> Harshbarger says he and his colleagues always knew the dice were mathematically possible.
> The mystery was whether that mathematical solution could be translated into the physical geometry of a die — something that could actually be manufactured and rolled.
> “I knew there was a solution with something crazy like 1,440 sides for each die,” he said. “That's not makeable.”
[1] https://www.cbc.ca/radio/asithappens/dice-mystery-board-game...
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.
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.
If I imagine a 3-sided die, for simplicity, you should be able to have this result if the sets are [1,5,9],[2,6,7],[3,4,8]. And so on for larger numbers of players. Why doesn't this work?
You also can't generally "and so on" constrained combinatorial arrangements like this.
(no affiliation)
I think there have been discussions about some of these sets here as well.
* https://en.wikipedia.org/wiki/Go_First_Dice
As well as the pages of the project:
TFA claims it's "new" in 2026, but the current state of the art seems to still be that of 2022.
I bought actual dice like these in 2024 from https://mathsgear.co.uk/collections/dice/products/go-first-d...
So well, is TFA just a big pile of slop?
ChrisArchitect•1d ago