Comment by thaumasiotes
6 hours ago
> I think it's more about guaranteeing the whole sequence, rather than who goes first?
What do you mean? The question is who goes first.
As a matter of practice, what happens in a board game is that everyone takes a position around the board before choosing who goes first. If turns proceed in a fixed sequence, that position will determine the sequence. If the order of turns is specified by the game (for example, many feature a turn order track), then that order will be used. You never need to decide on a sequence longer than one person.
But even if that wasn't the case, the article couldn't be more explicit:
> Eric Harshbarger was asked by a board game designer if he could come up with dice that would determine who goes first — without the possibility of a tie.
> The idea was simple: settle the first turn quickly and get on with the game.
This from the article appears somewhat questionable:
>> “It was a question that did not have an obvious answer and that's something that a mathematician will often jump at.”
The problem they're bragging about solving is using dice to quickly and unambiguously select one of five options with equal probability.
The obvious answer should be that you roll a single 10- or 20-sided die, divide by 2 or 4, round up, and there you have it.
From a site selling the dice: "With these dice all players will have an equal chance of ranking first, second, third and fourth. And only one roll is required."
Wikipedia distinguishes between "go first fair" and "permutation fair". I believe Harshbarger wanted to find permutation fair dice.
Pretty sure he means this: - assume heads beats tails - if both players get opposite results (HT, TH) then the winner is obvious - if both players get heads, player A is the winner - if both players get tails, player B is the winner.
If you're going to specify that the number of players is 2, there is no advantage over the much simpler system of:
Flip one coin. If heads, player A is the winner. If tails, player B is the winner.
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