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 of . Efron's dice are a set of four nontransitive dice invented by Bradley Efron. The four dice A, B, C, D have the following numbers on their six faces: Each die is beaten by the previous die in the list, with a probability of : B's value is constant; A beats it on rolls because four of its six faces are higher. Similarly, B beats C with a probability because only two of C's faces are higher. P(C>D) can be calculated by summing conditional probabilities for two events: The total probability of win for C is therefore With a