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euchre round robin schedule (Read 11972 times)
oliver
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euchre round robin schedule
04/24/06 at 19:30:44
 
Hi - trying to figure out the way to schedule a round robin tournament for euchre (team-based card game).  4 players constitute a game (2 people vs 2 people), and we have 10 players.  Thus, 2 players will be on bye for a given round.  We are trying to set up the tourney such that:
 
1) each player plays the same # rounds (and therefore must have same # byes)
2) want to optimize (ie balance) how often one plays with/against others
 
ex:
Round 1: (1,2) vs (3,4) and (5,6) vs (7,8) with 9,10 on bye
Round 2: etc
 
We are open to how many rounds we would play, though ideally it would be somewhere in the 10-15 rounds range.
 
(While this tourney has a specific # players, would be great if a scheduler existed that allowed one to plug in N players and X desired rounds.)
 
Thanks in advance,
Oliver
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Ian Wakeling
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Re: euchre round robin schedule
Reply #1 - 04/25/06 at 13:57:03
 
Oliver,
 
The general problem of N players and X rounds would be a very hard problem to automate well. The only easy solutions are the Whist designs when N is divisible by 4 and there are N-1 rounds (to see some of these follow the link above to "Schedules").
 
Moving on to your specific problem above, I would choose 15 rounds as this seems to me to offer the best opportunity for balance.
 

Rnd    Table 1        Table 2      Bye
 1  (0 1) v (6 8)  (2 7) v (3 9)  (4 5)
 2  (2 3) v (8 0)  (4 9) v (5 1)  (6 7)
 3  (4 5) v (0 2)  (6 1) v (7 3)  (8 9)
 4  (6 7) v (2 4)  (8 3) v (9 5)  (0 1)
 5  (8 9) v (4 6)  (0 5) v (1 7)  (2 3)
 
 6  (1 2) v (7 9)  (3 8) v (4 0)  (5 6)
 7  (3 4) v (9 1)  (5 0) v (6 2)  (7 8)
 8  (5 6) v (1 3)  (7 2) v (8 4)  (9 0)
 9  (7 8) v (3 5)  (9 4) v (0 6)  (1 2)
10  (9 0) v (5 7)  (1 6) v (2 8)  (3 4)
 
11  (3 6) v (4 7)  (8 1) v (9 2)  (5 0)
12  (0 3) v (1 4)  (5 8) v (6 9)  (2 7)
13  (2 5) v (3 6)  (7 0) v (8 1)  (4 9)
14  (4 7) v (5 8)  (9 2) v (0 3)  (6 1)
15  (1 4) v (2 5)  (6 9) v (7 0)  (3 8)

 
Above, I have used 0..9 to represent the 10 players.  The schedule has the following properties.
 
Each player has one bye in each block of 5 rounds.
For any one player there is at least 2 rounds of play between byes.
 
All pairs of players partner each other at least once and at most twice.
All pairs of players oppose each other at least twice and at most three times.
 
All players sit at the same table with all other players (either as a partner or an opponent) exactly four times. This "social" balance is the  reason why I chose 15 rounds in the first place.
 
Hope that's useful for the tourney your are planning,
 
Ian.
 
PS note all the repeated partnerships occur in rounds 11-15.
 
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oliver
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Re: euchre round robin schedule
Reply #2 - 04/25/06 at 16:27:58
 
Thank you!  This schedule looks great.
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