26 players horseshoies

[robo]

hi   I was helped out tremendously last year      I run a horseshoe league   this year 26 players(24 was apparently easy for scheduling)-  We play doubles   each player having a different partner each week. I have subs etc. If you win you get a point.  Seems that for 26 the scheduling entails some single play--which if that is the way it is so be it--any other suggestions ?  I have the whist for 26 players (doubles0 which entails the above,

Any other site etc ?

Thanks

Robo

[Ian Wakeling]

Hi,

How many weeks does the season last?  It will be the case that the best schedules will have either 13 or 26 weeks - if you had 6 doubles matches and two byes each week, then you would need 13 or 26 weeks to give everyone the same number of matches - alternatively if you had 6 doubles and one singles match each week then you would need 13 or 26 weeks to give everyone the same number of singles matches.  Would either of these options be practical?

Ian.

[robo]

Thanks    after further thought  and looking at whisk asymmetry which uses singles each week    I am leaving it the way it is but instead of singles playing I am having the 4 singles that would play each week play each other as a double.  I have 12 doubles matches each week and now a 13th doing it that way. It may not work out perfectly, but singles are a hassle.  Doubles I can get a sub, singles entails rematch  etc..

The way I work it is if you win you get a point--if a sub fills in for you you can't get a point.  You have a new partner pretty much each week,  What do you think? Last year was easy with 24 players.


Thanks  again

[Pakizogi]

I am kind of in the same boat as the horseshoe gentleman.  I run a 32 person mixed couple blind draw league.  I am trying to have each man play against each other once and match up the ladies to play against each other once as well while not playing with the same man more than once as well.  Is this even possible?  I have the men figured out playing a 15 week round robin schedule, but I can't seem to figure out how to approach getting the women to line up correctly.  I have spent countless hours on this and I feel like my brain is frazzled.......

Can anyone help?

[Ian Wakeling]

Yes, this is possible.  The problem has been studied by mathematicians since the 1970s, originally in the context of mixed doubles tennis for a club in NY State. There is a slight imbalance in the problem owing to the fact that there are 15 possible opponents of the same sex, but 16 possible partners/opponents of the opposite sex.  This is usually solved by making a spouse avoiding mixed doubles round robin, so in the schedule below the men are M1 to M16 and the women are F1 to F16.  The spouse pairs (M1 F1), (M2 F2), etc. never meet as partners or opponents, but otherwise the schedule meets your requirements above.

Round 1
(M1 F4 v M2 F3)
(M3 F2 v M4 F1)
(M5 F8 v M6 F7)
(M7 F6 v M8 F5)
(M9 F12 v M10 F11)
(M11 F10 v M12 F9)
(M13 F16 v M14 F15)
(M15 F14 v M16 F13)

Round 2
(M1 F7 v M3 F5)
(M2 F8 v M4 F6)
(M5 F3 v M7 F1)
(M6 F4 v M8 F2)
(M9 F15 v M11 F13)
(M10 F16 v M12 F14)
(M13 F11 v M15 F9)
(M14 F12 v M16 F10)

Round 3
(M1 F6 v M4 F7)
(M2 F5 v M3 F8)
(M5 F2 v M8 F3)
(M6 F1 v M7 F4)
(M9 F14 v M12 F15)
(M10 F13 v M11 F16)
(M13 F10 v M16 F11)
(M14 F9 v M15 F12)

Round 4
(M1 F13 v M5 F9)
(M2 F14 v M6 F10)
(M3 F15 v M7 F11)
(M4 F16 v M8 F12)
(M9 F5 v M13 F1)
(M10 F6 v M14 F2)
(M11 F7 v M15 F3)
(M12 F8 v M16 F4)

Round 5
(M1 F16 v M6 F11)
(M2 F15 v M5 F12)
(M3 F14 v M8 F9)
(M4 F13 v M7 F10)
(M9 F8 v M14 F3)
(M10 F7 v M13 F4)
(M11 F6 v M16 F1)
(M12 F5 v M15 F2)

Round 6
(M1 F11 v M7 F13)
(M2 F12 v M8 F14)
(M3 F9 v M5 F15)
(M4 F10 v M6 F16)
(M9 F3 v M15 F5)
(M10 F4 v M16 F6)
(M11 F1 v M13 F7)
(M12 F2 v M14 F8)

Round 7
(M1 F10 v M8 F15)
(M2 F9 v M7 F16)
(M3 F12 v M6 F13)
(M4 F11 v M5 F14)
(M9 F2 v M16 F7)
(M10 F1 v M15 F8)
(M11 F4 v M14 F5)
(M12 F3 v M13 F6)

Round 8
(M1 F2 v M9 F10)
(M2 F1 v M10 F9)
(M3 F4 v M11 F12)
(M4 F3 v M12 F11)
(M5 F6 v M13 F14)
(M6 F5 v M14 F13)
(M7 F8 v M15 F16)
(M8 F7 v M16 F15)

Round 9
(M1 F3 v M10 F12)
(M2 F4 v M9 F11)
(M3 F1 v M12 F10)
(M4 F2 v M11 F9)
(M5 F7 v M14 F16)
(M6 F8 v M13 F15)
(M7 F5 v M16 F14)
(M8 F6 v M15 F13)

Round 10
(M1 F8 v M11 F14)
(M2 F7 v M12 F13)
(M3 F6 v M9 F16)
(M4 F5 v M10 F15)
(M5 F4 v M15 F10)
(M6 F3 v M16 F9)
(M7 F2 v M13 F12)
(M8 F1 v M14 F11)

Round 11
(M1 F5 v M12 F16)
(M2 F6 v M11 F15)
(M3 F7 v M10 F14)
(M4 F8 v M9 F13)
(M5 F1 v M16 F12)
(M6 F2 v M15 F11)
(M7 F3 v M14 F10)
(M8 F4 v M13 F9)

Round 12
(M1 F14 v M13 F2)
(M2 F13 v M14 F1)
(M3 F16 v M15 F4)
(M4 F15 v M16 F3)
(M5 F10 v M9 F6)
(M6 F9 v M10 F5)
(M7 F12 v M11 F8)
(M8 F11 v M12 F7)

Round 13
(M1 F15 v M14 F4)
(M2 F16 v M13 F3)
(M3 F13 v M16 F2)
(M4 F14 v M15 F1)
(M5 F11 v M10 F8)
(M6 F12 v M9 F7)
(M7 F9 v M12 F6)
(M8 F10 v M11 F5)

Round 14
(M1 F12 v M15 F6)
(M2 F11 v M16 F5)
(M3 F10 v M13 F8)
(M4 F9 v M14 F7)
(M5 F16 v M11 F2)
(M6 F15 v M12 F1)
(M7 F14 v M9 F4)
(M8 F13 v M10 F3)

Round 15
(M1 F9 v M16 F8)
(M2 F10 v M15 F7)
(M3 F11 v M14 F6)
(M4 F12 v M13 F5)
(M5 F13 v M12 F4)
(M6 F14 v M11 F3)
(M7 F15 v M10 F2)
(M8 F16 v M9 F1)

[Pakizogi]

Thanks Ian, I was going bonkers..  This is very helpful.....