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{{ http:// | {{ http:// | ||
====Go First Dice Wiki==== | ====Go First Dice Wiki==== | ||
- | This wiki serves as a repository the active research about "Go First Dice". As it will likely be authored by more individuals than Eric Harshbarger alone, the information should be more current, accurate, and inclusive than that which is available on [[http:// | + | This wiki serves as a repository the active research about "Go First Dice". As it will likely be authored by more individuals than Eric Harshbarger alone, the information should be more current, accurate, and inclusive than that which is available on [[http:// |
- | + | ||
- | ===Introduction=== | + | |
- | "Go First Dice" are a set of dice that allows some number of players to each roll a different single die (picked arbitrarily from the set) and the following conditions hold: | + | |
- | + | ||
- | - There will never be ties. | + | |
- | - Each possible ordering of the players (determined by highest result, next highest result, etc) has a mathematically equal chance of occurring. | + | |
- | - The above conditions hold for every subset of the whole set. | + | |
- | + | ||
- | This wiki details the history of such sets of dice, some of the mathematics behind them, current sets of dice that satisfy the above conditions, what advances may still be made in the research, and even where some such sets may be purchased. | + | |
- | + | ||
- | ===History=== | + | |
- | The concept of Go First Dice was first proposed to Eric Harshbarger during the summer of 2010 by James Ernest (founder of [[https:// | + | |
- | - 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 " | + | |
- | - 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, | + | |
- | + | ||
- | 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... | + | |
- | + | ||
- | Below you will find more information about where all of these ideas have led. | + | |
+ | * [[introduction|Introduction]] | ||
+ | * [[history|History]] | ||
* Explanations | * Explanations | ||
* [[terminology|Terminology]] | * [[terminology|Terminology]] | ||
* [[fairness|The Different Types of Fairness]] | * [[fairness|The Different Types of Fairness]] | ||
- | * Fast Perm-Checking code | + | * [[fast_perm_check|Fast Perm-Checking code]] |
- | * " | + | * [[weave_method|" |
- | * [[supercomputer|Using a High Performance Computing Cluster]] | + | * [[no_problem|A Solution Looking For A Problem]] |
* Results | * Results | ||
* [[significant_solutions|Significant Solutions]] | * [[significant_solutions|Significant Solutions]] | ||
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* [[induction_chart|Induction Chart]] | * [[induction_chart|Induction Chart]] | ||
* [[records|Records]] | * [[records|Records]] | ||
- | | + | |
+ | * [[more_info|More Information/ | ||
* [[participants|Wiki Participants]] | * [[participants|Wiki Participants]] |