First of all thanks for all the Round Robin information. I don't know if you have a solution to my problem.
We play four man teams in pool. I'm trying to arrange the pairing so that each member of one team plays each member of the other team for a total of 16 games. I have a crude schedule made but the problem is that
some players will have much longer waits between games then others. I'd like to re-organize it so each player has as close to the same wait as possible. To further complicate it each player has to break twice and rack twice.
Any ideas would be much appreciated.
Thursday, January 29 2004, 03:46 pm
Franklin, PA
I didn't take the time to figure out if I could figure out the optimum arrangement. I did write a program to find the
best out of 1 million random permutations of the pairwise matchings. So, maybe this is good enough.
H A HW AW
- - -- --
a y 1 1
d z 2 2
c w 3 3
b y 4 3
d x 3 5
a w 5 3
b z 3 5
c y 5 4
a x 3 4
d w 5 4
c z 3 4
b x 5 3
d y 3 5
a z 5 3
b w 3 5
c x 5 4
H - Home
A - Away
HW - How many games ago H last played
AW - How many games ago A last played
A B C D are the home teams
W X Y Z are the away teams
minmax=5 minstd=1.1845783243
The
best plan is the one with the least most wait (minmax) and the least standard deviation at minmax (minstd). Using the minimum standard deviation hopefully means the perception of the distribution of waiting times are 'fair' to most players.
