Abstract: One embodiment of a plurality of dice with markings such that when the primary die is rolled a user either lands on a randomized result within the predetermined probability distribution or is directed to roll a secondary die which either provides a result or directs the user to roll a tertiary die. In the embodiments discussed here the final result is achieved on the first roll over 90% of the time. The embodiments described and shown are capable of representing complex distributions that include highly improbable outcomes, providing users with the convenient alternative of simply reading the result rather than performing comparative and mathematical operations on the results of multiple dice rolls.

Abstract: Certain embodiments of 60-sided and 120-sided replacement dice each having a probability distribution equivalent to that of a subject die with fewer faces than the corresponding replacement die such that each replacement die can be used in place of the corresponding subject die.