Round Robin Tournament Scheduling

Mah Jong tournament

mahjongman · 5 · 6472

mahjongman

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on: February 09, 2010, 12:05:38 PM
Mah Jong club needs tournament schedules for various numbers of players - say 8 to 16. Four players per table - all playing as individuals - no partners. The seating arrangements for each table are organized by drawing lots at the start of each table.
Thanks, Tony


Ian Wakeling

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Reply #1 on: February 11, 2010, 01:06:31 PM
You don't say how many rounds you would like to play, if this is variable too then are a lot of schedules you are asking for.  Use the first n rounds from this schedule if you have 16 players.  In general the other scenarios are going to be harder to solve, however if you are prepared to play a round with one table of 3 players, then you could handle 15 players simply by deleting player 16 from the schedule in the link.

Ian.


mahjongman

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Reply #2 on: February 11, 2010, 01:32:57 PM
No specific number of rounds. The club meets weekly so leagues can go on for several months. The main thing is to play each other player the same number of times. I am familiar with the social golfer solutions which seem to be based on a specific number of rounds. I have the schedule for 16 players over five rounds and I have solved it for 8 players playing everyone else 3 times over 7 rounds. That is the sort of solution I am looking for. Many thanks.


Ian Wakeling

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Reply #3 on: February 12, 2010, 03:54:59 AM
Tony,

With 12 players you can play 11 rounds where everybody plays each other three times.

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


With 14 players the problem is harder.  Counting pairs, it is easy to see that you will need to play 91 games at which point all players will have played each other six times each.  This can be arranged as 30 rounds with 2 byes and one additional game.

(A B C G)  (D L M N)  (K E F H)
(B C D H)  (E M N A)  (L F G I)
(C D E I)  (F N A B)  (M G H J)
(D E F J)  (G A B C)  (N H I K)
(E F G K)  (H B C D)  (A I J L)
(F G H L)  (I C D E)  (B J K M)
(G H I M)  (J D E F)  (C K L N)
(H I J N)  (K E F G)  (D L M A)
(I J K A)  (L F G H)  (E M N B)
(J K L B)  (M G H I)  (F N A C)
(K L M C)  (N H I J)  (G A B D)
(L M N D)  (A I J K)  (H B C E)
(M N A E)  (B J K L)  (I C D F)
(N A B F)  (C K L M)  (J D E G)
(A F I K)  (H J N C)  (B D E L)
(B G J L)  (I K A D)  (C E F M)
(C H K M)  (J L B E)  (D F G N)
(D I L N)  (K M C F)  (E G H A)
(E J M A)  (L N D G)  (F H I B)
(F K N B)  (M A E H)  (G I J C)
(G L A C)  (N B F I)  (H J K D)
(H M B D)  (A C G J)  (I K L E)
(I N C E)  (B D H K)  (J L M F)
(J A D F)  (C E I L)  (K M N G)
(K B E G)  (D F J M)  (L N A H)
(L C F H)  (E G K N)  (M A B I)
(M D G I)  (F H L A)  (N B C J)
(N E H J)  (G I M B)  (A C D K)
(B F I M)  (C G J N)  (D H K A)
(E I L B)  (F J M C)  (G K N D)
(H L A E)  (- - - -)  (- - - -)


Finally try searching the message board for the phrase '10 players', I think you may find something that you can adapt.

Ian.


mahjongman

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Reply #4 on: February 12, 2010, 11:54:41 AM
Ian
That's fantastic. I wish I knew how you worked it out - or maybe I don't!

You have saved me hours, possibly days, and I may never have found the solutions.
Thanks again
Tony