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Some notes

- Permutation-fairness is likely too strong of a condition at anything other than serious competitive tournaments. When playing a game casually, usually the group first sits down in a circle and then chooses someone to go first, taking turns clockwise from there; then if the method for choosing the first player is first-player-fair then it is also place-fair.

- Although having to sometimes resolve ties is annoying, there is one major benefit of choosing turn order by rolls of the same dice: You are guaranteed that any non-fairness in the dice do not affect turn order determination.



I mean, if you already accepted that you want to carry with you N amount of dice to solve the ordering of N participants, you can just

* Roll N sided die to decide first (result telling you which player in order is the first)

* Roll n-1 side die to decide second

* Roll n-2 side die to decide 3rd

* ...etc

Same amount of dice rolls, but dices at least can be used for something other than single purpose.


For up to 50 players: Roll 2d10 for a number 0-99. Ignore top 100 mod p (reroll). Otherwise chosen player is r mod p. r is result, p is number of players.


Doesn't this work for up to 100 players?


Yes, but at 51 to 75 it does get a bit tedious with the frequent algorithmic misses :-)




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