"Maria" Tournament

[jlhc55]

My friends and I are planning a tournament using the board game "Maria"

http://boardgamegeek.com/boardgame/40354/maria

Maria is a 3 player game, in which each player assumes a specific role in the War of Austrian Succession.  Players are either Austria, France, or Prussia/Pragmatic Army.  Each of the three roles is different (with Austria being the most difficult, for example)

Preparing a round-robin tournament for this game is proving difficult.  The primary problem is that in addition to the need for each player to play the others, he must do so while switching his role.  None of the round-robin tournaments I have found have taken this into account, and my rudimentary attempts to solve this problem have been unsuccessful.

If the above is confusing, I'll make the problem simpler.  Assume that there are three seats at each table.  Players need to play different players from different seats.

The general layout of the tournament is 9 players with 6 rounds (any more rounds would make the tournament prohibitively long, since a single game takes 3-4 hours and we would attempt to do this in a single weekend).  Each player must play each role exactly twice.  He must play every other player at least once, but not 3 times.  Finally, no subsequent game may have the same 3 players as any previous game (even if the roles have changed).

Below is the beginnings of the tournament structure(note that the first column is "Austria," second column "France," third column is "Prussia," for example)

Round 1:  
T1: A B C
T2: D E F
T3: G H I

Round 2:
T1: C D H
T2: I A E
T3: F G B

Note how each player has moved one role/seat to the right (doesn't necessarily need to go in that order, just how I arranged it) and is playing at a table with different players than his previous game.  

Following a pattern, I can get through Round 4 in a way such that each player plays all others once and only one role twice...

Round 3:
T1:  E C G
T2:  H F A
T3:  B I D

Round 4:
T1:  E H B
T2:  C F I
T3:  G A D

After round 4, however, my pattern breaks down and starts repeating entire games (though with players in different roles), or having players assume a certain role 3 times.  I am having trouble rounding out the tournament in a fair way.  Is this possible?  No need to use my tournament so far, it's just what I came up with.

Are there any other suggestions on how we can run this tournament?

We would also like the option of playing with 12 or 15 players, but my mind can't even start to wrap around that problem.

Thanks for the help!

[Ian Wakeling]

I can find solutions for two of your schedules by using software for generating experimental designs (for example there are similarities here to a crop experiment where different varieties are planted out in a grid pattern).   I haven't manged to find a good solution for the 12 player schedule.

9 players:

2 8 9
6 5 1
7 4 3

4 9 7
3 6 2
5 8 1

1 7 3
9 2 5
8 6 4

2 1 4
6 7 8
9 3 5

5 4 8
1 2 7
3 9 6

7 5 6
4 1 9
8 3 2
  
15 players:
  
 7  8 10
 6 13  2
11 15 14
 9  5  1
12  4  3

14 10  4
 6  8  5
13 11  9
 2 12 15
 3  1  7

 8  9  2
15 10  6
 3 14 13
 1 12 11
 5  4  7

13  7 15
 4  2  1
 5 11 10
 9  3  6
12 14  8

 4 15  9
11  3  8
 7  6 12
10  1 13
14  2  5

10  9 12
 8 13  4
 2  7 11
15  5  3
 1  6 14

[jlhc55]

That's great!  Thanks a lot.