Single Knockout Tournament Format
Single Knockout Tournament Format, also known as Single Elimination, is a format for pairing players to play games in tournaments.
In the first round, players are paired to play. Those players that lose are eliminated, knocked out of, the tournament. Those players that win, are promoted to the second round. This procedure is repeated till only a single player remains, that player is the tournament winner.
The number of rounds required is the ceiling of the log base 2 of the number of players in the tournament. (Example: 30 players necessitates 5 rounds of play because 2^5 == 32.) As a result, unless the number of players is equal to a power of 2, some players will play one more round than the others. Often the strongest players are not paired in the first round.
Mark Glickman?, creator of the Glicko Rating system adopted by the FIDE, has a paper entitled: Bayesian Optimal Design of Knockout Tournaments. The paper presents two approaches: one that maximizes the probability that the best player will advance to the next round, the other that maximizes the expected log-probability of game outcomes over all possible sets of pairings.