# Generalised Knockout

Keywords: Tournament

In this tournament format, players compete for the top half of the places they still can reach in that round; losers end up in the bottom half, and the process repeats inside each half until each player has a sufficiently unique score. (Sufficiently meaning that a decision can be made for eg prize money - but please read the Inconveniences section).

This format is of theoretical interest only, as it has no significant advantages over Swiss, but does have many downsides.

# Procedure

2. for each round
1. pair equal scored players
2. at the end of the round, double each player's current score, then add 1 point to the score of winners, jigo (if decided so) and byes
3. repeat until first place (1 player has a unique score) is known

# Pairing

• slide or fold pairing is recommended otherwise chances are the second best player will end up in the bottom half after e.g. the first round.
• Bye are given to the strongest player (the one most likely to go to te next round)

Example of detailed ordering inside a score category: (other orderings are likely to exist)

1. descending number of byes: always allocate byes first to maximally distribute byes (to check: maybe there is no need to count byes per player, as a player might mathematically never get more than one bye)
2. ascending strength
3. in case of odd number of players, last player in this list gets a bye.
4. Then proceed with slide pairing

Note that there can still be tiebreak issues here: who's to get the bye? See /bye discussion

• all players keep playing in all rounds (maybe because of this we might no longer call this a knockout tournament.)
• easy (an Excel sheet should suffice, but paper and pen will do fine; cutting A4 into little index cards make it even easier)
• players should not meet each other again: this guarantees a good "mix" of players

# Inconveniences

• players with the same number of victories might not meet each other
• the end score is no indication of strength - only the first and the last place are correctly determined in this system. Exception is for the trivial cases of three players or less.
• an early loss counts heavily (this is a key property of this system); a lucky win places a player relatively high in the end result. This effect could be reduced by increasing the number of games to decide a round. If you want to avoid this disadvantage, use double (or triple) knockout, or use Swiss.
• less suited for large tournaments (N=1000+ participants) as an increasing number of rounds (log2(N)) is needed to decide on the winner. (Swiss has the same issue)

# Notes

• This format could be useful in informal demonstrations involving an audience that is not supposed to have any prior ranking: it is a way to concentrate same-strength beginners (if time permits, each round could be decided by eg two winning games).