A Little Round Robin

Today a small example of practical tournament administration.

The Indiana Challenge Cup is contested by three teams of six players from each of the three backgammon clubs in Indiana. The players are ranked, within the team, in order of their standing in the local club. They’re put into three pools, one with the first and second ranked players, another with the thirds and fourths, and the last with the fifths and sixths. A round robin is played within each pool (except that players from the same club don’t play each other), and the club championship is determined by the overall number of wins by the members of each club.

Last year, as it happened, the ICC suffered from one of the common maladies of round robin tournaments – the ambiguous result. At the end of the four rounds, the scores were 12-12-12, so that tiebreakers needed to be applied. One team was eliminated on the basis of the record of their first-ranked player, and the other two teams had a doubles playoff round.

My club hosts the tournament this year, and I’ve put some thought into the preparation.

The first problem is to make pairings so that all of the right matches are played in the minimum of four rounds. The key to doing this is to recognize that each of the three pools is a six-player round robin, with one of the matches missing.

Let’s call the teams A, B, and C. Pool 1 is a round robin among A1, A2, B1, B2, C1, and C2. So, to make sure that the matches you don’t want to play all fall in the same round, start with those pairings as the base case:

To make a round robin with any number of players, one simply starts with any pairings at all for the first round. For subsequent rounds, hold one player in place – A1 in the example here – and rotate the others. All of the players except A1 rotate clockwise. Then, since the matches that shouldn’t be played are together in the first round, omit that round and play the others. The other two pools simply substitute A3 for A1, A4 for A2, B3 for B1, and so forth.

As usual for round robins, the results are tabulated on a matrix, To make this a little easier, I’ve color-coded each cell by round, with round one in yellow, round two in pink, and on to green and blue. Here’s one of the three.

Each player gets a “dance card”, listing their matches in the order in which they need to be played. I’ve color-coded that, also, which is probably overkill, but I thought it might be useful for each player to have a handy reference for the colors associated with each round. Here’s my own dance card. 

The summary score sheet also has a track that shows the cumulative score for a hypothetical playing of the tournament. Here is the summary sheet for an ICC score summary example. Please note, the numbers on this sheet are there only to show how I expect the sheet to be used – they are not real results – I simply flipped a coin for each of the 36 matches. That yielded a rather unlikely result in which the team from the suburbs of Chicago trounced the other two teams, with an indifferent 2-2 result for John O’Hagan. John is almost certainly the best player who will take part, being the only Hoosier ranked among the Giants of Backgammon.  I have never beaten him in real life.