Go First Dice Wiki

This page is read only. You can view the source, but not change it. Ask your administrator if you think this is wrong.
====A Solution Looking For A Problem====
In an attempt to deflect emails and other correspondence from people who are wondering what the point of all of this is, let me (Eric) state upfront: I understand that there are //plenty// of ways to quickly determine who goes first in a game.

The mathematics of this research problem long ago overshadowed its practicality. If you want to determine who goes first in a game, just roll dice... standard dice. Sure you may have to reroll ties, but I'm sure you'll manage. Or, get all of the spades from a deck of cards and have each player draw one randomly... that'll suffice for up to 13 players.

{{  http://www.ericharshbarger.org/dice/gfd_02.jpg?300}}
For that matter, if you want to create custom dice, you can fairly pick a random permutation for up to five players with a //single// die. The number of orderings of //n// players is //n//!:
  * 2! == 2
  * 3! == 6
  * 4! == 24
  * 5! == 120

So, for a three players, a specially designed d6 with "abc", "acb", "bac", bca", cab", and "cba" on the faces will, with a single roll, tell you what order the three players should play in (hey! I actually //do// make such custom dice, and [[https://mathartfun.com/dSpecial.html|you can find them for sale here at MathArtFun]]).

There exist pleasant shapes for 24-sided dice, so the 4 player orderings could be determined with a single roll (sorry, I don't make custom d24s). Even 5 players can be accommodated with a single roll of a specially made d120. In fact, I 3D printed such a d120 (pictured at right), but gave up inking it (it's also a bit too massive to be conveniently rolled).

So, sure, the research being done on the Go first Dice problem is not solving a huge problem. But, //mathematically// speacking, it's a pretty interesting topic (at least to me, and a few others). And besides, there is something cool about using a set of Go First Dice, each player getting to roll his or her own die, and //knowing// there will be no ties, and the numberings are perfectly fair...
Go First Dice Wiki

User Tools

Site Tools

Page Tools
