The Swiss Elimination tournament
– an explanation
By Ingvar Gråhök
This post will try to explain how Swiss Elimination tournaments work. While possibly not period (the earliest recorded use in chess tournaments is late 19th century), it is a tournament form that allows
everyone to fight roughly the same number of fights, while still allowing a strong “best competitor on the field” signal.
The tournament is performed in a number of rounds, where all competitors meet someone of the same (or approximately the same) number of wins. The first round pairings are just randomised.
The idea is that no one ever fights the same opponent twice, and in later rounds meeting people with the same (or almost the same) number of wins, allowing for a gradual emergence of the winner.
If you have an uneven number of competitors, one competitor in each round will need to meet the ‘no one’ competitor (this counts as a win). Strictly speaking, it should not matter who you pick, but in
later rounds, it’s probably better picking someone from the lower “accumulated total points” buckets, than picking someone from the higher buckets.
The number of rounds increase as you have more competitors. Specifically, if you double the number of competitors, you need one more round. So for 2 competitors, you need one round; for 4, you need
two rounds; for 8, you need three rounds, and so on.
For numbers that are not powers of two (2, 4, 8, 16, 32, …) you should use the number of rounds for the next-higher power of two. If you don’t want to keep count of the number of rounds in advance, you
can simply continue until you only have one competitor with the highest score. But knowing how many rounds you will have before the tournament starts allows you to plan time better, and may determine if
you run a single match at a time, or if you need to run two, or even three, in parallel.
A worked example
We have 10 particpants, named A through to J (perhaps non-traditional names, but we’ll stick with it for now). Since 2 competitors would require one round, 3-4 two rounds, 5-8 three rounds, and 9-16 four
rounds and 10 is between 9 and 16, this will be four rounds. With 10 people on the field, we have five pairs, for a total of 20 rounds. At an estimated 3 minutes per match, we are looking at about an hour of
|Competitors||D – E||A – C||I –
|H – F||B – G|
|1||C, E, F, G, I|
|0||A, B, D, H, J|
In this round, we’ll need to have a 1-point competitor meet a 0-point
competitor, since there’s no way of neatly pair five competitors
up. This is essentially a random choice.
|Competitors||C – E||F – G||A -I||B – D||H – J|
|2||E, G, I|
|1||C, D, F, J|
|0||A, B, H|
In this round, we’l end up with half of the 1-point competitors meeting people with a higher or lower score. Again, this is essentially a random choice.
|Competitors||E – G||C – I||D -F||A – J||B – H|
|2||F, G, J|
|1||C, D, H|
Final round, after this round, we’ll have a single competitor with 4 points and a single competitor with 0 points.
|Competitors||E – I||F – J||C – G||D – H||A – B|
|3||E, G, K|
|1||B, C, D|