I might be missing something, but a single 6 sided die can have all permutations for 3 players; a 24 sided die for 4 players; a 120 sided die has all permutations necessary for 5 players. Each one of these would even firmly support fewer players.
By the time you got to 120 sides you probably couldn’t label the sides with the order and would need a lookup table or something. That’s a disadvantage, I suppose.
You can take the product of the permutations as the result.
The only problem with that is that you need to pick an order to roll the dice in order to pick the order to rank the players.
But happily, we have a set of dice that pick the order to roll the dice. Now we only need to pick an order to roll the dice to pick the order to roll the dice to pick the order to play.
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I might be missing something, but a single 6 sided die can have all permutations for 3 players; a 24 sided die for 4 players; a 120 sided die has all permutations necessary for 5 players. Each one of these would even firmly support fewer players.
By the time you got to 120 sides you probably couldn’t label the sides with the order and would need a lookup table or something. That’s a disadvantage, I suppose.
I think the (implied) constraint is that each person gets to roll one die, and the highest die roll wins.
You can take the product of the permutations as the result.
The only problem with that is that you need to pick an order to roll the dice in order to pick the order to rank the players.
But happily, we have a set of dice that pick the order to roll the dice. Now we only need to pick an order to roll the dice to pick the order to roll the dice to pick the order to play.
But ...