Seating Arrangement Problem

[cabiness42]

Thanks for everyone's tips.

I ended up doing some simple trial and error, and got this far:

1) Everybody starts on the button exactly once
2) Everybody starts in the big blind exactly once
3) Everybody starts with each player on his/her immediate right at least once
4) Everybody starts with each player on his/her immediate left at least once


Some players do start in other positions more than once, and are the same distance from other players more than once, but I figure that those four criteria I listed are the most important for fairness.

[tshort]

Schostic generation of 8 x 8 latin squares would be a "fair" method of determining seating.

Latin squares are n x n tables with n symbols such that no column or row repeates a symbol. So, they would satisify your criteria of each person starting in each position relative to the button. Any given 8 x 8 latin square wouldn't guarantee fairness in relative position to other players. Randomly generating the latin squares would be a fair method of seating (although it could no longer be "fair" after the it is determined). Building in constraints to the random generation could further guarantee fairness.

[cabiness42]

Well, I'm pretty certain that I can't achieve fairness both in relation to the button and in relation to the other players. I figure the latter is more important, since position in relation to the button changes every hand but position in relation to the other players is fixed throughout the tournament.

[rufus]

[ QUOTE ]
Well, I'm pretty certain that I can't achieve fairness both in relation to the button and in relation to the other players. I figure the latter is more important, since position in relation to the button changes every hand but position in relation to the other players is fixed throughout the tournament.

[/ QUOTE ]

You can just high-card for the button on each SNG anyway....

If the number of players were prime, then you could assign a number to each player and step through increments:
1 2 3 4 5 6 7
1 3 5 7 2 4 6
1 4 7 3 6 2 5
and so on.

it's very easy to see that this will lead to a different 'local 3-some' each round. Since 8 is not prime, that won't quite work there. I like pococurante's suggestion of cutting/drawing lots for position each time around.

[pricklypete]

^^ makes sense