HELP!!! I need a schedule for a Euchre Tournament

[melina69]

I am having 44 individual players and 11 tables.
I would like to have everyone play with a different person and against different people if possible for each round.
We will be playing 7 games.
Can anyone help me set this schedule up???
Thanks,
Melina

[Ian Wakeling]

Hi Melina,

In the schedule below, I give 9 rounds of play (R1 to R9) with the property that a player's 9 partners and 18 opponents are all different people.  So for your tournament you can choose any seven out of the 9 rounds.  The schedule also has additional properties.  If you label the tables A to K as I have done below,  then a player will never play on the same table twice.  Finally note the cyclic nature of the 11 matches in each round which you can make good use of.  Let's say you divide the 44 players into two teams as follows, players 1-22 in team 1 and players 23-44 in team 2, then every match will be a partnership drawn from team 1 against a partnership from the other team.

There is a zipped Excel file attached with the same schedule.

Hope that helps,

Ian.

Note for golfers: this would work for a society of 44 players playing 9 rounds of foursomes.

    Table         Match
R1    A    [( 9 20) v (27 40)]
      B    [(10 21) v (28 41)]
      C    [(11 22) v (29 42)]
      D    [( 1 12) v (30 43)]
      E    [( 2 13) v (31 44)]
      F    [( 3 14) v (32 34)]
      G    [( 4 15) v (33 35)]
      H    [( 5 16) v (23 36)]
      I    [( 6 17) v (24 37)]
      J    [( 7 18) v (25 38)]
      K    [( 8 19) v (26 39)]

R2    A    [( 5 19) v (28 35)]
      B    [( 6 20) v (29 36)]
      C    [( 7 21) v (30 37)]
      D    [( 8 22) v (31 38)]
      E    [( 9 12) v (32 39)]
      F    [(10 13) v (33 40)]
      G    [(11 14) v (23 41)]
      H    [( 1 15) v (24 42)]
      I    [( 2 16) v (25 43)]
      J    [( 3 17) v (26 44)]
      K    [( 4 18) v (27 34)]

R3    A    [( 8 16) v (32 42)]
      B    [( 9 17) v (33 43)]
      C    [(10 18) v (23 44)]
      D    [(11 19) v (24 34)]
      E    [( 1 20) v (25 35)]
      F    [( 2 21) v (26 36)]
      G    [( 3 22) v (27 37)]
      H    [( 4 12) v (28 38)]
      I    [( 5 13) v (29 39)]
      J    [( 6 14) v (30 40)]
      K    [( 7 15) v (31 41)]

R4    A    [( 3 12) v (25 41)]
      B    [( 4 13) v (26 42)]
      C    [( 5 14) v (27 43)]
      D    [( 6 15) v (28 44)]
      E    [( 7 16) v (29 34)]
      F    [( 8 17) v (30 35)]
      G    [( 9 18) v (31 36)]
      H    [(10 19) v (32 37)]
      I    [(11 20) v (33 38)]
      J    [( 1 21) v (23 39)]
      K    [( 2 22) v (24 40)]

R5    A    [( 2 17) v (23 34)]
      B    [( 3 18) v (24 35)]
      C    [( 4 19) v (25 36)]
      D    [( 5 20) v (26 37)]
      E    [( 6 21) v (27 38)]
      F    [( 7 22) v (28 39)]
      G    [( 8 12) v (29 40)]
      H    [( 9 13) v (30 41)]
      I    [(10 14) v (31 42)]
      J    [(11 15) v (32 43)]
      K    [( 1 16) v (33 44)]

R6    A    [( 7 13) v (24 43)]
      B    [( 8 14) v (25 44)]
      C    [( 9 15) v (26 34)]
      D    [(10 16) v (27 35)]
      E    [(11 17) v (28 36)]
      F    [( 1 18) v (29 37)]
      G    [( 2 19) v (30 38)]
      H    [( 3 20) v (31 39)]
      I    [( 4 21) v (32 40)]
      J    [( 5 22) v (33 41)]
      K    [( 6 12) v (23 42)]

R7    A    [( 6 18) v (33 39)]
      B    [( 7 19) v (23 40)]
      C    [( 8 20) v (24 41)]
      D    [( 9 21) v (25 42)]
      E    [(10 22) v (26 43)]
      F    [(11 12) v (27 44)]
      G    [( 1 13) v (28 34)]
      H    [( 2 14) v (29 35)]
      I    [( 3 15) v (30 36)]
      J    [( 4 16) v (31 37)]
      K    [( 5 17) v (32 38)]

R8    A    [( 4 22) v (30 44)]
      B    [( 5 12) v (31 34)]
      C    [( 6 13) v (32 35)]
      D    [( 7 14) v (33 36)]
      E    [( 8 15) v (23 37)]
      F    [( 9 16) v (24 38)]
      G    [(10 17) v (25 39)]
      H    [(11 18) v (26 40)]
      I    [( 1 19) v (27 41)]
      J    [( 2 20) v (28 42)]
      K    [( 3 21) v (29 43)]

R9    A    [( 1 14) v (26 38)]
      B    [( 2 15) v (27 39)]
      C    [( 3 16) v (28 40)]
      D    [( 4 17) v (29 41)]
      E    [( 5 18) v (30 42)]
      F    [( 6 19) v (31 43)]
      G    [( 7 20) v (32 44)]
      H    [( 8 21) v (33 34)]
      I    [( 9 22) v (23 35)]
      J    [(10 12) v (24 36)]
      K    [(11 13) v (25 37)]

Note added Dec 1st :  An 11 round schedule with the same properties as above is possible.  It would be equivalent to 4 mutually orthogonal Latin Squares (MOLS) of size 11.

[Ian Wakeling]

Melina,

I had another thought.  If you don't care for the table balance and don't need to divide the 44 players into teams (or mixed male/female partnerships), then 11 rounds are possible where a player's 11 partners and 22 opponents are all different.

Ian.

R1    A    [( 7 38) v (24 22)]
      B    [(35  5) v (23 12)]
      C    [(33 25) v ( 6 16)]
      D    [( 4 40) v (30 29)]
      E    [(26 14) v (32 28)]
      F    [(20 41) v ( 1 13)]
      G    [(11 10) v ( 8 43)]
      H    [( 3 27) v (42 17)]
      I    [(36 31) v (44 37)]
      J    [(19 21) v (34 39)]
      K    [( 9  2) v (15 18)]

R2    A    [( 8 39) v (25 12)]
      B    [(36  6) v (24 13)]
      C    [(23 26) v ( 7 17)]
      D    [( 5 41) v (31 30)]
      E    [(27 15) v (33 29)]
      F    [(21 42) v ( 2 14)]
      G    [( 1 11) v ( 9 44)]
      H    [( 4 28) v (43 18)]
      I    [(37 32) v (34 38)]
      J    [(20 22) v (35 40)]
      K    [(10  3) v (16 19)]

R3    A    [( 9 40) v (26 13)]
      B    [(37  7) v (25 14)]
      C    [(24 27) v ( 8 18)]
      D    [( 6 42) v (32 31)]
      E    [(28 16) v (23 30)]
      F    [(22 43) v ( 3 15)]
      G    [( 2  1) v (10 34)]
      H    [( 5 29) v (44 19)]
      I    [(38 33) v (35 39)]
      J    [(21 12) v (36 41)]
      K    [(11  4) v (17 20)]

R4    A    [(10 41) v (27 14)]
      B    [(38  8) v (26 15)]
      C    [(25 28) v ( 9 19)]
      D    [( 7 43) v (33 32)]
      E    [(29 17) v (24 31)]
      F    [(12 44) v ( 4 16)]
      G    [( 3  2) v (11 35)]
      H    [( 6 30) v (34 20)]
      I    [(39 23) v (36 40)]
      J    [(22 13) v (37 42)]
      K    [( 1  5) v (18 21)]

R5    A    [(11 42) v (28 15)]
      B    [(39  9) v (27 16)]
      C    [(26 29) v (10 20)]
      D    [( 8 44) v (23 33)]
      E    [(30 18) v (25 32)]
      F    [(13 34) v ( 5 17)]
      G    [( 4  3) v ( 1 36)]
      H    [( 7 31) v (35 21)]
      I    [(40 24) v (37 41)]
      J    [(12 14) v (38 43)]
      K    [( 2  6) v (19 22)]

R6    A    [( 1 43) v (29 16)]
      B    [(40 10) v (28 17)]
      C    [(27 30) v (11 21)]
      D    [( 9 34) v (24 23)]
      E    [(31 19) v (26 33)]
      F    [(14 35) v ( 6 18)]
      G    [( 5  4) v ( 2 37)]
      H    [( 8 32) v (36 22)]
      I    [(41 25) v (38 42)]
      J    [(13 15) v (39 44)]
      K    [( 3  7) v (20 12)]

R7    A    [( 2 44) v (30 17)]
      B    [(41 11) v (29 18)]
      C    [(28 31) v ( 1 22)]
      D    [(10 35) v (25 24)]
      E    [(32 20) v (27 23)]
      F    [(15 36) v ( 7 19)]
      G    [( 6  5) v ( 3 38)]
      H    [( 9 33) v (37 12)]
      I    [(42 26) v (39 43)]
      J    [(14 16) v (40 34)]
      K    [( 4  8) v (21 13)]

R8    A    [( 3 34) v (31 18)]
      B    [(42  1) v (30 19)]
      C    [(29 32) v ( 2 12)]
      D    [(11 36) v (26 25)]
      E    [(33 21) v (28 24)]
      F    [(16 37) v ( 8 20)]
      G    [( 7  6) v ( 4 39)]
      H    [(10 23) v (38 13)]
      I    [(43 27) v (40 44)]
      J    [(15 17) v (41 35)]
      K    [( 5  9) v (22 14)]

R9    A    [( 4 35) v (32 19)]
      B    [(43  2) v (31 20)]
      C    [(30 33) v ( 3 13)]
      D    [( 1 37) v (27 26)]
      E    [(23 22) v (29 25)]
      F    [(17 38) v ( 9 21)]
      G    [( 8  7) v ( 5 40)]
      H    [(11 24) v (39 14)]
      I    [(44 28) v (41 34)]
      J    [(16 18) v (42 36)]
      K    [( 6 10) v (12 15)]

R10   A    [( 5 36) v (33 20)]
      B    [(44  3) v (32 21)]
      C    [(31 23) v ( 4 14)]
      D    [( 2 38) v (28 27)]
      E    [(24 12) v (30 26)]
      F    [(18 39) v (10 22)]
      G    [( 9  8) v ( 6 41)]
      H    [( 1 25) v (40 15)]
      I    [(34 29) v (42 35)]
      J    [(17 19) v (43 37)]
      K    [( 7 11) v (13 16)]

R11   A    [( 6 37) v (23 21)]
      B    [(34  4) v (33 22)]
      C    [(32 24) v ( 5 15)]
      D    [( 3 39) v (29 28)]
      E    [(25 13) v (31 27)]
      F    [(19 40) v (11 12)]
      G    [(10  9) v ( 7 42)]
      H    [( 2 26) v (41 16)]
      I    [(35 30) v (43 36)]
      J    [(18 20) v (44 38)]
      K    [( 8  1) v (14 17)]

[melina69]

Ian,
Thank you so much.  This is such a difficult part of the tournaments that we have every year.
Is there a formula for figuring the schedules as you do?
Once again, THANK YOU
Melina

[Ian Wakeling]

Unfortunately there is no easy formula that I can give you.  Often with this type of problem, the approach needed will depend on the actual number of players and rounds.  For the two schedules above I am using a cyclic approach which is similar to the one that I discuss in this posting.  If you search the internet for "Kirkman's Schoolgirl Problem" or the "Social golfer problem" you might get a feel for some of the mathematical or computational tecniques that can lead to solutions.

Good luck with your tournament.

Ian.

[Mikey_Christ]

Hi. I am stumped and cannot figure out my Euchre problem I have.

I have a Euchre tournament coming up in a couple of weeks and there will be twelve players. I would like every player to partner up with every single other player (because it's played in pairs), as well as play every single other player (each round will be a team of two playing another team of two). I would like to try to minimise the number of times a player plays an opponent.

Please, could someone give me the formula, or a competition layout, because this has been bugging me all afternoon.

I try lots of combinations but I tend to have players play people three times, and awww... I'll just shut up. My head is killing me after trying to make the competition round robin.

[Ian Wakeling]

Sounds like you want a Whist tournament.  Follow the schedules link at the top of this page, then click to display 'Whist' and finally dial in 12 players.  Adjacent pairs of matches form the tables, for example Table 1 would be Match 1 vs Match 2.  If you play the 11 rounds like this, then everyone will partner all the other players once, and oppose all the other players twice.

Ian.

[Mikey_Christ]

Thanks Sylvester. I am a bit of a noob (only a bit?) and didn't see the link or had time to explore this site.

Thanks for the help. I hope you get Tweety.

[Mikey_Christ]

I successfully ran a Euchre competition using the whilst round robin. Everybody enjoyed themselves and it wouldn't have been so good if it wasn't for this awesome forum.

Thanks Ian Sylvester. I ran a 16 person whilst and it was top notch.

Great Success! High-Five.

[melina69]

Hi Again Ian~
It's that time of the year again and I am having trouble creating my Euchre schedule.  I am going to have 36 or 40 players.  Not sure which yet.
I would like them to play with and against different players, at different tables for 7 games.
Can you please help me?  
Melina

[Ian Wakeling]

Hi Melina,

No problem, I have some off the shelf solutions that should work well for this year's tournament.

Here is a solution for 40 players, it is possible to play upto 13 rounds and always have different partners and opponents. Each block of 10 rows gives the assignments to the 10 tables in a round. Of course it doesn't matter how you assign the partnerships among each set of 4 players, so I have left this out.

Regards,  Ian.

 2 13 19 22
 5 10 20 21
 4 11 16 25
15 26 32 35
18 23 33 34
17 24 29 38
 6  9 28 39
 7  8 31 36
 3 12 30 37
 1 14 27 40

 1  3 20 23
 6 11 21 22
 5 12 17 26
14 16 33 36
19 24 34 35
18 25 30 39
 7 10 27 29
 8  9 32 37
 4 13 31 38
 2 15 28 40

 2  4 21 24
 7 12 22 23
 6 13 14 18
15 17 34 37
20 25 35 36
19 26 27 31
 8 11 28 30
 9 10 33 38
 1  5 32 39
 3 16 29 40

 3  5 22 25
 8 13 23 24
 1  7 15 19
16 18 35 38
21 26 36 37
14 20 28 32
 9 12 29 31
10 11 34 39
 2  6 27 33
 4 17 30 40

 4  6 23 26
 1  9 24 25
 2  8 16 20
17 19 36 39
14 22 37 38
15 21 29 33
10 13 30 32
11 12 27 35
 3  7 28 34
 5 18 31 40

 5  7 14 24
 2 10 25 26
 3  9 17 21
18 20 27 37
15 23 38 39
16 22 30 34
 1 11 31 33
12 13 28 36
 4  8 29 35
 6 19 32 40

 6  8 15 25
 3 11 14 26
 4 10 18 22
19 21 28 38
16 24 27 39
17 23 31 35
 2 12 32 34
 1 13 29 37
 5  9 30 36
 7 20 33 40

 7  9 16 26
 4 12 14 15
 5 11 19 23
20 22 29 39
17 25 27 28
18 24 32 36
 3 13 33 35
 1  2 30 38
 6 10 31 37
 8 21 34 40

 8 10 14 17
 5 13 15 16
 6 12 20 24
21 23 27 30
18 26 28 29
19 25 33 37
 1  4 34 36
 2  3 31 39
 7 11 32 38
 9 22 35 40

 9 11 15 18
 1  6 16 17
 7 13 21 25
22 24 28 31
14 19 29 30
20 26 34 38
 2  5 35 37
 3  4 27 32
 8 12 33 39
10 23 36 40

10 12 16 19
 2  7 17 18
 1  8 22 26
23 25 29 32
15 20 30 31
14 21 35 39
 3  6 36 38
 4  5 28 33
 9 13 27 34
11 24 37 40

11 13 17 20
 3  8 18 19
 2  9 14 23
24 26 30 33
16 21 31 32
15 22 27 36
 4  7 37 39
 5  6 29 34
 1 10 28 35
12 25 38 40

 1 12 18 21
 4  9 19 20
 3 10 15 24
14 25 31 34
17 22 32 33
16 23 28 37
 5  8 27 38
 6  7 30 35
 2 11 29 36
13 26 39 40

I also have this schedule for 36 players and upto 8 rounds of play.

 1  2  3  4
 5  6  7  8
 9 10 11 12
13 14 15 16
17 18 19 20
21 22 23 24
25 26 27 28
29 30 31 32
33 34 35 36

 1  5  9 13
 2  6 10 17
 3  7 11 21
 4  8 12 25
14 18 22 29
15 19 23 33
16 26 30 34
20 27 31 35
24 28 32 36

 1  6 11 25
 2  7  9 16
 3  5 10 20
 4 14 21 33
 8 15 18 32
12 13 17 22
19 27 30 36
23 28 31 34
24 26 29 35

 1 10 18 21
 2  8 13 29
 3 14 31 36
 4  9 20 23
 5 15 17 28
 6 12 16 19
 7 26 32 33
11 24 27 34
22 25 30 35

 1 14 24 30
 2 12 18 34
 3  9 17 32
 4  6 28 35
 5 21 29 36
 7 10 19 25
 8 16 23 27
11 13 20 33
15 22 26 31

 1 12 23 26
 2 11 22 36
 3  6 13 24
 4 10 16 32
 5 18 27 33
 7 20 28 30
 8 14 19 35
 9 15 29 34
17 21 25 31

 1 19 28 29
 2  5 23 30
 3 12 15 27
 4 11 18 31
 6  9 26 36
 7 14 17 34
 8 10 22 33
13 21 32 35
16 20 24 25

 1  7 15 35
 2 14 25 32
 3 16 18 28
 4 17 27 29
 5 11 19 26
 6 20 22 34
 8  9 21 30
10 13 23 36
12 24 31 33

[melina69]

Thank you Thank you
You help a great deal in this situation.  We'd be lost without your help.
Melina