===History===
The concept of Go First Dice was first proposed to Eric Harshbarger during the summer of 2010 by James Ernest (founder of [[https://en.wikipedia.org/wiki/Cheapass_Games|Cheapass Games]]). At the time James asked if Eric might be able to develop a set of dice (presumedly 6-sided) that would have "go first" properties. Both understood that this was really a "solution looking for a problem" (there are plenty of perfectly acceptable ways to quickly determine who might go first in a game), but mathematically, wouldn't it be great if a set of dice could be created such that players could each take any one of the dice and roll against one another such that: 
  - There would not be a tie,
  - Each player has an equal chance of rolling highest (note this is a weaker condition than stated above in the Introduction -- see the "Fairness" entry below),
  - And, we would like the above conditions to hold even if any subset of eight players roll against one another (for example, if only five players are participating, each would take a die, and roll and each would then have exacly a 1/5 chance of rolling the high number). 

The first condition is easy to satisfy: simply use different numbers on each die. For example, if eight 6-sided dice were being used, just figure out how to distribute the numbers 1 through 48 across the forty-eight faces among all the dice. There could never be a tie then. The real work, of course, comes in satisfying the second and third conditions. And, it turns out that the original proposal (using eight 6-sided dice) is quickly proven to be mathematically impossible...