Tournament with 2 group of players

[Pif_81]

hello,
I would like to organize friendly tournaments with the following rules:
- A group of top players.       (A.. Z)
- A group of weaker players. (1 .. 26)
example: if there are 14 players in total, two groups of 7 players

The purpose is to play with a different partner each round and against different players in each round.

Example: with 8 players

Round     1          2          3
       A1 - B2    A2 - C4    A4 - D1
       C3 - D4    B1 - D3    B3 - C2

It is not necessary to randomize the round (I can randomize the player name),not necessary to manage the court balance,
the exact number of players is variant and this number is always even (I play if necessary)

Can you help me.
Thanks.

[Ian Wakeling]

If you have a multiple of 4 players (not 12 or 20) then you could use the spouse avoiding schedules.  Just replace the 'H' by 'T' and then your top players are T1...Tn   and the weak players are W1...Wn.   This will not be a fully balanced solution as you have no good reason to prevent T1 playing with or against W1 for example, so you could add an extra round (see the schedule for 16 players).  In fact there is no balanced solution possible since if I am T1, then there are n weaker players to play with (or against) me, but only (n-1) top players to play against me.  Unfortunately I have no schedules that might help if there are 4n+2 players (e.g. the 14 that you mention).

Hope that helps.

[Pif_81]

Thank you for your help.

I know the problem that there are (n-1) oponents and (n) partners.
But I don't understand why there is no schedule for 4n+2 players,
even if you use ghost players (e.g. 14 players = 2 ghosts every round)

[Ian Wakeling]

Thanks for your reply.  I couldn't have been thinking straight earlier since you are perfectly correct about 4n+2,  there is even an example for 18 players when you follow the link above!

Here is an updated version of the list with a few more schedules:

8 players
10 players - see below
12 players - no balanced schedule exists.
14 players - see below
16 players
18 players
20 players - no balanced schedule exists but see here
22 players - see below
24 players
32 players

10 players:
[(H1 W2):(H5 W4)] [(H2 W5):(H4 W1)]
[(H3 W4):(H2 W1)] [(H4 W2):(H1 W3)]
[(H5 W1):(H4 W3)] [(H1 W4):(H3 W5)]
[(H2 W3):(H1 W5)] [(H3 W1):(H5 W2)]
[(H4 W5):(H3 W2)] [(H5 W3):(H2 W4)]

14 players:
[(H6 W3):(H1 W2)] [(H3 W4):(H2 W5)] [(H5 W6):(H4 W1)]
[(H7 W4):(H5 W3)] [(H4 W6):(H3 W2)] [(H2 W7):(H6 W5)]
[(H5 W7):(H3 W6)] [(H7 W1):(H6 W4)] [(H4 W5):(H1 W3)]
[(H4 W2):(H7 W5)] [(H2 W3):(H5 W1)] [(H1 W4):(H3 W7)]
[(H2 W1):(H4 W7)] [(H1 W5):(H7 W6)] [(H6 W2):(H5 W4)]
[(H1 W6):(H2 W4)] [(H6 W7):(H4 W3)] [(H3 W1):(H7 W2)]
[(H3 W5):(H6 W1)] [(H5 W2):(H1 W7)] [(H7 W3):(H2 W6)]

22 players:
[(H01 W10):(H09 W11)] [(H10 W04):(H11 W02)] [(H08 W07):(H03 W05)] [(H05 W09):(H07 W01)] [(H04 W08):(H02 W03)]
[(H02 W07):(H06 W04)] [(H07 W09):(H04 W10)] [(H03 W08):(H05 W11)] [(H11 W06):(H08 W02)] [(H09 W03):(H10 W05)]
[(H08 W05):(H10 W01)] [(H05 W02):(H01 W03)] [(H04 W11):(H09 W06)] [(H06 W10):(H11 W08)] [(H02 W04):(H03 W09)]
[(H03 W11):(H07 W02)] [(H11 W10):(H02 W05)] [(H09 W04):(H06 W01)] [(H01 W07):(H04 W03)] [(H10 W09):(H05 W06)]
[(H11 W09):(H03 W07)] [(H09 W08):(H07 W04)] [(H01 W06):(H02 W10)] [(H10 W03):(H06 W11)] [(H08 W01):(H04 W02)]
[(H07 W03):(H02 W06)] [(H03 W01):(H06 W08)] [(H11 W05):(H04 W09)] [(H09 W02):(H05 W07)] [(H01 W11):(H08 W04)]
[(H10 W08):(H01 W09)] [(H08 W06):(H09 W07)] [(H05 W03):(H11 W04)] [(H04 W01):(H03 W10)] [(H06 W05):(H07 W11)]
[(H09 W01):(H11 W03)] [(H01 W05):(H03 W06)] [(H10 W02):(H07 W08)] [(H08 W11):(H02 W09)] [(H05 W10):(H06 W07)]
[(H06 W02):(H04 W05)] [(H02 W11):(H05 W01)] [(H07 W10):(H08 W03)] [(H03 W04):(H10 W06)] [(H11 W07):(H01 W08)]
[(H05 W04):(H08 W10)] [(H04 W07):(H10 W11)] [(H06 W09):(H01 W02)] [(H02 W08):(H09 W05)] [(H07 W06):(H11 W01)]
[(H04 W06):(H05 W08)] [(H06 W03):(H08 W09)] [(H02 W01):(H10 W07)] [(H07 W05):(H01 W04)] [(H03 W02):(H09 W10)]

[Pif_81]

Thank you for your quickly answer.

[Pif_81]

Hi,

an other question, have you a prgramme to do this ? what is the method to do this ?

[Ian Wakeling]

Yes they were generated by a programme - the method is not simple as it is implementing a number of combinatorial constructions. For the methods try searching the following terms SAMDRR and SOLSSOM (in full a Spouse Avoiding Mixed Doubles Round Robin and a Self Orthogonal Latin Square with a Symmetric Orthogonal Mate).  Chapter III.5 in this book is a good source.

[Pif_81]

Hello,

I'm preparing excel file to make my tournament but can you complete with schedule
(if it is possible) for 26, 28, 30 and other until 40 players

After that I can send you to have your opinion.

Thanks you.