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Comment by e12e | Hacker News Reader

I think it's more about guaranteeing the whole sequence, rather than who goes first?

At least for two players, if you use a two sided die (a coin), have player one win ties on ones, player two win ties of twos - and otherwise highest wins - then that is trivially done?

I would have to do a little more math to see if it generalizes by induction... I'm not sure you would get a guaranteed sequence - but I think at least guaranteed fair winner works by just increasing the die (7, 9 and 11 would be tricky because if physics again... I suppose. Unless you just ignore highest tie for missing player (reroll on extremely rare 9 9s on a d10 for nine players)?

Ed: I suppose we break smaller ties, by letting closest and highest win (for ten players, 4, 6 and 7 roll 5 - 6 is closest and over/highest of the close players to 5, then come 7?)

Ed2: nevermind we end up biased towards "high" players that often win on "high" ties, like 5 or 6.

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> 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.

Except that as a sibling comment mentions; that generalizes to any size of group - for six players you could roll one d6, and have "that" player go first.

But apparently the constraints are: every player rolls one die once.

> But apparently the constraints are: every player rolls one die once.

That doesn't eliminate the natural scheme, it just adds some useless die rolls. You can have each of two players flip a coin and choose player A when player A flips heads or player B when player A flips tails.

Useless depends on context here; I believe the idea is that each player gets a feeling of agency (they go in the order dictated by "their" luck, not leaving the decision to someone elses roll).

The most pragmatic would probably be to shuffle N cards from ace(one) through N - and let everyone draw).

But that doesn't involve dice.

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