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
Nontransitive dice the same average roll. For example, These variant dice are useful, e.g., to introduce students to different ways of comparing random variables (and how only comparing averages may overlook essential details). A set of four dice using all of the numbers 1 through 24 can be made to be nontransitive. With adjacent pairs, one die's probability of winning is 2/3. For rolling high number, B beats A, C beats B, D beats C, A beats D. These dice are basically the same as Efron's dice, as each number of a series of successive numbers on a single die can all