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Two chess players can finish on the same tournament points yet rank differently under Buchholz and Sonneborn–Berger. Buchholz adds their opponents’ final scores. Sonneborn–Berger weights each opponent’s final score by the points the player scored against that opponent. Buchholz Cut-1 starts with Buchholz but removes one lowest opponent score.
Check the event’s tie-break order before comparing the numbers. In the fictional records below, both players score 2.5 points. Player A has the higher Buchholz, while Player B has the higher Sonneborn–Berger. Which one ranks ahead depends on the criterion the event applies first.
Start with the tournament’s ordered rules
The FIDE Play-Off and Tie-Break Regulations effective from 1 March 2026 apply to FIDE-rated competitions. Articles 2 and 4 distinguish shared places, play-offs and an ordered list of tie-breaks. They do not establish a universal rule that Buchholz must come before Sonneborn–Berger, or vice versa.
For an off-the-board tie-break list, apply the first listed criterion to the tied players. Use the next criterion only for the subgroup still tied after that comparison. You do not add Buchholz and Sonneborn–Berger together to produce a combined total unless a tournament has specifically defined such a criterion.
There is also a fallback in the regulations. If the tournament rules specify neither shared places nor a ranking method, Article 2.1 directs the use of off-the-board tie-breaks and Article 4.1.1. The latter requires the Chief Arbiter, when necessary, to complete and publish the list before the tournament starts. Article 4.2 provides for drawing lots after the list is exhausted, unless the tournament rules say the remaining ties will not be broken. An omitted rule therefore does not mean you can simply choose your preferred calculation.
What BH, BH-C1 and SB calculate
For the individual, fully played records used here:
- Buchholz (BH): add the final tournament scores of all the player’s opponents. Your result against each opponent does not change that opponent’s contribution to BH.
- Buchholz Cut-1 (BH-C1): remove one lowest opponent score from the BH sum. If two opponents share the lowest score, remove one of those values, not both.
- Sonneborn–Berger (SB): for each opponent, multiply that opponent’s final tournament score by your points against them, then add the products. With a win worth 1, a draw 0.5 and a loss 0, a win contributes the opponent’s full score, a draw half, and a loss zero.
These definitions follow FIDE Articles 8.1, 14.1.1(a) and 9.1 respectively. The note to Article 8 says the Buchholz family must not be used in round-robins. The examples below therefore use a non-round-robin, Swiss-style setting. SB here is the individual calculation, not an extended team version.
Player A: 2.5 points, BH 15 and SB 4.5
The next two tables are separate fictional five-game player records, not a complete event or a certified set of pairings and standings. Other players’ records are not shown. Assume both players and all their opponents played every round over the board, with no byes, forfeits, withdrawals or repeated opponents. That keeps unplayed-round adjustments outside this calculation.
Player A loses to A1 and A2, draws with A3, and beats A4 and A5. The player’s own score is 0 + 0 + 0.5 + 1 + 1 = 2.5 points. The opponent scores below are their final tournament points, not their ratings or their points before meeting A.
| Opponent | Opponent’s final points | A’s result and points | BH contribution | SB contribution |
|---|---|---|---|---|
| A1 | 5 | Loss: 0 | 5 | 5 × 0 = 0 |
| A2 | 4 | Loss: 0 | 4 | 4 × 0 = 0 |
| A3 | 3 | Draw: 0.5 | 3 | 3 × 0.5 = 1.5 |
| A4 | 2 | Win: 1 | 2 | 2 × 1 = 2 |
| A5 | 1 | Win: 1 | 1 | 1 × 1 = 1 |
A’s BH = 5 + 4 + 3 + 2 + 1 = 15. For BH-C1, remove the lowest opponent score, 1: 15 − 1 = 14. This removes a value from the BH calculation; it does not erase A’s win or reduce A’s own 2.5 tournament points.
A’s SB = 0 + 0 + 1.5 + 2 + 1 = 4.5. The losses against the opponents who finished on 5 and 4 still contribute to BH, but contribute zero to SB.
Player B: the same 2.5 points, BH 11 and SB 8
Player B beats B1 and B2, draws with B3, and loses to B4 and B5. B’s own score is also 1 + 1 + 0.5 + 0 + 0 = 2.5 points. The distribution of results across opponents is different from A’s.
| Opponent | Opponent’s final points | B’s result and points | BH contribution | SB contribution |
|---|---|---|---|---|
| B1 | 4 | Win: 1 | 4 | 4 × 1 = 4 |
| B2 | 3 | Win: 1 | 3 | 3 × 1 = 3 |
| B3 | 2 | Draw: 0.5 | 2 | 2 × 0.5 = 1 |
| B4 | 1 | Loss: 0 | 1 | 1 × 0 = 0 |
| B5 | 1 | Loss: 0 | 1 | 1 × 0 = 0 |
B’s BH = 4 + 3 + 2 + 1 + 1 = 11. For BH-C1, remove just one of the two lowest values of 1: 11 − 1 = 10. Removing both would be two cuts, not Cut-1.
B’s SB = 4 + 3 + 1 + 0 + 0 = 8. B has a lower sum of opponent scores than A, but a higher result-weighted sum. Neither calculation changes the fact that both players earned 2.5 tournament points.
The order of criteria changes this comparison
| Player | Tournament points | BH | BH-C1 | SB |
|---|---|---|---|---|
| A | 2.5 | 15 | 14 | 4.5 |
| B | 2.5 | 11 | 10 | 8 |
Suppose fictional Event Alpha lists BH first. A ranks ahead of B because 15 is greater than 11; there is no need to compare their SB values. If fictional Event Beta instead lists SB first, B ranks ahead because 8 is greater than 4.5. A BH-C1-first comparison would also place A ahead here, using 14 versus 10.
These are examples of what different announced orders would do, not two universal event formats. If the first criterion left players tied, you would move to the next criterion for those still tied. A high value in a later column cannot override a tie already resolved by an earlier one.
Byes and unplayed games need additional rules
Do not apply these tables unchanged to a real record with a bye, forfeit or withdrawal. FIDE Articles 15 and 16 address unplayed rounds, including score adjustments, dummy-opponent treatment for a player’s own calculation and a Cut-1 exception. Article 16.6 also permits specified alternative provisions announced in advance.
That is why inserting an opponent score of zero for every unplayed round is not a safe shortcut. You need the type of unplayed round, the complete relevant record and the applicable event rules. Similarly, BH-C1 is not the same as Sonneborn–Berger Cut-1 or Buchholz Median-1; their modifiers remove different elements. This guide calculates only ordinary BH, BH-C1 and individual SB for the fully played examples above.
Questions about chess tie-breaks
Can equal tournament points yield different BH and SB rankings?
Yes. Both fictional players score 2.5, but A’s BH is 15 against B’s 11, while B’s SB is 8 against A’s 4.5. An event using BH first would put A ahead in this comparison; one using SB first would put B ahead. Check the published order rather than selecting the column with the largest-looking number.
How do you calculate Buchholz?
For the fully played individual example, add the final tournament scores of the player’s opponents. A’s opponents finish on 5, 4, 3, 2 and 1, giving BH 15. Use the opponents’ final scores, not their ratings, and check any unplayed-round adjustments in a real event. The FIDE regulations prohibit the Buchholz family in round-robins.
What does BH-C1 remove?
It removes one lowest opponent score from the Buchholz sum in the example’s fully played setting. B has two opponents on 1 point, but drops only one: 11 − 1 = 10. It does not remove all opponents tied for the lowest score, the player’s own worst result, or a tournament point. Unplayed rounds can invoke the separate Cut-1 exception.
Does Sonneborn–Berger add tournament points?
It does not add points to the player’s tournament score. Individual SB adds products: each opponent’s final score multiplied by the points scored against that opponent. Under the example’s scoring, a win contributes the full opponent score, a draw half and a loss zero. B’s products total 8, while B’s tournament score remains 2.5.
What changes with byes or unplayed games?
The simple fully played calculation may require adjustments under FIDE Articles 15 and 16 and any applicable event provisions. A bye is not automatically an ordinary game against a zero-point opponent. Use the relevant category and rules, including the Cut-1 exception when applicable; the two fictional records here contain no unplayed rounds.
Explore HypaForecast
Browse market questions and the details on the 5-minute and 15-minute BTC pages. These links are general site navigation, separate from the fictional chess examples.
Sources and scope
The source is the FIDE Play-Off and Tie-Break Regulations effective from 1 March 2026, approved by the FIDE Council on 2 February 2026 and read on 21 October 2026. Articles 1–4 establish scope and ranking procedures; Articles 8.1, 9.1 and 14.1.1(a) define the calculations used here. Articles 15–16 explain why unplayed rounds require more than the simple examples.
All tables and numerical records were created for this guide. They illustrate two players’ calculations, not a full tournament’s pairings, final standings or an arbiter’s ruling. The guide uses no live results, ratings, forecasts or probabilities, and does not cover team tie-break calculations.
HypaForecast publishes educational guides and operates a prediction-market service. This guide explains chess tie-break calculations; it is not an event ruling or an estimate of who will win.
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