All-play-all Tournaments and the Berger Tables

Berger Tables

3-4 teams
Round 1		Round 2		Round 3
H	A	H	A	H	A
1	(4)	1	2	3	1
2	3	(4)	3	2	(4)

5-6 teams
Round 1		Round 2		Round 3		Round 4		Round 5
H	A	H	A	H	A	H	A	H	A
1	(6)	1	2	3	1	1	4	5	1
2	5	5	3	4	5	2	3	4	2
3	4	(6)	4	2	(6)	(6)	5	3	(6)

7-8 teams
Round 1		Round 2		Round 3		Round 4		Round 5		Round 6		Round 7
H	A	H	A	H	A	H	A	H	A	H	A	H	A
1	(8)	1	2	3	1	1	4	5	1	1	6	7	1
2	7	7	3	4	7	2	3	4	2	2	5	6	2
3	6	6	4	5	6	7	5	6	7	3	4	5	3
4	5	(8)	5	2	(8)	(8)	6	3	(8)	(8)	7	4	(8)

Each team plays each other team in ascending numerical order, alternating colours/venues. When a team would be scheduled to play itself, it instead plays the highest-numbered team. This formula gives you two ways to generate each pairing - once from the point of view of each team.

The Swiss System

The Swiss System in 30 seconds

Every competitor plays in every round.
A win is worth 1 point and a draw is worth ½ a point.
At the start of every round, every competitor is paired with an opponent with the same score, or as close to the same score as possible.
You can't play the same person twice. (So you have to keep track of who has played who.)

The Swiss System in 10 minutes

Floating

Since players should be paired against opponents with the same score, the first thing to do is divide them into score groups. A score group is simply all of the players with the same score. After Round 1, you'll have a 1 score group, (usually) a ½ score group, and a 0 score group.

Start with the 1 score group. If you have an even number of 1s, you can pair every 1 with another 1. If you have an odd number, you have to borrow one player from the ½ score group to make it up to an even number.

The pairing between the 1 and the ½ is a float. The 1 who gets paired with the ½ is a downfloater. The ½ who gets paired with the 1 is an upfloater.

Make a note of who your downfloaters and upfloaters are. If possible, don't float the same player in the same direction twice. So if the 1 beats the ½, and then the 2 score group also ends up with an odd number of players in it, choose a different 2 to be floated down.

Colour Preferences

Chess is a game between White and Black. White wins about 45% of games and Black about 35%, so you should give each player roughly equal numbers of Whites and Blacks over the course of the tournament.

The easiest way to do that is to pair White seekers with Black seekers.

If you had White in the first round, you're a Black seeker in the pairings for the second round. If you had Black, you're a White seeker.

The sequence of Blacks and Whites that you've had so far in the tournament is your colour history. For Round 2, you want to pair people with a colour history of "B" against people with a colour history of "W", so that the B player gets White and the W player gets Black.

This will result in two players reaching Round 3 with colour histories of BW and WB. This is good. Either of those players can now take either colour pieces in Round 3.

If you don't have equal numbers of White seekers and Black seekers, you'll have to pair two White seekers together or two Black seekers together. That means they'll get a colour history of WW or BB. A WW player must be given Black in Round 3. A BB player must be given White. These players have an absolute colour preference.

Chess Clocks and Time Controls

A chess clock is used for keeping track of time for both players.