# Round Robin Tournament Scheduling

by Richard A. DeVenezia, Back to Home Read Guestbook Message Board

Just looking for tables ? Go here...

The problem of scheduling a tournament in which all participants compete against each other one-on-one in a series of rounds probably goes back to pre-history. This page presents some thoughts of the author on the problem and some software to explore various ways to look at it.

The terminology of a round robin may differ according to it's application. The pairing of two items (one-on-one) might be known as a game, match, outing. An item that is paired might be known as a player or team. A round might be known as a week or meet.

## Whist

A whist tournament is a variation of a round robin. In a whist tournament the team a player is on varies over the course of the tournament. By the end of the tournament each player has been teamed with each player one time, and opposed each player two times. It might help to think of round robins as based on pairs, and whist as based on pairs of pairs.

Schedules for whist tournments involving 4n people are available here. Additional information and schedules (1 to 24 Bridge tables, 4n or 4n+1 players) can be found at Durango Bill's website, be sure to check it out.

## Cyclic algorithm

While updating the first fit algorithm (see below) I did some newsgroup searches and turned up a cyclic algorithm for scheduling. One item is locked while the others rotate. At each step of the rotation the round is planned by pairing items.

• sci.math.num-analysis newsgroup thread discussing planning and proving a round robin algorithm
• Some javascript for visualizing the cyclic algorithm
• Java applet based on the Ron Shepard post
• This is a visual gist of the algorithm when scheduling ten items.
Press 'Go' to start rotating the reddish cells clockwise.
 3 4 5 6 1 2 10 9 8 7 Pair 1 Pair 2 Pair 3 Pair 4 Pair 5 0

## Tidbits

• Eelke Spaak's Tournament Scheduler page can generate schedules using names and locations you enter. I like the ease of use and minimalist interface.
• If you have an odd number of players, invite a ghost to play. Whoever plays the ghost gets a bye.
• Random House dictionary word of the day, April 26, 2001. [link contributed by Ian Wakeling]
• Why is it called Round-Robin anyway? I don't know.
I have read various sources that state the term first appeared to describe how people would sign documents of grievance in a circular fashion to preserve anonymity of status within the group. E.g. Naval officers ( see here ) or 17th-century French politicians. Back in those days of yore it seems the head griever quickly became headless.
• Interested in balancing Home and Away?
• See Berger Pairing tables. The tables utilize rearrangement patterns and are used in chess tournaments.
• Warren Porter has webpage for generating round robin pairings for a variety of constraints, including chess play arrangements per Berger, Porter, Crenshaw and sequential play, as well as Court Balanced scheduling based on Ian Wakelings spreadsheet.
• Ian Wakeling posted a Court Balanced Round Robin spreadsheet in the message boards.
• And finally, the author implemented Ians algorithm on the schedules page.

## First fit algorithm

My first analysis of the problem (and by no means complete, succinct, accurate or appropriate) was in 1991. The analysis looked at the problem from the standpoint of a first fitting pair algorithm that would scan lists of pairs and determine their eligibility for inclusion in a round. The products of this analysis are thus:

## Social squares

Plan a schedule for M teams of M players. In each round all M teams will play. M+1 rounds will be played. In each round each player is teamed with all new people; in other words, each player is teamed with each other player only once.

## Team play

Plan a tournament for 12 players. Two person teams. Everyone gets teamed with everyone else one time. Everyone plays against a team having everyone else on it twice. In combinatoric literature this is a Whist tournament.

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