of lots less often.
Where it applies: The tail of the list.
art. 4.2
random selection
Used only once the list of tie-breaks is exhausted. The regulations may instead state that the places simply remain shared.
Where it applies: The last line of the sequence in your regulations.
This is where organizers go wrong most often. A line like «Buchholz Cut-1» reads like a coefficient in its own right, but in the current edition it is a base measure plus a modifier from a separate article. The same Cut-1 can be attached to the average opponent rating or to Sonneborn-Berger just as easily.
The weakest opponent's contribution is removed from the sum. This kills the luck of the draw, where one player happens to be paired against someone who withdrew after round one.
The same idea with the two weakest contributions removed. Used in long events, where the spread in opponent strength is wider.
Both ends of the distribution are trimmed. This is the principle behind the American Median and Modified Median tie-breaks, though the US Chess versions have their own rules about which end to trim.
A deeper version of the same principle for long events.
Applies to the Koya system: the 50 percent threshold can be moved in steps, narrowing or widening the set of opponents that count.
The Buchholz variants were separate items in the edition up to September 2023. That is where the shorthand BH-C1 and AROC 1 in regulations comes from - everyone still understands it, but formally it now denotes a base measure combined with a modifier.
A bye, a missed round, an opponent who does not show up - these are games that never happened, and yet the tie-break still has to be computed. The naive answer of putting a zero there wipes out the score of a player who did nothing wrong, so the regulations introduce a dummy opponent: the missed round counts as a game against a fictitious player whose score is capped.
The regulations also separate the reasons: a pairing-allocated bye, a win because the opponent failed to appear, a voluntarily requested half-point bye and a forfeit loss are all handled differently. A voluntarily unplayed final round counts as a draw.
And the practical detail that catches people out: when the worst results are cut, voluntarily unplayed rounds are removed first, even if their contribution is not the lowest. Taking a bye in the closing rounds is therefore less harmless than it looks - the tie-break drops more than expected. The full arithmetic of the capped dummy opponent, with worked numbers, is on the Buchholz page.
A widespread belief holds that FIDE has a default order. It does not: the regulations list the tie-breaks but do not arrange them into a mandatory chain. The list for a given event is written and published by the organizer, and it has to be published before round one. So what follows is not «the rule» but three real templates worth copying.
World Rapid and Blitz Championship regulations
This is not a «default rule» - it is one specific event's regulations. But it is the most convenient thing to copy when writing your own.
US Chess recommended tie-break order
American terminology differs from FIDE's for the same arithmetic: Solkoff is plain Buchholz, and Modified Median is Buchholz with an end trimmed - which end depends on whether the player has a plus, minus or even score.
FIDE Handbook C.07, arts. 6, 9.1, 9.2
Buchholz is absent and cannot be there: in a round-robin everybody faces the same field, which is why the regulations rule it out outright.
Note how far apart the first two are: FIDE events lead with Buchholz Cut-1, American events lead with Modified Median, and the same crosstable can therefore produce different placings depending on which tradition your regulations follow. Neither is wrong - the document that decides is the regulations of your own event, which is precisely why they have to be written down beforehand.
American tournament practice grew up with its own vocabulary, and the overlap with FIDE terminology is not obvious from the names. Three places where people get caught:
Both are the plain sum of the final scores of all your opponents. Same formula, different name, different side of the Atlantic. If a US crosstable shows a Solkoff column and a European one shows BH, they are the same quantity.
The plain Median, historically the Harkness system, drops both the highest and the lowest opponent score. The Modified Median drops depending on how the player finished: a plus score drops the lowest opponent, a minus score drops the highest, and an even score drops both. That conditional behaviour has no direct FIDE analogue.
What US Chess calls the Cumulative tie-break is the sum of the running totals after each round, which FIDE lists as the progressive score. It is the standard fourth measure in the American recommended order and a common one in junior events everywhere.
If your event runs online, or the results are published on a service, the order is set by the platform rather than by you.
Buchholz Cut-1 → Buchholz → Sonneborn-Berger → direct encounter → number of wins → wins with Black → average opponent rating Cut-1 → starting rating
The longest chain among the online platforms: it essentially never reaches a drawing of lots.
Sonneborn-Berger
If the organizer disables tie-breaks, both players simply advance.
Sonneborn-Berger
One measure instead of a sequence: a single number and a transparent algorithm, with no regulation settings to configure.
columns TB1, TB2, TB3 - the organizer decides what goes in them
What each column actually contains is always printed in the header of that tournament's page. Two events rarely put the same thing in TB1.
The best argument for thinking about the order in advance: in these events it cost somebody the gold.
Four players finished on 9½ after 13 rounds: Abdusattorov, Nepomniachtchi, Carlsen and Caruana. Only the top two on Buchholz Cut-1 went to the play-off: 103.0 for Abdusattorov and 100.5 for Nepomniachtchi against 97.0 for Carlsen and 95.0 for Caruana. Abdusattorov won the play-off and took the title at 17, while Carlsen publicly called the rule a poor one.
Bluebaum and Sargissian both finished on 8½ out of 11, and the regulations provided for no play-off games. The first tie-break was the average rating of opponents: 2594 against 2578, a gap of 16 points. Curiously, Sargissian was the higher of the two on Buchholz - so the European champion was decided not by the result but by the order of tie-breaks in the regulations.
The United States and Ukraine both finished on 20 match points, and gold went to the Americans on the Olympiad version of Sonneborn-Berger: 413.5 against 404.5. The oddity is that a German win over Estonia in the final round changed the standings of Ukraine's opponents and flipped the outcome.
Ten players finished the Swiss stage on 9½ and the top eight on tie-break went through to the knockout. Dubov came tenth: he overslept a game and took a forfeit loss, and an unplayed game is treated differently in the arithmetic from one lost at the board. Had he simply sat down and lost, he would have qualified.
A high tie-break score lifts you up the table
Tie-breaks are only ever compared inside a group of players on equal points. A player on fewer points stays below, whatever their coefficient says.
Cut and Median are the same thing
A cut trims only from the weak end. A median trims both the weakest and the strongest. They are different rules and they produce different placings from the same crosstable.
You can calculate your tie-break right after your last game
The arithmetic uses the final scores of your opponents. While other boards are still playing, those numbers are still moving, so an interim figure means very little.
More wins means a higher place on equal points
Only if the number of wins is listed before the other measures in your regulations. In most sequences it comes after the coefficients, so a player with two wins and three draws can finish above one with three wins.
Taking a bye in the last round is harmless
An unplayed round is handled by special rules, and when the worst results are cut it is removed first. A late bye or a withdrawal can drop your tie-break noticeably more than you expect.
The order of tie-breaks can be settled after the event
The regulations require the list to be published before play starts. Choosing the order afterwards is the classic cause of a dispute, because each of the tied players benefits from a different choice.
The wording takes one line and saves the organizer an evening of argument. List the measures in order of application and say what happens if all of them come out level.
Sample wording
«Players level on points shall be ranked by the following tie-breaks in descending order of priority: Buchholz with the lowest opponent score cut, Buchholz, the result of the direct encounter, the number of wins. If all tie-breaks are equal the places shall be shared, and the prize money for those places pooled and divided equally».
If the event is still ahead of you, the step-by-step preparation guide is in how to organize a chess tournament, and how long a Swiss needs to be is worked out in how many rounds a Swiss system needs. For a round-robin you will want the Berger tables and the Sonneborn-Berger calculator.
In the Vibe Chess app the standings show whichever tie-break fits the format: Buchholz in a Swiss, Sonneborn-Berger in a round-robin, and players level on points are ordered by it automatically. There are no columns to reconcile and nothing to compute by hand, and the finished event exports as a TRF report that arbiter software accepts.
The word carries two meanings. One is a numerical measure that orders players who finished on the same number of points; it sits in the columns next to the score in the crosstable. The other is a set of extra games at a faster time control, played to separate a tie in a decisive event. This page is about the first meaning.
They belong to different systems rather than competing. Buchholz measures the strength of your opposition and works in a Swiss. In a round-robin the FIDE regulations forbid it outright, because everyone faces the same field and the numbers coincide - there Sonneborn-Berger applies, weighting the result against each opponent.
Because in most regulations the number of wins is listed after the strength-of-opposition measures. First the sequence asks how hard your path was or how valuable your wins were, and only then counts games won. If you want wins to decide earlier, that has to be written into the regulations.
None in the arithmetic. Solkoff is the American name for the plain sum of the opponents' scores, which FIDE calls Buchholz. The American Modified Median is the same base measure with an end trimmed, and which end depends on whether the player finished with a plus, minus or even score.
Strictly speaking, no. In the current FIDE edition a cut is a modifier applied to a base measure: Buchholz with Cut-1, average opponent rating with Cut-1, and so on. The Buchholz variants were separate articles in the edition up to September 2023, which is why the shorthand BH-C1 still appears in regulations and still means exactly that combination.
After each round you record the player's running total, then add all those totals together. Results of 1, ½, 1 give running totals of 1, 1½ and 2½, so the cumulative score is 5. It comes out higher for the player who led from the first rounds than for one who caught up at the end.
Under special rules, and this is the subtlest part of the whole regulation. A missed round must not zero out the tie-break, so it is counted as a game against a dummy opponent whose score is capped. And when the worst results are cut, voluntarily unplayed rounds are removed first, even when their contribution is not the lowest.
Because an unplayed game is processed differently from a played one. At the 2024 World Blitz Championship this cost Dubov a knockout place: had he sat down and lost the game, he would have gone through.
The regulations have to specify a final procedure: play-off games, a drawing of lots, or shared places with the prize money pooled. The 2026 edition deliberately added new measures so that events reach a drawing of lots less often.
Yes, if the regulations allow it: the prizes for the shared places are pooled and split equally. That is what happened at the 2018 Sinquefield Cup, where the three leaders declined a play-off and were all declared tournament winners.
The organizer. They fix the list and its order in the regulations before the event starts, and the rules explicitly require that list to be published in advance. The arbiter only applies what is written and cannot change the order mid-event.
Three or four in sequence is normally enough. One leaves a real chance of a repeat tie, especially in small events, while a list of eight goes unread anyway. A workable set for a club event: a coefficient, the direct encounter, the number of wins.
The ones you can explain to a child and a parent: the number of wins and the direct encounter, with a coefficient first or second. In short five to seven round events ties on points happen constantly, so a published list is not optional there.
Yes, straight from the final crosstable. For Buchholz, add up the opponents' scores; for Sonneborn-Berger, take the scores of those you beat plus half the scores of those you drew with. For a round-robin you can check the arithmetic in our calculator, and tournament software computes every measure automatically.