Dice acts using sex dice. Dice may have numbers that do not form a counting sequence starting at one. One variation on the standard die is known as the "average" die. These are six-sided dice with sides numbered codice_3, which have the same arithmetic mean as a standard die (3.5 for a single die, 7 for a pair of dice), but have a narrower range of possible values (2 through 5 for one, 4 through 10 for a pair). They are used in some table-top wargames, where a narrower range of numbers is required. Other numbered variations include Sicherman dice and
Sicherman dice dice is a mathematical exercise in elementary combinatorics, involving a re-labeling of the faces of a pair of six-sided dice to reproduce the same frequency of sums as the standard labeling. The Sicherman dice are crazy dice that are re-labeled with only positive integers. The table below lists all possible totals of dice rolls with standard dice and Sicherman dice. One Sicherman die is coloured for clarity: 1–2–"2"–3–"3"–4, and the other is all black, 1–3–4–5–6–8. The Sicherman dice were discovered by George Sicherman of Buffalo, New York and were originally reported by Martin Gardner in a 1978 article in "Scientific