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terminology [2023/03/19 11:53]
harshec 		terminology [2024/01/28 16:58] (current)
harshec
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 ====Terminology==== ====Terminology====
-  * **Alphabetic String.** An alphabetic string (or just "string") is a representation of a dice set that is more convenient than the traditional "array listing" and takes advantage of the fact that it is assumed that no numeric values are repeated across the dice. In an alphabetic string of //n// dice, the first //n// letters of the alphabet (traditionally lowercase) are concatenated into a single string so that a letter's position in the string indicates that that particular numeric value is assigned to that die. For example, the alphabetic string ''cbabccccbabc'' is equivalent to the d2+d4+d6 set:<code>+  * **Alphabetic String.** An alphabetic string (or just "string") is a representation of a dice set that is more convenient than the traditional "array listing" and takes advantage of the fact that it is assumed that no numeric values are repeated across the dice. In an alphabetic string of //n// dice, the first //n// letters of the alphabet (traditionally lowercase) are concatenated into a single string so that a letter's position in the string indicates that that particular numeric value is assigned to that die. For example, the alphabetic string <code>cbabccccbabc</code> is equivalent to the d2+d4+d6 set:<code>
 Die 1: 3, 10 Die 1: 3, 10
 Die 2: 2, 4, 9, 11 Die 2: 2, 4, 9, 11
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   * **Column Grouped.** (see "Symmetry")\\ \\    * **Column Grouped.** (see "Symmetry")\\ \\ 
   * **Column Paired.** (see "Symmetry")\\ \\    * **Column Paired.** (see "Symmetry")\\ \\ 
-  * **Fairness.** There are different levels of fairness that a set of dice can exhibit. The original "go first dice" question dealt with only the weakest type of fairness, but the problem has now morphed into a search for dice with the permutation fairness (the strongest type). The three levels of fairness, from weakest to strongest are:+  * **Fairness.** There are different levels of fairness that a set of dice can exhibit. The original "go first dice" question dealt with only the weakest type of fairness, but the problem has now morphed into a search for dice with the permutation fairness (the strongest type). The three levels of fairness, from weakest to strongest are listed below ([[fairness|and there is a separate page about concepts of fairness with a bit more explanation]]).
     * **Go-First Fairness.** Each player has an equal chance of rolling the highest number, and that person would go first.     * **Go-First Fairness.** Each player has an equal chance of rolling the highest number, and that person would go first.
     * **Place fairness.** Each player has an equal chance of not only rolling highest, but also ending up in any ranking/position. In other words, each player also has an equal chance of rolling the second highest number, the third highest number (if three or more players rolling), and so on.      * **Place fairness.** Each player has an equal chance of not only rolling highest, but also ending up in any ranking/position. In other words, each player also has an equal chance of rolling the second highest number, the third highest number (if three or more players rolling), and so on. 
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   * **Inhomogeneous (aka Heterogeneous).** Not homogeneous.\\ \\    * **Inhomogeneous (aka Heterogeneous).** Not homogeneous.\\ \\ 
   * **Mirrored/Palindromic.** (see "Symmetry")\\ \\    * **Mirrored/Palindromic.** (see "Symmetry")\\ \\ 
 +  * **Nice Dice.** A "nice" set comprises dice that are all isohedral shapes that are not lenses or rolling logs ("nice" is definitely subjective, since 2//n//-lens-shaped dice with small //n// values are definitely functional and pleasing enough for some folks' tastes). Also, a d2 (a coin) is not considered "nice", but that is purely the opinion of this author (Eric). "Nice" side counts, therefore, are the following: 4, 6, 8, 12, 20, 24, 30, 48, 60, and 120.\\ \\ 
   * **Permutation Fairness.** (see "Fairness")\\ \\    * **Permutation Fairness.** (see "Fairness")\\ \\ 
   * **Place Fairness.** (see "Fairness")\\ \\    * **Place Fairness.** (see "Fairness")\\ \\ 
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 Die 4: 4, 5, 9,  16, 20, 21, 28, 29, 33, 40, 44, 45 Die 4: 4, 5, 9,  16, 20, 21, 28, 29, 33, 40, 44, 45
 </code> </code>
-    * **Mirror Symmetry** occurs when a dice set's alphabetic string is palindromic (reads the same forward as it does backward). This type of symmetry is often called "Palindromic", for obvious reasons. Here is an example: ''ccbbbaaaaaabbbccccccccbbbaaaaaabbbcc''. Physical dice within a set that has mirror symmetry have the property that all pairs of opposite faces (of all of the dice) add up to the same number.+    * **Mirror Symmetry** occurs when a dice set's alphabetic string is palindromic (reads the same forward as it does backward). This type of symmetry is often called "Palindromic", for obvious reasons. Here is an example: <code>ccbbbaaaaaabbbccccccccbbbaaaaaabbbcc</code> Physical dice within a set that has mirror symmetry have the property that all pairs of opposite faces (of all of the dice) add up to the same number.
  
  
  
terminology.1679241208.txt.gz · Last modified: 2023/03/19 11:53 by harshec

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