## How seatings work

Pantheon offers several options of how seatings can be made:

- Random seating
- Swiss seating
- Interval-based seating
- Predefined seating

Here are some details about them.

### Random seating

- This seating can be used any time during the tournament, because it doesn't take into account any previous data.
- When using this seating, players are shuffled randomly.
- There can be (and most likely will be) intersections, if this seating is used on later stages of a tournament.
- This is the only seating you can use in the beginning of the tournament.

### Swiss seating

- This seating uses both current positions of players in the rating table and the games history to minimize intersections.
- Swiss seating can't be used if no games were played yet.
- The seating has two goals:
- Minimization of intersections count (as possible)
- Players should play with more or less equal opponents according to the current rating (as possible, too)

- Basic seating algorithm:
- Take current rating table and select first player (the one who has biggest score).
- Look down the table and search for the first player with the biggest score, who didn't play with the selected one yet, and select them too.
- Look down the table and search for the first player with the biggest score, who didn't play with both the selected ones yet, and select them too.
- Last player is found the same way. This is our first table. Selected players are excluded from the table.
- The steps above are repeated until all tables are determined.
- On later stages of tournament, it might be impossible to find suitable combination of players, in this case the condition "who didn't play with the selected ones yet" is replaced by "who has the least intersection when the selected ones".
- The algorithm generates more than one combination at a time, counting total intersections count. The combination which has the least total intersections count is then selected.
- There is also a complexity limit (in general, the solution is found in non-polynomial time). When generation time is expired, the best combination of already generated is selected.
- In case of table count being not a multiple of power of 2, last tables are formed according to the residual principle. This means that on last tables the probability of intersection is increased drastically.

### Interval-based seating

- This seating uses only current positions of players in rating table.
- Interval-based seating can't be used if no games were played yet.
- The input of the algorithm is integer interval.
- If the interval is 1, tables will play according to current positions: 1-2-3-4, 5-6-7-8, and so on.
- If the interval is 2, tables will play as follows: 1-3-5-7, 2-4-6-8, and so on.
- And so on.

- Note that tables are selected sequentially, e.g. first table is selected, then second one, then third one. In case of odd interval, first 12 players will play at first three tables, second 12 - at second three tables, and so on.
- In case of table count being not a multiple of selected interval, last tables are formed according to the residual principle. This means that on last tables the probability of intersection is increased drastically.

### Predefined seating

- This kind of seatings doesn't go well along with previous three, because it requires preparing a seating script in advance.
- Tournament administrator defines the seating script in event settings, using local identifiers of players (integers from 1 to N).
- Next, it's required to define which player has which local identifier on players management page.
- After that, the tournament can be started.
- There is "Current game" field on script definition page, which is updated automtically every time the game results are confirmed.
- Technically, you can change the tournament type to use automatic seatings, they will use ratings table and history of games. Though, it's generally not recommended to change the tournament type backwards (from automatic seatings to predefined), because it would require you to define a script with some fake games in the beginning and set appropriate game index in the "Current game" field.

Mahjong Pantheon dream team, 2024.