Round-Robin: How Many Games for 3 to 20 Participants? Algorithm, Formula and Table

You are planning your next tournament and wondering: how many games will that actually be? Five teams have confirmed, everyone is supposed to play everyone. Or five players at the table tennis table in the club lounge, same setting, same question. The answer is identical in both cases because the math only depends on the number of participants, not the sport. Whether you are planning soccer, table tennis, padel league, chess, or skat: the number of matchups follows a formula you can memorise in a minute.

This article gives you, for every participant count from 3 to 20, the exact number of games, the games per participant, the number of rounds, and the gross time on a single pitch. Plus the algorithm behind it: the Circle Method that pro leagues have used for over a hundred years to build their schedules. The method is deterministic, fair, and always produces the same result for the same team count. You do not need spreadsheet magic and you do not need an AI tool, you need a formula and a rotation.

If you are looking for the bigger picture on tournament organisation and not just the game count, the main guide to organising a football tournament covers it. For a ready-made schedule for 5, 7, or 10 teams with time budget and tiebreaker recommendations, see the schedule spoke. This article is the algorithm and formula reference for every team count in between and beyond.

The formula: N·(N-1)/2

The question "how many games for N participants in a round-robin" is, at its core, a combinatorial puzzle. Each of the N participants plays every other participant exactly once. For a single participant that means N-1 opponents. If you add that up across all N participants, you get N·(N-1) matchups. But each matchup is counted twice: the game between A and B shows up once in A's opponent list and once in B's. So you divide by 2 and arrive at the formula:

Number of games = N · (N-1) / 2

In combinatorics this is called "N choose 2", written as a binomial coefficient. It is the number of ways to pick two participants from N without caring about order. For a tournament without home and away, this is exactly the right quantity: every pairing is played exactly once, the order does not matter (A vs B is the same game as B vs A).

For N=5 that gives 5·4/2 = 10 games. Visualised, the set of all pairings looks like this:

The upper triangular half shows all 10 pairings. The lower half is redundant (A vs B equals B vs A) and the diagonal is empty because no one plays themselves. Exactly this logic drives the division by 2 in the formula.

For 10 participants that is already 45 games, for 20 participants 190 games. The game count grows quadratically with the team count. If you double N, you roughly quadruple the game count: 5 teams → 10 games, 10 teams → 45 games, 20 teams → 190 games. That is the main reason Round-Robin becomes impractical for large fields. For a one-day club tournament this is usually the upper practical limit: at around 10 to 12 participants a pure Round-Robin becomes tight, and you switch to groups plus knockout. More on that below.

Why the formula works: a second look

If you want to derive the formula by hand, you can use the handshake argument: imagine all N participants shake each other's hand exactly once. How many handshakes happen? Person 1 shakes N-1 hands. Person 2 shakes only N-2 new hands (Person 1's hand was already counted). Person 3 shakes N-3 new hands, and so on. The sum is (N-1) + (N-2) + ... + 1 + 0, which by the Gauss summation formula equals exactly N·(N-1)/2.

Both derivations arrive at the same result. That is not a coincidence; it is standard combinatorics. Anyone familiar with probability theory or statistics will recognise the binomial coefficient "N choose 2" immediately. For practical use at the club, it is enough to remember: N teams = N·(N-1)/2 games, done.

The table for 3 to 20 participants

The table gives you the first reality check for your tournament planning. Three notes on how to read it:

Gross duration assumes one pitch. For club tournaments in indoor halls, one pitch is the default case. If you can run two pitches in parallel, the time roughly halves, because each round has twice as many simultaneous matches. The number of rounds stays the same, only the parallel matchups per round double.

Game length is a conservative assumption. Ten minutes of playing time plus two minutes of break gives 12 minutes gross per game. For F-Youth or Bambini, 6 to 8 minutes is enough; for D-Youth you go up to 12 to 15 minutes of playing time. If you want to derive exact kickoff times from this gross duration, find the math in Planning kickoff times for football tournaments.

Odd participant counts cost you an extra round. For 6 teams it is 5 rounds; for 7 teams it is 7 rounds. The reason: with an odd team count, one team has to sit out (bye) every round, otherwise the pairing math doesn't work. Over the whole tournament each team gets exactly one bye.

If you would rather not build the schedule by hand, a schedule generator produces the matchups, pitch allocation, and tiebreakers in one click. The generator implements the same Circle Method we walk through below; you only save yourself the manual transcription of the rotation into a spreadsheet.

Using the table to check your hall window

Most club tournaments have a fixed hall window: 3-hour half-day, 5-hour extended half-day, or a full day. The gross-duration column tells you at a glance which participant counts fit which window. With 3 hours of hall time and one pitch, 6 teams (15 games = 3 hours) just barely fit. 7 teams (21 games = 4.2 hours) is already too much for 3 hours; you need either more time or a different mode. 8 teams (28 games = 5.6 hours) need either two pitches or a switch to groups plus knockout.

The gross duration is also calculated without setup or teardown. Realistically, plan 30 minutes before kickoff for arrival and team registration, and 30 minutes at the end for the award ceremony and teardown. So if you want a net 3 hours of hall time, your game net-time is 2 hours. In 2 hours on one pitch you fit about 10 games, which equals 5 teams in a Round-Robin. Anything more either needs shorter playing time or a second pitch.

How many games for N teams? Examples for the most common team counts

The table above gives you the numbers for any N. For the team counts that show up most often at the club, a second look is worth it: what does the concrete round structure look like, and what does it mean for the day plan?

5 teams: 10 games in 5 rounds

With 5 teams you have 10 games total, each team plays 4 games, distributed across 5 rounds with 2 parallel matches plus one bye team per round. This is the smallest setup where the bye mechanic is unavoidable. Here is the schedule the Circle Method produces (Team A is fixed, B through E rotate around it):

Round 1: A vs E, B vs D    Bye: C
Round 2: A vs E, B vs C    Bye: D
Round 3: A vs D, E vs C    Bye: B
Round 4: A vs C, D vs B    Bye: E
Round 5: A vs B, D vs E    Bye: C

Over the five rounds, each team gets exactly one bye. That is a direct consequence of the rotation: because the virtual bye team rotates just like the other teams around Team A, it moves to a different team each round.

Gross duration at 10 minutes playing time on one pitch: 10 × 12 minutes = 120 minutes, around 2 hours. With a 15-minute buffer, you land at 2 hours 15 minutes net hall time. With two pitches (rare for 5 teams), you finish in 1 hour 15 minutes.

In practice, a 5-team Round-Robin is the standard for a compact half-day indoor tournament. Tiebreaker recommendation: goal difference first, then head-to-head, then goals scored. The order must be fixed before the first kickoff, otherwise discussion erupts after the last game. If you want to supplement the tiebreaker with a secondary factor such as fair-play points, announce that in writing too.

For 5 players at a table (table tennis, skat, chess) the same game count applies. For a 5-pair padel league day, 10 matches is a realistic frame. With a typical padel match of 20 to 30 minutes, you need around 5 hours of court time, which is right for a full league matchday.

6 teams: 15 games in 5 rounds

Six teams is the last even count where a pure Round-Robin runs cleanly without byes. 15 games total, each team plays 5 games, in 5 rounds with 3 parallel matches per round. At 12 minutes gross on one pitch, you are at 3 hours of pure playing time. With buffers, you land at 3.5 hours. Already tight for a half-day hall slot, but doable.

Round 1: A vs F, B vs E, C vs D
Round 2: A vs E, F vs D, B vs C
Round 3: A vs D, E vs C, F vs B
Round 4: A vs C, D vs B, E vs F
Round 5: A vs B, C vs F, D vs E

No byes needed here. This setup works well for a two-thirds-day indoor tournament. If you only have an hour and a half of hall time, 6-team Round-Robin is too big and you either go to 4-team groups with a placement game or reduce the team count.

Practice tip for 6 teams on one pitch: check the breaks between consecutive games of the same team. In the standard Circle Method rotation, Team A has a game in Round 1, then a break for two other teams' games, then another game. That break length is reasonable: two games × 12 minutes = 24 minutes between your own games, just enough to sit down briefly and drink something but not so long that the muscles cool off. If you build the schedule by hand and "improve" it, you can accidentally shorten or stretch these breaks. Stick with the standard rotation, it is not optimised for nothing.

Tiebreaker for 6 teams: the standard order goal difference, head-to-head, goals scored works but is statistically thin at 5 games per team. A narrow loss can send you from first to third if goal difference decides. If you want more stability, you can put head-to-head ahead of goal difference. Important: in writing, beforehand.

7 teams: 21 games in 7 rounds with bye

With 7 teams the effort is noticeable. 21 games total, each team plays 6 games, but across 7 rounds because one team sits out each round. Over the whole tournament each team gets exactly one bye. Gross duration on one pitch: 21 × 12 = 252 minutes, around 4 hours without buffer. For a normal half-day in the hall, that is tight.

If you do not want to map 7 teams as a pure Round-Robin time-wise, the standard workaround is: one four-group and one three-group play their mini-league in parallel, then semi-final and final. That reduces the game count from 21 to 6 + 3 + 3 = 12 games plus an optional placement game. Gross duration on one pitch drops to 2.4 hours instead of 4.2. The ready-made schedule is in the 5/7/10 teams schedule spoke.

If you still want the classic 7-team Round-Robin, document the bye distribution carefully. In the Circle Method rotation, every team sits out exactly once, but the position of the bye inside the tournament differs. Team A sits out in Round 7 (at the end), Team B in Round 4 (middle), Team C in Round 1 (at the start). That looks harmless but in long tournaments the bye at the start or end can be strategically awkward. The team that sits out in Round 1 has a cold opening. The team that sits out in Round 7 waits through the whole event without active participation.

A practical tip: if you want to influence the bye distribution, assign the teams to the Circle Method's positions before the start so that weaker teams get the byes at the start and stronger teams at the end. That makes the suspense arc more attractive for spectators: exciting final rounds with the top teams, less pressure at the start for the underdogs.

8 teams: 28 games in 7 rounds

Eight teams is the upper limit for a realistic Round-Robin in club format. 28 games total, each team plays 7 games, in 7 rounds with 4 parallel matches per round. On a single pitch you need 28 × 12 = 336 minutes, around 5.5 hours. That is a full day in the hall.

With two parallel pitches you halve the time to 2.5 to 3 hours, and it becomes attractive. If you only have one pitch, you almost always switch to two 4-team groups plus knockout: that reduces the game count to 12 group games plus 3 knockout games (semi-final + final + placement game) = 15 games. Gross duration on one pitch: 3 hours. Realistic for a normal indoor tournament slot.

If you still want to run 8 teams as a Round-Robin, perhaps because the format is a season league spread over weeks, you have a comfortable setup: 7 matchdays with 4 parallel matches each. On every matchday each team plays exactly once. That fits classic hobby league rhythms where you meet once a week or every two weeks.

A practical example: an 8-team club hobby tournament in the hall. You book the hall for every second Sunday from 2 to 5 pm. On each Sunday, 4 games of 30 minutes net are played (15 minutes per half, 5 minutes break between games, 30 minutes buffer time). That makes 7 matchdays across 14 weeks, around 3.5 months. You only need one referee per matchday (or the teams referee each other), and at the end each team has played 7 games. The table decides; all further tiebreakers are set in advance.

Tiebreaker for 8 teams: at 7 games per team the statistics are already reliable. The standard order goal difference, head-to-head, goals scored works reliably here.

10 teams: 45 games in 9 rounds

Ten teams as a pure Round-Robin is rare in club practice. 45 games on one pitch take 9 hours gross. That will not fit into a single day in most cases. The practical alternative: two 5-team groups plus semi-final and final. That gives 20 group games plus 4 knockout games = 24 games. On two pitches in parallel, doable in 3.5 hours. With one pitch only, you need around 5 hours, which is long but acceptable for a full-day tournament. There is also a ready-made schedule for this.

If you still run a 10-team Round-Robin as a season league, you have the same setup as the Bundesliga in miniature: 9 matchdays with 5 parallel matches each, everyone plays everyone once. For a hobby league with one matchday per week, this lasts a good 2 months; with a matchday every 14 days, around 4.5 months. Realistic for a winter season at the club.

One interesting property of the Circle Method at 10 teams: because the team count is even, there are no byes. Every team plays on every matchday. The mid-game pause on one pitch is, however, tight at 24 minutes between two own games when you only have one pitch. With two pitches it relaxes to 48 minutes between own games, much more comfortable.

A practical note: with 10 teams in a Round-Robin you should explicitly verify the pitch allocation. The same team cannot be scheduled on two pitches in the same round. That sounds trivial but goes wrong surprisingly often in hand-made schedules. A schedule generator does the pitch allocation automatically and collision-free.

12 teams: 66 games in 11 rounds

Twelve teams as a pure Round-Robin only makes sense in a multi-day format. 66 games × 12 minutes = 13.2 hours gross. The usual club solution: three 4-team groups plus knockout phase, which gives 18 group games plus 4 or 5 knockout games depending on mode. Gross time on two pitches: around 3 hours. If you still need the classic 66-game plan (for example for a club league season), the Spielplan-Karte PDF has the matchup list in Berger order.

For 12 teams in a season league, that is 11 matchdays with 6 parallel matches each. This is the typical scale for an engaged hobby league. With weekly play, the season lasts around 3 months. With one matchday every 14 days, it is 6 months.

A common mistake at 12 teams: the temptation to squeeze the whole thing into one day and simply shorten the playing time. At 5 minutes playing time per game instead of 10, you reduce the gross time to 7 hours. Doable, but the playing time gets so short that the game becomes athletically unsatisfying: 5 minutes is not enough for real tactical engagement. For Bambini and F-Youth this is appropriate, but for older age groups or adults it feels like a warm-up. Better to switch modes and use groups plus knockout; then you have athletically meaningful 10- to 12-minute games.

The Circle Method: how the schedule is built

The formula tells you how many games there are. But how do you get to the concrete plan that says A plays E in Round 1 and A plays D in Round 2? That is where the Circle Method comes in. It is the oldest and cleanest algorithm for producing a Round-Robin schedule, documented at the latest in 19th-century chess tournament organisation.

The basic principle in one sentence: one participant stays fixed, all others rotate around them. Each rotation step produces one round with N/2 parallel matches.

How to read the visualisation: Team 1 sits at the top of the first frame, fixed. The other teams (2 through 6) are arranged in a circle around it. The pairings per round are produced by joining opposite teams (Team 1 at the top with Team 4 at the bottom, Team 2 at the top right with Team 5 at the bottom left, and so on). After each round, Teams 2 through 6 rotate one position clockwise. Team 1 stays fixed, otherwise the algorithm would not terminate.

After N-1 rounds every team has played every other team exactly once. With 6 teams that is 5 rounds, and at the end all 15 pairings are covered.

The same algorithm runs in the AreaCopa codebase under the hood: the function generateRoundRobin in src/lib/round-robin.ts implements the Circle Method byte-for-byte. So when you call the schedule generator, you are building yourself a Berger table, automated.

What happens with an odd team count?

With an odd team count, the Circle Method does not work out directly. If you have 5 teams, there is one team without an opponent in each round. The standard solution: you add a virtual bye team that brings the odd N up to an even count and run the rotation as usual. The team paired with the bye in any round simply sits out.

Across the five rounds every team gets exactly one bye. So the bye distribution is fair over the whole tournament, even if it looks imbalanced per round. Important in practice: the team sitting out should never have a bye in two consecutive rounds. The Circle Method delivers that property automatically, because the bye moves to a different team in every round.

Walkthrough: Circle Method for 6 teams step by step

If you want to follow the algorithm yourself, you can produce the full 6-team schedule with a pencil and a piece of paper in five minutes. Here is the recipe:

Step 1: Write the teams in two rows, A through C in the top row, D through F in the bottom row, with A in the top left:

A  B  C
F  E  D

The pairings for Round 1 are the vertical pairs: A-F, B-E, C-D.

Step 2: Rotate all teams except A clockwise by one position. A stays fixed. The rotation works like this: B moves to the bottom left, then to the bottom right, then to the top right, then back to the start. F takes B's place at the top, E moves to the bottom left, and so on:

A  F  B
E  D  C

Round 2: A-E, F-D, B-C.

Step 3: Repeat the rotation for each further round. After 5 rounds you are done; all 15 pairings have been played exactly once.

That is the Circle Method in its simplest form. With an odd team count, you add a virtual bye team and treat it exactly like a real team. The team that is paired with the bye in any round sits out.

The method is mathematically elegant because it automatically guarantees that every pairing appears exactly once. The proof lies in the algebra of cyclic groups: the rotation corresponds to a permutation of order N-1, and across N-1 steps every one of the N-1 possible relative positions is visited exactly once.

Berger tables: the written form of the algorithm

If you search for Round-Robin schedules in practice, you quickly run into the term Berger table. The name traces back to the Austrian chess organiser Johann Berger, who in 1893 first documented the systematic round pairings for chess tournaments in writing. The algorithm behind it is the Circle Method. Berger did not invent it; he poured it into a handy table form that has been in almost every chess organisation handbook since.

A Berger table for 4 participants looks like this:

The numbers are the start numbers of the participants. The parallel pairings per round are next to each other. With 4 participants that is 3 rounds of 2 matches each, 6 games in total. Matches the formula: 4·3/2 = 6.

Berger tables are deterministic: the same participant count always yields the same round structure. That is their practical value. You do not have to reinvent the schedule every time, and everyone involved can rely on a known order. In the chess world, Berger tables are so widespread that the draw often consists of only assigning the start numbers to concrete players.

For a club football tournament, you do not need a Berger table out of a book. If you generate the schedule automatically, you get the same output. But anyone working traditionally with paper or wanting to post the plan in the club lounge appreciates the table form. The Spielplan-Karte PDF for this article is essentially nothing else: a Berger table in readable format for N=4 through 8.

Where Berger tables still dominate today

In chess, Berger tables are the standard for every tournament with a fixed participant count, from the club championship to the FIDE Grandmaster tournament. In table tennis, Berger tables are used for team and individual competitions, from district cup to Bundesliga. In bridge, there are bridge-specific Berger variations that additionally account for seating positions (North, South, East, West).

In football, pure Berger tables are rarer because most leagues play double Round-Robin (home and away). The DFB schedule generator for the Bundesliga uses the Berger logic at its core: in the first half of the season the matchups are set by a fixed scheme, in the second half they are mirrored (with home rights flipped).

In table form, Berger has another advantage: it is deterministic in both directions. You can read out of the Berger table which pairing plays in which round, and you can derive from a single pairing in which round it is played. That is useful when you want to know, for example, when does Team 3 play Team 5? You have the answer in two seconds from the printed Berger table.

Double Round-Robin: home and away

In a Bundesliga season, every team plays every other twice: once at home and once away. That is double Round-Robin. The formula adjusts accordingly: N·(N-1) games in total, not N·(N-1)/2. With 18 teams as in the German Bundesliga, that is 18·17 = 306 games per season, distributed across 34 matchdays with 9 parallel matches each.

For a club tournament, double Round-Robin is almost always overkill. With 6 teams that is 30 games instead of 15, so 6 hours gross instead of 3. It is worth it in only two cases: first, when you run a club championship over multiple weeks and the home and away factor is real (different field, different commute for the parents, different atmosphere). Second, when you have a very small tournament with 4 or 5 teams and want to fill the programme because single Round-Robin would be over too quickly.

In all other cases, single Round-Robin or groups plus knockout gives you a better ratio of game count to effort. If you are not sure whether classic Round-Robin or a different mode fits better, you can compare modes directly:

The comparison table shows: for 5 to 8 teams, single Round-Robin is the fairest variant; for larger fields, groups plus knockout is worth the switch. Double Round-Robin is the rarest variant, mainly relevant for season leagues.

When double Round-Robin really makes sense

Three scenarios where double Round-Robin is the right choice. First: season leagues with a real home and away advantage. In the German first Bundesliga, teams play differently in foreign stadiums than at home; that affects results measurably. For the season-end table to be fair, every team has to have played every other once at home and once away. That balances the influence of the home advantage.

Second: club championships across multiple weeks where teams play on different days or under different conditions. If your club has four teams and runs a club championship across the winter season, double Round-Robin starts to make sense: 12 games across 6 matchdays, a real season with every team as guest and host.

Third: small tournaments where single Round-Robin would be too short. With 4 teams in single Round-Robin you only get 6 games. If you want to fill a full club day with that, it is tight. Double Round-Robin lifted to 12 games fills the day without having to attach extra knockout games.

Outside these three scenarios, single Round-Robin or groups-plus-knockout is almost always the better choice.

Round-Robin in padel tournaments

Padel is structurally different from singles tennis or table tennis as a doubles sport. In padel, two always play two, which raises the question of who plays whom to a different level: do you mean pairs or individual players? Several tournament formats have developed from this, only some of which are actually Round-Robin in the classic sense.

Padel league with fixed pairs

If you run a padel tournament or padel league with fixed doubles pairs, the Round-Robin math applies one-to-one. With N pairs you play N·(N-1)/2 matchups; each matchup is a padel match across two sets or a fixed playing time. With 6 fixed pairs that is 15 matches. This is the clean standard variant and shows up often in club sport: a winter season with 6 pairs, everyone plays everyone once, the table decides the season.

Americano with fixed pairs

Americano is the padel term for a Round-Robin tournament, often run in a single day. If you play Americano with fixed pairs (each pair stays together for the whole tournament), it is mathematically identical to the padel league: N·(N-1)/2 matches with N pairs. With 8 pairs that is 28 matches. On one court at 20 minutes per match, that takes around 9 hours, which means you almost always need two or more courts.

The qualifier "with fixed pairs" matters. There are also Americano variants in which players change partners within the tournament. Those fall into the next category.

Americano with rotating partners

When players rotate partners within an Americano so that each player partners every other player at least once, that is no longer classic Round-Robin. The math behind it is called the Social Golfer Problem: given N players, how many rounds do you need so that every player has partnered every other at least once? The answer depends on N and is, in the general case, an open problem in combinatorics.

In practice this means: an 8-player Americano with rotating partners does not give you 28 matches, but often only 6 to 8 rounds of 2 parallel matches each. The games per player are 6 to 8, not N-1. If you are planning such a format, you cannot rely on the N·(N-1)/2 formula.

Mexicano and King of the Court

Mexicano tournaments are seeding-based: after each round the pairs are recomposed based on the current standings. Player 1 plays with Player 4 against 2 and 3 (typical setup), so the pairings change dynamically. The number of matchups per player depends on the round count you set as organiser, not on the participant count. With Round-Robin it shares only the superficial property that there is no knockout elimination.

King of the Court is even further away: the winning pair stays on the court, the losing pair is swapped out. The order of matches arises from results, not from a fixed schedule. That is a training and fun format, not a tournament format in the strict sense.

If you need AreaCopa for padel tournaments

AreaCopa is currently football-focused: the modes, the data model, and the playing times are tailored to football tournaments. If you want to build Round-Robin plans for padel tournaments, drop us a short line at info@areacopa.com and tell us which padel format you need: fixed pairs in a league, Americano with fixed pairs, Americano with rotation, Mexicano. We are collecting demand before we build.

What concretely helps us: number of players or pairs, desired match length, number of courts, planned frequency (one-off tournament or season league). On that basis we can estimate whether a padel mode has enough volume to enter our roadmap. Until that is the case, we will not build it, but we are happy to listen.

Spielplan-Karte to print

The two most important things from this article as a print template: the reference table for every N between 3 and 20, and the matchup lists for the most common club formats. You print the card, stick it on the boards next to the scoreboard, and everyone involved sees immediately which round is currently running and which pairings are coming up.

Conclusion

The number of games in Round-Robin follows from a single formula: N·(N-1)/2. With 5 participants that is 10 games; with 8 participants 28; with 12 participants 66. Each participant has exactly N-1 matchups, distributed across N-1 rounds for an even team count or N rounds for an odd team count with one bye per round. The Circle Method gives you the concrete plan: one participant stays fixed, all others rotate around them. Berger tables are nothing more than the written form of this output.

For the practical club setting: up to about 8 participants, pure Round-Robin is the fairest mode; above 10 you switch to groups plus knockout. Double Round-Robin is reserved for season leagues. If you would rather not build the plan by hand, let the Circle Method run automatically and get the finished schedule rendered in your browser.

Sources

• Berger, Johann (1893). Schach-Jahrbuch für 1892/93. Veit & Co, Leipzig. First systematic documentation of round pairings for chess tournaments in the Round-Robin mode.
• IFAB Laws of the Game 2024/25, Procedures to Determine the Result of a Match. International Football Association Board. Standard for tiebreaker conventions in Round-Robin final tables.
• DFB Booklet Wettbewerbsformen im Kinderfußball, status 09/2024. Deutscher Fußball-Bund. Mandatory since the 2024/25 season for U6 to U11 festival formats, with concrete guidelines for playing times and game counts per participant.