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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.

www.ericharshbarger.org_dice_gfd_02.jpg 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 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…

no_problem.txt · Last modified: 2023/03/25 15:01 by harshec