A Swiss tournament gives everyone the same number of games and still produces a winner. It has three moving parts: a pairing rule, a fixed number of rounds, and a tiebreak for players who finish on the same record. Most end-of-night arguments are about the third. Someone finishes 3-1, misses the cut, and wants to know why the other 3-1 got the seat.
This post covers all three, works one tiebreak through with real numbers, and then deals with byes, drops, draws and the top cut. To run one now, the free Swiss tournament generator pairs each round in your browser. For the rest of a tournament night (format, seeding, check-in, prizes), see how to run a Discord tournament.
How Swiss pairing works
Nobody is eliminated. Each round, players are sorted into score groups (everyone on 2-0, everyone on 1-1, everyone on 0-2) and paired inside their group:
- Like plays like. A win moves you up a group, so winners keep meeting winners, and after a few rounds the field has sorted itself by strength.
- No rematches, as long as the draw can avoid one. Late in a small field it sometimes can't.
- Floats. A score group with an odd number of players sends one of them down to be paired with the next group. Who floats is where pairing systems differ most.
Round 1 has no scores, so it pairs by seed, top half against bottom half: with eight players, 1 plays 5, 2 plays 6, 3 plays 7, 4 plays 8. The top seeds don't knock each other to 0-1 before the field has sorted itself. Chess adds a fourth rule, balancing who has White. Card games and esports decide who goes first with a die roll or the game itself, so they stop at three.
The consequence that matters later: two players on the same record have not played the same schedule. One 3-1 may have beaten the top of the field and the other the bottom. Tiebreaks measure that difference.
How many rounds?
The standard rule is enough rounds for exactly one player to finish undefeated. Each round halves the undefeated group, so for N players that's log₂ N, rounded up. Each row leaves one unbeaten player, and the table shows how many finish with one and two losses, assuming the field halves cleanly (N × C(rounds, losses) ÷ 2^rounds):
| Players | Rounds | 1 loss | 2 losses |
|---|---|---|---|
| 8 | 3 | 3 | 3 |
| 16 | 4 | 4 | 6 |
| 32 | 5 | 5 | 10 |
| 64 | 6 | 6 | 15 |
| 128 | 7 | 7 | 21 |
Odd fields, byes, draws and drops move a few players around, but this is the picture top cut math starts from. Fewer rounds leave several undefeated players and let a tiebreak decide first place. Add a round when:
- The middle of the table matters, as in a seeding qualifier. Each extra round splits the big middle groups.
- Draws are common. A draw keeps two players level, so draw-heavy fields need longer to produce one leader. Magic's tournament rules recommend 9 rounds from 227 players and 10 from 410, where the log₂ rule would wait for 257 and 513.
- Your top cut would land in the middle of a large score group. See the top cut section.
More rounds than players minus one can't avoid rematches: six players have run out of new opponents by round 6.
Tiebreaks, worked through on one event
Here is a nine-player, four-round Swiss paired by the same engine Team Up uses. The results are made up; the pairings are what the engine drew from them. Nine is odd, so each round the lowest-ranked player who hasn't had a bye sits out and scores a win.
Round 1: Ash beat Eli, Bea beat Fay, Cole beat Gus, Dev beat Hana. Ivo has the bye.
Round 2: Ash beat Dev, Bea beat Ivo, Cole beat Eli, Gus beat Fay. Hana has the bye.
Round 3: Cole beat Ash, Bea beat Dev, Hana beat Gus, Ivo beat Eli. Fay has the bye.
Round 4: Bea beat Cole, Hana beat Ash, Ivo beat Gus, Dev beat Fay. Eli has the bye.
Final points: Bea 4, Cole 3, Hana 3, Ivo 3, Ash 2, Dev 2, Eli 1, Fay 1, Gus 1. Bea wins. Second place is a three-way tie at 3-1, and two of those records include a bye:
| Player | Opponents (final points) | Beat |
|---|---|---|
| Cole | Gus 1, Eli 1, Ash 2, Bea 4 | Gus, Eli, Ash |
| Ivo | bye, Bea 4, Eli 1, Gus 1 | Eli, Gus |
| Hana | Dev 2, bye, Gus 1, Ash 2 | Gus, Ash |
None of the three played each other, so head-to-head can't separate them.
Buchholz is the sum of your opponents' final points: the standard chess tiebreak, and a measure of how hard your schedule was. Cole 1 + 1 + 2 + 4 = 8, Ivo 4 + 1 + 1 = 6, Hana 2 + 1 + 2 = 5.
Median-Buchholz drops your best and worst opponent first, so one outlier can't decide it. FIDE's regulations name Median-1 the most commonly used modifier; Cut-1 drops only the worst. Cole keeps 1 + 2 = 3, Hana 2, Ivo 1. On four rounds that throws away half of everyone's schedule, which is why median versions belong to longer events.
Sonneborn-Berger adds the final points of the opponents you beat, plus half of those you drew. Cole 1 + 1 + 2 = 4, Hana 1 + 2 = 3, Ivo 1 + 1 = 2.
Opponents' match-win percentage (OMW%) is the card-game version. Under Magic's tournament rules a win is 3 match points and a draw 1, a player's match-win percentage is their match points ÷ (3 × rounds played), and anything under 0.33 counts as 0.33. OMW% averages your opponents' percentages, leaving byes out (a bye still counts as a win in your own record). Bea is at 1.00, Ash and Dev at 0.50, and Eli, Fay and Gus at 0.25, lifted to 0.33 by the floor. Cole (0.33 + 0.33 + 0.50 + 1.00) ÷ 4 = 54.0%, Ivo (1.00 + 0.33 + 0.33) ÷ 3 = 55.3%, Hana (0.50 + 0.33 + 0.50) ÷ 3 = 44.3%.
| Tiebreak | Cole | Ivo | Hana |
|---|---|---|---|
| Buchholz | 8 | 6 | 5 |
| Median-Buchholz | 3 | 1 | 2 |
| Sonneborn-Berger | 4 | 2 | 3 |
| OMW% | 54.0% | 55.3% | 44.3% |
Three systems give Cole second place. OMW% gives it to Ivo. Two details decided that:
- The 33% floor. Without it, Cole and Ivo are both on exactly 50.0%. The floor stops a loss to a 0-4 player from sinking your tiebreak, and here it settled second place.
- The bye rule. The table counts a bye as having no opponent, so it adds nothing to Buchholz. FIDE instead scores a bye as a game against a virtual opponent who finishes on the player's own points. That adds 3 each to Ivo and Hana, making their Buchholz 9 and 8: under FIDE's rule Ivo is second, and Cole drops into a tie with Hana.
Neither convention is wrong, but they don't agree, so use your game's and publish it before round 1. Chess arbiters choose from FIDE's Buchholz-family list. Magic uses OMW%, then game-win percentage, then opponents' game-win percentage. Riftbound's tournament rules (updated October 2026) use the same three, then a random tiebreak.
Byes and drops
Byes are scored as a win; Magic records one as a 2-0 match win. The usual recipient is the lowest-ranked player who hasn't had one, as above. Whatever your rule, its effect on tiebreaks matters more than the bye itself.
Drops are normal in Swiss and nowhere else: someone is out of contention after round 3 and goes home. The convention is the same everywhere. A dropped player keeps every result they earned, isn't paired again, and still counts in their past opponents' tiebreaks, because deleting their games would rewrite everyone else's Buchholz or OMW%. A drop can also turn an even field odd, so the next round has a bye. After the cut, a dropped player usually isn't replaced; Riftbound's rules say nobody advances in their place.
Top cut math
Many Swiss events, card games especially, end with a top cut: the top 4, 8 or 16 play a single-elimination playoff. Cut size and round count together decide which records make it:
| Field | Rounds | Top | Who makes it |
|---|---|---|---|
| 16 | 4 | 4 | 4-0, and 3 of the four 3-1s |
| 16 | 4 | 8 | 4-0, all 3-1s, 3 of six 2-2s |
| 32 | 5 | 8 | 5-0, all 4-1s, 2 of ten 3-2s |
| 64 | 6 | 8 | 6-0, all 5-1s, 1 of fifteen 4-2s |
| 128 | 7 | 8 | 7-0 and all 6-1s, exactly |
X-1 (one loss, any number of wins) is usually safe. X-2 is the bubble, where a seat or two goes to a large score group by tiebreak. At 64 players and six rounds, fifteen 4-2 players chase one seat, and the tiebreak from the last section decides it. If that's too harsh for your event, play one more round or cut deeper. A power-of-two cut (4, 8, 16) gives a playoff with no byes.
Intentional draws come out of the same math. In the last round, two players who are in at their current record can agree to draw, and each takes a guaranteed seat instead of risking a loss into the bubble. Where allowed, the rules are strict: Riftbound permits a mutually agreed draw but forbids checking other tables' results first, and bans agreeing one in exchange for anything. Scoring changes the value too. Under 3/1/0 match points a draw is a third of a win; under chess scoring (1, ½, 0) it's half.
Swiss, round robin or double elimination?
- Round robin for four to eight players with time to spare. Everyone plays everyone, so no tiebreak guesses at schedule strength, but it grows fast: 28 matches for eight players, 120 for sixteen.
- Swiss when the field is too big for that and everyone should play all night. Sixteen players finish in four rounds and 32 matches, with the whole table ranked, not just the winner.
- Double elimination when you want a knockout with a second chance. Sixteen players is 30 or 31 matches, about the same as Swiss, but the losers bracket spreads them over roughly twice as many rounds, and eliminated players stop playing.
Swiss with a top cut combines the last two: everyone gets their rounds, and the night still ends on a final.
How Team Up runs Swiss
Team Up tournaments run Swiss in your Discord server. The specific choices:
- Rounds default to log₂ of the field, rounded up; you can set your own. Round 1 is top half against bottom half, and each later round pairs itself the moment the previous one is fully reported, by score group with no rematches. If no rematch-free draw exists, it pairs anyway and labels the round Repeat pairing instead of stalling.
- Scoring is chess-style: win 1, draw ½, bye 1. Draws are recorded on the dashboard; the Report result button in Discord records a winner. A match that won't happen can be skipped, scoring nothing, so the round can close.
- Tiebreaks, in order: points, Buchholz, head-to-head among the tied players, score difference (where game scores were recorded), then seed. Buchholz is the plain sum, and a bye adds nothing to it, exactly as in the worked example, so Cole is second there. Team Up doesn't compute OMW%. For a card game whose rules name OMW%, the two usually agree, but tell players which one the standings use.
- Byes go to the lowest-ranked player who hasn't had one.
- Drops keep their results and their place in the standings and aren't paired again. An unplayed match they were in becomes a win for the opponent, with no Elo recorded.
- Top cut: make Swiss the first stage of a two-stage tournament, and the top N go to a single or double elimination playoff, drawn automatically when the last Swiss match is reported. N is a fixed number or a percentage of whoever turns up, rounded to 4, 8 or 16 by default. A dropped player doesn't take a seat; the next player in the standings does.
- Check-in before round 1 finds the no-shows, and when you start you can drop them before the first pairing. The live Discord message (
/tournaments display) shows the current matchups and the standings as images and redraws them after every result. - Pod Swiss does the same for free-for-all games: pods of three to ten, points for finishing position, and a pod-strength version of Buchholz.
Card-game communities can start from the Riftbound page, which sets up a weekly Swiss night on a leaderboard that carries over between weeks. With no server or account, the Swiss generator runs the same pairing and standings code in your browser, and the bracket generator draws the elimination half.
Frequently Asked Questions
What is Buchholz in a Swiss tournament?
A tiebreak: the sum of the final scores of everyone you played, so two players on the same record are separated by who had the harder schedule. Median-Buchholz drops your best and worst opponent first; Cut-1 drops only the worst.
What does X-1 mean in a top cut?
A record with one loss after the Swiss rounds, whatever the number of wins: 4-1 over five rounds, 6-1 over seven. X-1 usually makes a top 8, and X-2 is usually the bubble, where tiebreaks decide the last seats.
Why do card games use OMW% instead of Buchholz?
Both measure strength of schedule. OMW% averages opponents' win rates with a 33% floor, so an opponent who lost every match can't sink you, and it fits 3/1/0 match points and best-of-3 play. Magic and Riftbound use it, followed by game-win percentage.
Does a bye count toward tiebreaks?
It depends on the rules. Magic counts a bye as your win but leaves it out of your opponents' averages. FIDE scores it against a virtual opponent on your own final score. Team Up leaves it out of Buchholz. Publish your rule with the rest of the event's rules.