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

You are planning your next tournament and asking yourself: how many games will there be? Five teams have confirmed and everyone plays everyone else. Or five players at the table tennis table in the club room, the same setting, the same question. The answer is identical in both cases because the maths depends only on the number of participants, not the sport. Whether you are planning football, or soccer as it is known in North America, table tennis, a padel league, chess or cards: the number of matches follows a formula you can memorise in a minute.

This article gives you the exact number of games, games per participant, number of rounds and gross duration on one pitch for every participant count from 3 to 20. Plus the algorithm behind it: the circle method, which professional leagues have been using for over a hundred years to build their schedules. The method is deterministic, fair and always delivers the same result for the same team count. You need no Excel magic and no AI tool; you need a formula and a rotation.

Anyone looking for the bigger picture on tournament organisation, not just the number of games, will find it in the main guide to organising a football tournament. Anyone who wants a ready-made schedule for 5, 7 or 10 teams with a time budget and tiebreaker recommendation can check the schedule spoke. For exactly four teams there is a dedicated format reference with four variants from round robin to pure knockout in the cuadrangular article. For the single-day tournament format with three slot templates (morning/afternoon/all day) there is the day tournament spoke. This article is the algorithm and formula reference for all team counts in between and beyond.

The Formula: N·(N-1)/2

The question "how many games with N participants in round robin" is at its core a combinatorial problem. Each of the N participants plays every other participant exactly once. For a single participant that is N-1 opponents. If you add that up for all N participants you get N·(N-1) encounters. You count every encounter twice: the game between A and B appears once in A's 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 choose two participants from N without regard to order. For a tournament without home and away legs this is exactly the right quantity: each pairing plays exactly once, and the order does not matter (A vs B is the same game as B vs A).

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

The upper triangle shows all 10 pairings. The lower half is redundant (A vs B = B vs A) and the diagonal is empty because no one plays themselves. This logic is exactly what leads to dividing by 2 in the formula.

With 10 participants that is already 45 games, with 20 participants 190. The number of games grows quadratically with the team count. If you double N, the number of games roughly quadruples: 5 teams to 10 games, 10 teams to 45 games, 20 teams to 190 games. That is the main reason why round robin becomes impractical with large fields. For a single-day club tournament this is usually the upper practical limit: from about 10 to 12 participants, a pure round robin becomes tight on time and you switch to groups plus knockout. More on that below.

Why the formula works: a second look

Anyone who wants to derive the formula by hand can also use the handshake argument: imagine all N participants shaking each other's hand exactly once. How many handshakes are there? Person 1 shakes N-1 hands. Person 2 shakes only N-2 new hands because the handshake with person 1 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 sum formula equals exactly N·(N-1)/2.

Both derivations reach the same result. This is not a coincidence but standard combinatorics. Anyone familiar with probability or statistics will recognise the binomial coefficient "N choose 2" immediately. For practical club use it is enough to know: with 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 points on interpretation:

Gross duration is calculated with one pitch. For club tournaments in a hall one pitch is the standard. If you can run two pitches in parallel, the time halves almost linearly because twice as many games happen simultaneously per round. The number of rounds stays the same; only the parallel matches per round doubles.

Game time per match is a conservative assumption. Ten minutes of playing time plus two minutes of break gives 12 minutes gross per game. For younger age groups 6 to 8 minutes suffice; for older groups you go up to 12 to 15 minutes of playing time. Anyone who wants to derive the exact kick-off times from this gross figure will find the calculation in Planning kick-off times for a football tournament.

Odd participant counts cost you an extra round. With 6 teams there are 5 rounds, with 7 teams there are 7 rounds. The reason: with an odd team count one team must sit out each round (bye), otherwise the pairing maths does not work out. Across the whole tournament each team sits out exactly once.

Anyone who does not want to build the schedule manually uses a schedule generator that produces the pairings, pitch assignments and tiebreakers in one click. The generator implements the same circle method we will walk through step by step below; it just saves you the manual transfer of the rotation into a spreadsheet.

How to use the table to check your hall window

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

The gross duration also excludes setup and teardown. Realistically allow 30 minutes before kick-off for admission and player registration, and 30 minutes at the end for the prize ceremony and teardown. If you want 3 hours of net hall time, your net playing time is 2 hours. In two hours on one pitch you can fit about 10 games, which corresponds to 5 teams in round robin. More will not fit without shortening game time or using a second pitch.

How Many Games With N Teams? Examples for the Most Common Team Counts

The table above provides the numbers for every N value. For the team counts that come up most often in club settings it is worth a second look: what does the concrete round plan look like, and what does that mean for the day's planning?

5 teams: 10 games in 5 rounds

With 5 teams you have 10 games in total; everyone plays 4 games spread across 5 rounds with 2 parallel matches plus one team sitting out. This is the smallest configuration where the bye mechanic is already mandatory. Here is the ready-made schedule as produced by the circle method (team A fixed, B through E rotate around it):

Round 1: B vs E, C vs D    Bye: A
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

Across the five rounds every team sits out exactly once. This is a direct consequence of the rotation: because the virtual bye team rotates around team A just like the other teams, it passes to a different team each round.

Gross duration with 10 minutes of game time on one pitch: 10 x 12 minutes = 120 minutes, roughly 2 hours. With a 15-minute buffer you land at 2 hours 15 minutes of net hall time. If you have two pitches (rare with 5 teams), you finish in 1 hour 15 minutes.

In practice, 5-team round robin is the standard for a compact half-day hall tournament. Tiebreaker recommendation: goal difference ahead of head-to-head ahead of goals scored. The order must be fixed before the first kick-off, otherwise teams will argue after the last game. Anyone who wants to add a second tiebreaker such as fair play points should also announce that in writing beforehand.

With 5 players at a table (table tennis, chess), the same game count applies. Anyone planning a 5-person padel singles league day is also in a realistic range with 10 matches. With a typical padel match of 20 to 30 minutes, you need roughly 5 hours on one court, which is the right frame for a complete matchday in a season league.

6 teams: 15 games in 5 rounds

Six teams are the last even team count where a pure round robin runs cleanly without byes. 15 games in total, everyone plays 5 games in 5 rounds with 3 parallel matches each. At 12 minutes gross per game on one pitch you are at 3 hours of pure playing time. With buffer times you land at 3.5 hours. Already borderline 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 are needed here. The setup works well for a hall tournament with a two-thirds-day slot. If you only have 1.5 hours of hall time, 6-team round robin is too large and you either go to 4-team groups with a placement game or reduce the team count.

Practical tip for 6 teams on one pitch: look at the gaps between two games of the same team. In the standard circle method rotation, team A plays in round 1, then has a gap for two other teams' games, then plays again. This gap length is acceptable: two games of 12 minutes = 24 minutes between your own games, just enough to sit down and drink something but not so long that muscles cool down. If you build the schedule manually and try to improve it, you can accidentally shorten or stretch these gaps. Stick to the standard rotation; it is not optimised by chance.

Tiebreaker for 6 teams: the standard order of goal difference, head-to-head, goals scored works, but is statistically thin over 5 games per team. A narrow defeat can drop you from first to third if goal difference decides the top. Anyone who wants more stability can put head-to-head before goal difference. Important: in writing beforehand.

7 teams: 21 games in 7 rounds with bye

With 7 teams the effort becomes noticeable. 21 games in total, everyone plays 6 games but in 7 rounds because one team sits out per round. Across the whole tournament every team sits out exactly once. Gross duration on one pitch: 21 x 12 = 252 minutes, just over 4 hours without buffer. That is tight for a standard half-day hall slot.

Anyone who cannot fit 7 teams into a pure round robin timewise uses the standard workaround: a group of four and a group of three play their mini-league in parallel, then semifinals and final. That reduces the game count from 21 to 6 + 3 + 3 = 12 games plus a possible placement game. Gross duration on one pitch drops to 2.4 hours instead of 4.2 hours. The ready-made schedule for that is in the schedule spoke for 5, 7 and 10 teams.

Anyone who still wants to run the classic 7-team round robin should document the bye distribution carefully. In the circle method rotation every team sits out exactly once, but the position of the bye within the tournament differs. Team A sits out in round 7 (at the end), team B in round 4 (in the middle), team C in round 1 (at the start). That seems harmless at first, but in longer tournaments a bye at the start or end can be strategically inconvenient. The team sitting out in round 1 has a cold opening. The team sitting out in round 7 waits through the entire event without being actively involved.

Tip: if you want to influence the bye distribution, assign teams to circle method positions so that weaker teams get the byes at the start and stronger teams get them at the end. The narrative arc for spectators becomes more attractive: exciting final rounds with the top teams, less pressure at the start for the underdogs.

8 teams: 28 games in 7 rounds

Eight teams are the upper limit for a realistic round robin in a club format. 28 games in total, everyone plays 7 games in 7 rounds with 4 parallel matches each. On a single pitch you need 28 x 12 = 336 minutes, roughly 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 that becomes attractive. If you only have one pitch, you almost always switch to two groups of four plus knockout: that reduces the game count to 12 group games plus 3 knockout games (semifinals + final + placement game) = 15 games. Gross duration on one pitch: 3 hours. Realistic for a standard hall tournament slot.

Anyone who still wants to run 8 teams in round robin, for example because the format is intended as a season league with teams competing over several weeks, has a pleasant setup: 7 matchdays with 4 parallel games each. On each matchday every team plays exactly once. That fits well with classic hobby league rhythms where you meet once a week or every two weeks.

Practical example: an 8-team hobby tournament in the club hall. You book the hall every other Sunday from 14:00 to 17:00. Each Sunday 4 games of 30 minutes net are played (15 minutes game time per half, 5 minutes break between games, 30 minutes buffer). That gives 7 matchdays over 14 weeks, roughly 3.5 months. You only need one referee per matchday (or teams referee each other), and at the end every team has played 7 games. The table decides; all further tiebreakers are fixed in advance.

Tiebreaker for 8 teams: with 7 games per team the statistics are already robust. The standard order of 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 settings. 45 games on one pitch take 9 hours gross. That will not fit into one day in most cases. The practical variant: two groups of five plus semifinals and final. That gives 20 group games plus 4 knockout games = 24 games. On two pitches in parallel that is doable in 3.5 hours. With just one pitch you need around 5 hours, which is long but acceptable for a full-day tournament. There is also a ready-made schedule for this.

Anyone who still runs a 10-team round robin as a season league has the same setup as the Bundesliga in miniature: 9 matchdays with 5 parallel games, everyone plays everyone once. In a hobby league with one matchday per week that takes just over 2 months; with one matchday every two weeks roughly 4.5 months. Realistic for a winter season at the club. How you build a full season with a standings table out of this is covered in the guide on how to start a soccer league.

An interesting property of the circle method with 10 teams: because the team count is even, there are no byes. Every team plays on every matchday. The gap on one pitch is only 24 minutes between two of the same team's games, which is very tight if you only have one pitch. With two pitches that relaxes to 48 minutes between your own games, which is considerably more comfortable.

A practical note: with 10 teams in round robin you should explicitly check the pitch assignments. It must not happen that the same team is scheduled on two pitches in the same round. That sounds obvious but goes wrong surprisingly often in hand-built schedules. A schedule generator handles pitch assignments 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 x 12 minutes = 13.2 hours gross. The usual club solution: three groups of four plus knockout, giving 18 group games plus 4 or 5 knockout games depending on the format. Gross time on two pitches: roughly 3 hours. Anyone who still needs the classic 66-game plan (for example for a season league) can get the fixture list in Berger order from the schedule card PDF.

With 12 teams in a season league there are 11 matchdays, each with 6 parallel games. That is the typical scale for an active hobby league. Playing weekly, the season lasts around 3 months. With one matchday every two weeks it is 6 months.

A common mistake with 12 teams: the temptation to squeeze everything into one day by shortening game time. With 5 minutes of game time instead of 10, you reduce gross time to 7 hours. That is doable, but the game time becomes so short that it is sportingly unsatisfying: 5 minutes are not enough for a real tactical contest. For the youngest age groups that is appropriate, but for older groups or adults it feels like warm-up. Better to switch format and do groups plus knockout; then you have sportingly relevant 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 tells you team A plays team E in round 1 and team D in round 2? This is where the circle method comes in. It is the oldest and cleanest algorithm for building a round-robin schedule, documented at the latest in the 19th century in chess tournament organisation.

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

How to read the visualisation: team 1 sits fixed at the top in the first frame. The other teams (2 through 6) are arranged in a circle around it. The pairings per round are formed by connecting opposite teams (team 1 top vs team 4 bottom, team 2 upper right vs team 5 lower 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 have been assigned.

This same algorithm is inside every serious schedule generator: the software runs the rotation for you and you save yourself the manual Berger table. When you use the schedule generator, you are building a Berger table automatically.

What happens with an odd team count?

With an odd team count the circle method does not work 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 to raise the odd N to an even number and run the rotation as usual. The team paired against the bye in a given round sits out.

Over five rounds every team sits out exactly once. Across the whole tournament the bye distribution is therefore fair, even if it looks unbalanced per round. Important in practice: the team sitting out should never sit out twice in a row. The circle method delivers this property automatically because the bye moves to a different team each round.

Walkthrough: circle method for 6 teams step by step

Anyone who wants to follow the algorithm themselves can get to the complete 6-team schedule with a pen and a piece of paper in five minutes. Here is the guide:

Step 1: Write the teams in two rows, A through C in the top row, D through F in the bottom row, with A 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 one position clockwise. A stays fixed. The rotation goes like this: B moves to the lower left, then lower right, then upper right, then back to its starting position. F takes B's place at the top, E moves to the lower 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; each of the 15 pairings has been played exactly once.

This 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 paired against the bye in a given 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 over N-1 steps all N-1 possible relative positions are visited exactly once.

Berger Tables: The Written Form of the Algorithm

When you search for round-robin schedules in practice, you quickly encounter the term Berger table. The name goes back to Austrian chess official Johann Berger, who in 1893 put the system of round pairings for chess tournaments into writing. The algorithm behind it is the circle method. Berger did not invent it but cast it into a handy table format that has appeared in almost every chess organisation handbook since.

A Berger table for 4 participants looks like this:

The numbers are the participants' starting numbers. Per round the parallel pairings sit side by side. With 4 participants there are 3 rounds with 2 matches each, giving 6 games in total. This matches the formula: 4·3/2 = 6.

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

For a football club tournament you do not need a Berger table from a book. If you generate the schedule automatically, you get the same output. Anyone who prefers working with paper or wants to post the plan in the club room, however, will reach for the table format. The schedule card for this article is nothing else: a Berger table in readable format for N=4 to 8.

Where Berger tables still dominate today

In chess, Berger tables are standard for every tournament with a fixed participant count, from a club championship to a FIDE grandmaster event. In table tennis, Berger tables are used for team and individual competitions, from district cup to the Bundesliga. In bridge there are bridge-specific Berger variations that additionally account for seat 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 Berger logic at its core, however: in the first half of the season matches are fixed according to a set scheme, and in the second half they are mirrored (with reversed home rights).

In table form Berger has another advantage: it is deterministic in both directions. You can read from the Berger table which pairing takes place in which round, and you can deduce from an individual pairing which round it plays in. That is useful when you want to know, for example: when does team 3 play team 5? In the printed Berger table you have the answer in two seconds.

Double Round Robin: Home and Away

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

For a club tournament double round robin is almost always overkill. With 6 teams that is 30 instead of 15 games, meaning 6 hours gross instead of 3. It only pays off in two cases: first, when you are running a club championship over several weeks and the home and away factor is real, meaning a different pitch, a different journey for the parents, a 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 a groups-plus-knockout variant gives you a better ratio of game count to effort. Anyone unsure whether classic round robin or another format fits better can compare the formats directly:

The comparison table shows: for 5 to 8 teams single round robin is the fairest option; for larger fields it is worth switching to groups plus knockout. Double round robin is the rarest variant, mainly relevant in 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 top Bundesliga teams play differently in opposing stadiums than at home, and this measurably influences results. For the table to be fair at season's end, every team must have played every other team once at home and once away. This balances the influence of home advantage.

Second: club championships over several weeks where teams play on different days or under different conditions. If your club has four teams and runs a winter season championship, double round robin is the better choice: 12 games over 6 matchdays make for a real season with each team as host and guest.

Third: small tournaments where single round robin would be too short. With 4 teams in single round robin there are only 6 games. If you want to fill an entire club day, that is tight. Double round robin scaled up to 12 games fills the day without having to add knockout games.

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

Padel Tournaments with Round Robin

Padel is structurally different from tennis singles or table tennis as a doubles sport. In padel it is always two against two, which raises the question "who plays who?" to a different level: do you mean pairs or individual players? From this various tournament formats have developed, of which only some are 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 maths applies one to one. With N pairs you play N·(N-1)/2 matches, each match consisting of two sets or a fixed playing time. With 6 fixed pairs that is 15 matches. This is the clean standard variant and common 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 one day. If you play americano with fixed pairs (each pair stays together throughout the tournament), it is mathematically identical to a 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 roughly 9 hours, meaning you almost always need two or more courts.

The key qualifier is "with fixed pairs". There are also americano variants where players switch partners during the tournament. Those fall into the next category.

Americano with rotating partners

When players switch partners within the americano so that everyone plays alongside everyone else at least once, it is no longer classic round robin. The underlying maths is the social golfer problem: given N players, how many rounds do you need for everyone to have partnered everyone else at least once? The answer depends on N and is in the general case even 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 with 2 parallel matches each. Games per player are 6 to 8, not N-1. Anyone planning such a format cannot rely on the N·(N-1)/2 formula.

Mexicano and King of the Court

Mexicano tournaments are seeding-based: after each round pairs are reassembled 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 matches per player depends on the number of rounds you set as organiser, not on the participant count. This shares with round robin only the superficial property that no knockout elimination takes place.

King of the Court goes even further: the winning pair stays on the court and the losing pair is exchanged. The order of matches follows from the results, not a fixed schedule. This is a training and fun format, not a tournament format in the strict sense.

When you need schedules for padel tournaments

AreaCopa is currently football-focused: the formats, data model and game times are tailored to football (soccer) tournaments. If you want to build round-robin schedules for padel tournaments, drop us a 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 collect demand before we build.

What helps us concretely: number of players or pairs, desired playing time per match, number of courts, planned frequency (one-off tournament or season league). On that basis we can assess whether a padel mode has enough volume to be added to our roadmap. As long as that is not the case, we will not build it, but we are happy to listen.

Schedule Card for Printing

The two most important things from this article as a print template: the reference table for all N values between 3 and 20, and the fixture lists for the most common club formats. You print the card, stick it to the boards next to the scoreboard, and everyone involved can immediately see 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 encounters. With an even team count they are spread across N-1 rounds; with an odd team count across N rounds with one bye per round. The circle method delivers 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 practical club use this means: up to about 8 participants pure round robin is the fairest format; from 10 onwards you switch to groups plus knockout. Double round robin is reserved for season leagues. Anyone who does not want to build the schedule by hand lets the circle method run automatically and gets the ready-made schedule displayed in the 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 format.
• 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 standings.
• DFB booklet Wettbewerbsformen im Kinderfußball, as of 09/2024. Deutscher Fußball-Bund. Binding since the 2024/25 season for festival formats U6 to U11, with specific requirements on game times and number of games per participant.