Chess tiebreaks explained: Buchholz, Sonneborn-Berger and direct encounter

Short answer

When two or more players finish on the same score, the tournament applies, in order, the tiebreaks set out in its regulations. The most common are Buchholz (the sum of the opponents' scores), cut-1 Buchholz (the same sum without the weakest opponent), Sonneborn-Berger (opponents' scores weighted by your result against each), direct encounter and number of wins. Each rewards something different, and the same standings can change hands depending on the order chosen.

The essentials in a few lines

• Tiebreaks only apply after points, and the order of criteria is fixed in the regulations before the tournament starts.
• Buchholz adds up the final scores of all your opponents; cut 1 removes the opponent who scored least.
• Sonneborn-Berger adds the scores of the opponents you beat and half the scores of those you drew with; losses count for nothing.
• Rounds without a game — a bye, a forfeit or a withdrawal — have their own treatment in the regulations and can weigh on your Buchholz.
• In team events the first criterion is usually match points, and game points become a tiebreak or a weighting factor.

What a tiebreak is for

The lazy explanation is that tiebreaks are a lottery, because they depend on other people's results. They do — and that is exactly what they measure. In a Swiss, each player faces a different set of opponents, and two scores of 3.5 out of 5 can have cost very different efforts. The tiebreak tries to estimate which of the two paths was harder, using the information the tournament has once the last round ends.

That is why the Swiss is the format that relies most on tiebreaks and the round robin (all-play-all) the one that needs them least: when everybody plays the same opponents, the scores are already comparable, and the natural criterion is the direct encounter between the tied players. In a Swiss, the comparison has to go through the strength of whoever each player faced.

The practical consequence is that the tiebreak is not an arbiter's detail. It decides prize money, qualification places, titles and, in events with rating categories, who takes the section trophy. It is worth reading the tiebreak section of the regulations before entering, for the same reason it is worth reading the time control.

Buchholz and cut Buchholz

The most widely used number in Swiss events is also the easiest to misread. Buchholz does not look at your result against each opponent, only at who they turned out to be by the end of the tournament. Beating or losing to a player who finished on 4 points is worth the same to your Buchholz: 4.

The table below shows a fictitious eight-player, five-round Swiss, built for this guide, in which Bruno, Carla and Gabi finished tied on 3.5 points. On plain Buchholz, Bruno comes first with 14: he played Gabi and Carla, the other two leaders, plus Elisa, who scored 3.

Now apply cut 1. Carla played Hugo, who lost every game and finished on zero. That is exactly what the cut is for: removing from the sum an opponent the pairings put in your way who says little about the strength of your tournament. Without Hugo, Carla has 12.5 and moves ahead of Bruno (12) and Gabi (11.5).

The cut changes the winner without a single game changing its result. That is why the order of criteria matters as much as the definition of each one: the same tournament, with plain Buchholz or cut 1 as the first tiebreak, hands the trophy to different people.

Sonneborn-Berger

Where Buchholz asks whom you played, Sonneborn-Berger asks whom you took points from. In the example, Bruno faced the strongest field but lost precisely to Gabi. Her 3.5 points, which counted towards his Buchholz, vanish from his Sonneborn-Berger.

Gabi's sum is 3.5 (she beat Bruno) + 1.75 (half of Carla's 3.5, a draw) + 2 (Ana) + 2 (Fábio) = 9.25. Bruno's is 2 + 2 + 3 (the wins over Ana, Fábio and Elisa) + 1.75 (the draw with Carla) = 8.75. Carla, who drew three times, ends on 7.5. Third criterion, third winner.

Sonneborn-Berger was born in the round robin, where Buchholz is useless — everyone plays the same opponents, so everyone would have the same Buchholz. In a Swiss it sits alongside Buchholz, and many regulations use it as the second or third criterion. In team events an adapted version of Sonneborn-Berger is common, as the section on teams shows.

Direct encounter, wins, average rating and progressive score

Direct encounter is the most intuitive criterion and the most limited. It only settles things cleanly when all the tied players have met each other. In the example, all three did: Gabi scored 1.5 in those games, Carla 1 and Bruno 0.5. If the regulations put direct encounter first, Gabi would be champion. In a larger group of tied players, where not everyone has met, the comparison is partial, and the regulations say what to do.

Number of wins favours those who take risks: a player with three wins and two losses moves ahead of one with a single win and four draws. In the example, it leaves Bruno and Gabi level (three wins each) and Carla behind. Average rating of opponents measures the strength of the path by starting rating rather than final score — which makes it blind to what the opponents did afterwards.

Progressive score adds up the running total after each round. A player who started with three wins and finished with two draws has a higher progressive score than one who took the opposite route, although both have the same total. The argument for it is that whoever scores early faces stronger opponents in the rounds that follow.

Rounds without a game

This is where tiebreaks most surprise players who have not read the regulations. The point from a bye counts in full in your score, but it need not count the same way in your Buchholz. If the tournament assigns a low-scoring virtual opponent to the empty round, your Buchholz falls; if it assigns a neutral value, it stays roughly where it would have been. The same reasoning applies to a win by forfeit: the point goes in, but the game never happened.

There is a second, less visible effect: an opponent's bye also affects your tiebreak. If someone you played took a half-point bye without playing, their final score changes, and that shows up in your Buchholz and your Sonneborn-Berger.

The practical advice is simple. If you intend to request a bye, do it knowing the cost: read how the regulations treat the empty round and weigh it against the half point. In long events, a bye in the first round and one in the last can carry different weight, depending on the rule applied.

Tiebreaks in team events

The difference between the two kinds of point catches out even people who have followed chess for years. A team that wins three matches 2.5–1.5 has 6 match points and 7.5 game points; another that wins two 4–0 and loses one 1.5–2.5 has only 4 match points, with 9.5 game points. On match points the first team is ahead, although it scored less on the board.

A common tiebreak in this format is the team Sonneborn-Berger: for each opponent, multiply their final match points by the game points you scored against them, then add the products. The Chess Olympiad uses a version of this criterion that discards the opponent with the fewest match points. Under it, a team can score more game points than a rival on the same match points and still finish behind, having scored against opponents who ended lower down.

For anyone who plays team chess at a club or company, the lesson is the same as in individual events: the regulations decide whether the board counts for more than the match, and that changes the strategy for line-ups and for how much risk to take on the last board still playing.

What you control

The honest answer disappoints anyone looking for a tiebreak tactic: most of the number is decided by other people, on other boards. What is left, though, is not trivial, and nearly all of it goes through the board. Scoring against players who will finish well counts in Sonneborn-Berger; turning a comfortable draw into a win counts in number of wins; and losing early to an opponent who then sinks down the table cuts your Buchholz in a way no later game fully recovers.

There is also what not to do. Withdrawing before the end costs you the final rounds and, under many regulations, affects your opponents' tiebreaks. Requesting a bye without reading the rule can cost more than the half point brings in.

And there is the part that usually goes unnoticed: once the tournament ends, the list of criteria is published with the standings, with each player's value for each one. Checking your own tiebreak is a matter of reading the right table — the guide to Chess-Results shows where it is.

None of these numbers replaces the point left on the board. The half point you failed to convert in round three is worth more than any tiebreak: it would have avoided the tie.

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