Round Robin Tournament Scheduling

Partial Whist (golf) competition

sdu60 · 3 · 4250

sdu60

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on: May 08, 2009, 10:22:14 AM
12 players enter a round robin golf tournament which consists of 5 rounds only.
They play in fours, that is two against two and each round will therefore consist of 3 games.
Ideally they would like the draw to permit them to play only once with the same person and once against each opponent or at least once against players they have not partnered. The objective is to "see" each player at least once.

Using the Whist draw system (12 people - 3 tables) is a start but the objective there is to play once with a person and twice against. This requires 11 rounds for 12 players. By limiting the number of times a player meets an opponent to one should reduce the number of rounds required - I think>  However I have not been able to produce a reasonable or optimised result. Most efforts result in some competitors "meeting" a fellow competitor 3 times while not meeting other competitors at all. (" meeting"means either playing against or partnering)

Can anyone propose an optimised draw?


Ian Wakeling

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Reply #1 on: May 09, 2009, 01:24:25 AM
All such schedules will have a minimum of 6 pairs of competitors who never meet.  This is an unavoidable problem that is discussed here.

So I think the following is about the best you can do:

 (10  9 v  4  2)  ( 3 12 v  6  8)  (11  7 v  5  1)                                        
 ( 6 10 v  5  3)  ( 4 12 v  7  9)  (11  8 v  1  2)                                        
 ( 7  6 v  1  4)  ( 5 12 v  8 10)  (11  9 v  2  3)                                        
 ( 8  7 v  2  5)  ( 1 12 v  9  6)  (11 10 v  3  4)                                        
 ( 9  8 v  3  1)  ( 2 12 v 10  7)  (11  6 v  4  5)  


Players play in partnership with 5 of the other players exactly once, and in opposition with a different 5 players exactly twice.  In other words no pairs of competitors are meeting three times.
« Last Edit: May 09, 2009, 01:25:55 AM by Ian »


Carey

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Reply #2 on: February 18, 2011, 04:13:22 AM
 :) Thank you so much, you have saved the last of my hair!!  I have had awful trouble in trying to avoid some players having to meet 3 times but you have done that nicely. Everyone will miss playing with 2 members which is as good as it gets.   Cheers  John C