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« Last post by **Ian Wakeling ** on* October 14, 2019, 03:56:59 AM* »
I doubt there is any systematic way to achieve what you want. The fundamental problem is that goal (1) and goal (2) are mutually incompatible. Goal (1) can be achieved by repeating rounds 1 to 3 above three times; then everyone will have their byes exactly 3 rounds apart, however the schedule is optimally bad for (2), as you always have a bye with the same three players.

There is a way to optimize (2) as follows:

2 6 8 1

3 4 9 2

1 5 7 3

5 12 9 6

6 10 7 4

4 11 8 5

10 9 1 11

11 7 2 12

12 8 3 10

where the 9 people a player shares a bye with are all different. But this comes at a price, any pair of the blocks of 4 above have exactly one player in common, so no matter how the rows are ordered there will be 8 occasions where a player has two byes in a row.

What you are asking for is a trade off between the two goals, and that suggest some sort of search algorithm that gives differential weights to (1) and (2).

For me, living with the repeated byes is the better option, since if you have optimal mixing within the byes, then you also have optimal mixing among the groups of 8 who meet together.