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.

Table of contents
Procedure

Pairing

Advantages

Inconveniences

Notes

See also

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Procedure

all players start with a score of 0
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

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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)

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)
ascending strength
in case of odd number of players, last player in this list gets a bye.
Then proceed with slide pairing

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

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Advantages

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

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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)

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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).

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