Swiss style tournaments
Swiss style tournaments seem more inclusive than single- and double-elimination tournaments, in that no player is ever forced to drop from the tournament. After each round, all players are matched up against other players with the same win-loss record. So in the fifth round of play, all the 4-0 players compete against each other, all the 3-1 players compete against each other, etc., down to the players who are all 0-4, playing against each other. Generally the tournament continues until there is only one undefeated player, or sometimes for one or two rounds beyond that, in order to ensure that players who have previously lost a round (or two) could still win the tournament. (For fairness' sake, the number of rounds must be announced after the number of entrants is known but before the tournament begins.)
If the number of players is large, Swiss-style tournaments are easy for tournament organizers to run because there is less need to fill in slots of a bracket with "byes" (see below). A maximum of one bye is needed per round of a Swiss tournament, and that is only needed if there is an odd number of players competing in that round.
In some Swiss tournaments, the tournament continues for a certain number of rounds, at which point the main tournament ends and the top 8 players continue on to play an 8-player single- or double-elimination playoff tournament for the victory.
At a certain point in a Swiss-style tournament, it becomes obvious to players when they have been mathematically eliminated from being able to win or place high, but they can continue playing if they choose -- perhaps to boost their rating, if the tournament organizer reports player ratings to the sport's ratings authority.
Brackets, and Initial Matchups
Often a "bracket" is physically drawn on a sheet of paper or whiteboard for the benefit of spectators and players, especially in single- and double-elimination tournaments, showing who is playing whom, and making it easy to see who will be matched up in future rounds depending on who wins each game.
A 16-player, single-elimination tournament bracket. The quarterfinals have been completed, and the semifinal games will be Lisa vs. Ernie, and Andrew vs. Robert. Then the finals will be a game between the two people who won in the semifinals.
The easiest way for a tournament organizer to match up participants in the first round of a tournament is to do so randomly. However, a more satisfactory tournament (for spectators) can often be created by initially matching the best (or "top seeded"😉 several players against players who are not in the "best" rank, and placing these players in the bracket such that it is probable that the best four players will end up playing each other in the semifinals.
By looking at a single-elimination bracket it quickly becomes clear that tournaments are easy to run only if they have a number of players which is a power of 2: i.e. 8, 16, 32, 64, 128, 256, etc. Having this exact number of players ensures that all players have somebody to compete against every round. In tournaments open to the general public, it is unlikely that this exact number of players will enroll, and in any case players may decide to voluntarily drop from the tournament at any point, so "byes" are used to fill holes in the bracket.
A player gets a bye when there is simply no opponent for him to play that round. Getting a bye is considered fortunate for a player; he is guaranteed to advance to the next round. Sometimes many byes are granted in a particular round because of holes in the bracket. The aim of the byes is to have the number of players be equal to a power of 2 in the next round, or possibly the round after that.
In some tournaments such as the playoffs of the NFL, byes are prizes to be earned by teams who do well in previous play.
Sometimes a "tiebreaker" statistic is needed to separate players who have the same win-loss record, particularly for the purpose of awarding prizes to the top players. For example, after five rounds of play in a Swiss-style tournament, 4th through 7th places are often taken by players who all have a 3-2 record. Often-used tiebreakers are score averages in the individual games played so far in the tournament, opponents' winning percentages, the total number of points scored by the player in the tournament, the total number of points scored by all the player's opponents in the tournament, and so forth. (The inability to boost one's tiebreaker statistics is considered the only disadvantage of receiving a bye in a previous round.)