80 players 10 rounds 4 players/group

[realCool]

Hi

I'm organizing a mahjong tournament where 80 players will participate. In Mahjong there are always 4 players per table competing against each other. 10 rounds will be played.
By searching through this forum I already found a solution for 32 players in groups of 4, that participate in a round robin tournament without playing against the same person twice. For 32 players you need 10 rounds. Now I'm not sure how many rounds are possible with 80 players. Theoretically it should be 26. (79 opponents divided by 3 is 26,33), but I know that it can happen that the solution has fewer rounds.
I also searched the internet for different tournament types and read a little bit about this.  To me it seems the tournament system, which allows the most accurate ranking is round robin followed by the swiss system. As I only have time for 10 rounds I'm not sure if an incomplete round robin (depending on how many rounds are the maximum for 80 players, the number of omitted rounds can be big or small) or a swiss system (or maybe something completely different?) would be better.
In both cases I do not really have a solution for the tournament brackets. I think that applying the swiss system by taking the 1st ranked person then add the 2nd ranked if they have not played etc. can lead to problems, so that no pairings are possible anymore. I experienced that when I first tried to find a solution for a small scale tournament with trial and error by hand. If you start wrong a solution is not possible.
I know that this forum is about round robin tournaments only, but the question is connected to that, so I hope it is ok that I post this here.

Summarized I would like to know:

Which tournament type should be used in the described case?
How to organize a bracket for this tournament type?

[Ian Wakeling]

It is certainly possible to produce a 10 round schedule where each player sees 30 different opponents over the course of the tournament - I can produce this if you like.  I suspect that it might be possible to go as far as 26 rounds and 78 different opponents but I don't have an example of a schedule like this.

An alternative might be to split in to groups, but you would need the right number of players.  If there were 84 players you could split in to 3 groups of 28.  Within a group you could arrange 9 rounds of play during which each player opposed all 27 other groups members.  Assuming you now have a score for each of the 84 players you could use these to decide who plays who in round 10.   The numbers also work if you split 80 players in to 5 groups of 16 players - but then it only takes 5 rounds of play to see all 15 other group members and it is not clear to me what you might do after that.

[realCool]

Thanks for your answer =)

The 80 players are predetermined so I cannot change that number. :/ As such the best solution would then probably be the 10 round schedule with 30 different opponents. If you could produce this for me that would be great =)

[Ian Wakeling]

Here is the 10 round schedule.  There is one row per round, but these will probably wrap around on your screen as the line lenght is long.  The Excel version attached may be more convenient.  Hope that helps.


(52 38 53 56) (18 76 34 15) (70 57 25 26) (6 66 9 8) (37 50 69 59) (17 61 77 44) (35 4 13 46) (80 16 68 39) (64 19 40 2) (12 43 74 51) (42 33 27 72) (7 48 63 36) (60 30 22 20) (67 24 71 78) (49 54 1 73) (32 75 79 55) (14 62 23 3) (10 28 45 65) (47 58 29 11) (41 31 21 5)
(53 39 54 57) (19 77 35 16) (61 58 26 27) (7 67 10 9) (38 41 70 60) (18 62 78 45) (36 5 14 47) (71 17 69 40) (65 20 31 3) (13 44 75 52) (43 34 28 73) (8 49 64 37) (51 21 23 11) (68 25 72 79) (50 55 2 74) (33 76 80 56) (15 63 24 4) (1 29 46 66) (48 59 30 12) (42 32 22 6)
(54 40 55 58) (20 78 36 17) (62 59 27 28) (8 68 1 10) (39 42 61 51) (19 63 79 46) (37 6 15 48) (72 18 70 31) (66 11 32 4) (14 45 76 53) (44 35 29 74) (9 50 65 38) (52 22 24 12) (69 26 73 80) (41 56 3 75) (34 77 71 57) (16 64 25 5) (2 30 47 67) (49 60 21 13) (43 33 23 7)
(55 31 56 59) (11 79 37 18) (63 60 28 29) (9 69 2 1) (40 43 62 52) (20 64 80 47) (38 7 16 49) (73 19 61 32) (67 12 33 5) (15 46 77 54) (45 36 30 75) (10 41 66 39) (53 23 25 13) (70 27 74 71) (42 57 4 76) (35 78 72 58) (17 65 26 6) (3 21 48 68) (50 51 22 14) (44 34 24 8)
(56 32 57 60) (12 80 38 19) (64 51 29 30) (10 70 3 2) (31 44 63 53) (11 65 71 48) (39 8 17 50) (74 20 62 33) (68 13 34 6) (16 47 78 55) (46 37 21 76) (1 42 67 40) (54 24 26 14) (61 28 75 72) (43 58 5 77) (36 79 73 59) (18 66 27 7) (4 22 49 69) (41 52 23 15) (45 35 25 9)
(57 33 58 51) (13 71 39 20) (65 52 30 21) (1 61 4 3) (32 45 64 54) (12 66 72 49) (40 9 18 41) (75 11 63 34) (69 14 35 7) (17 48 79 56) (47 38 22 77) (2 43 68 31) (55 25 27 15) (62 29 76 73) (44 59 6 78) (37 80 74 60) (19 67 28 8) (5 23 50 70) (42 53 24 16) (46 36 26 10)
(58 34 59 52) (14 72 40 11) (66 53 21 22) (2 62 5 4) (33 46 65 55) (13 67 73 50) (31 10 19 42) (76 12 64 35) (70 15 36 8) (18 49 80 57) (48 39 23 78) (3 44 69 32) (56 26 28 16) (63 30 77 74) (45 60 7 79) (38 71 75 51) (20 68 29 9) (6 24 41 61) (43 54 25 17) (47 37 27 1)
(59 35 60 53) (15 73 31 12) (67 54 22 23) (3 63 6 5) (34 47 66 56) (14 68 74 41) (32 1 20 43) (77 13 65 36) (61 16 37 9) (19 50 71 58) (49 40 24 79) (4 45 70 33) (57 27 29 17) (64 21 78 75) (46 51 8 80) (39 72 76 52) (11 69 30 10) (7 25 42 62) (44 55 26 18) (48 38 28 2)
(60 36 51 54) (16 74 32 13) (68 55 23 24) (4 64 7 6) (35 48 67 57) (15 69 75 42) (33 2 11 44) (78 14 66 37) (62 17 38 10) (20 41 72 59) (50 31 25 80) (5 46 61 34) (58 28 30 18) (65 22 79 76) (47 52 9 71) (40 73 77 53) (12 70 21 1) (8 26 43 63) (45 56 27 19) (49 39 29 3)
(51 37 52 55) (17 75 33 14) (69 56 24 25) (5 65 8 7) (36 49 68 58) (16 70 76 43) (34 3 12 45) (79 15 67 38) (63 18 39 1) (11 42 73 60) (41 32 26 71) (6 47 62 35) (59 29 21 19) (66 23 80 77) (48 53 10 72) (31 74 78 54) (13 61 22 2) (9 27 44 64) (46 57 28 20) (50 40 30 4)

[realCool]

The Excel Sheet is great thank you very much =)
I have been researching a little bit more about different tournament systems and it seems that most systems are only defined for 2 players. So now I'm quite interested in an adaptable version for 4 players but until now I had no luck finding a forum or something else where this could be discussed? Do you know such a place maybe?

[Ian Wakeling]

Don't know of anywhere else, but you are welcome to ask your questions here.  There are a few schedules on the message board that you might find useful.  

For example this one for 40 players.