Multiple Dice to Produce a Randomized Result from a Predetermined Probability Distribution

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.

I claim: 
     
         1 . A method for producing a randomized result within a predetermined probability distribution comprising:
 a. rolling a primary die with means for indicating said randomized result and means for directing a user to roll a secondary die, and   b. following any direction given by said primary die to roll said secondary die with means for indicating said randomized result,   
       wherein when said primary die and said secondary die are used in combination they produce said randomized result. 
     
     
         2 . The method from  claim 1  wherein said primary die has an insufficient quantity of faces to produce said randomized result when used in isolation because said predetermined probability distribution includes results which are less probable than the probability of rolling any given face on said primary die. 
     
     
         3 . The method from  claim 1  wherein said primary die is selected from the group consisting of 120-sided and 60-sided dice. 
     
     
         4 . The method from  claim 1  wherein said secondary die is selected from the group consisting of 120-sided, 100-sided, 60-sided, 50-sided, 48-sided, 30-sided, 24-sided, 20-sided, 12-sided, 10-sided, 8-sided, 6-sided and 4-sided dice. 
     
     
         5 . The method from  claim 1  wherein said secondary die has means for directing said user to roll a tertiary die and when said primary die, said secondary die, and said tertiary die are used in combination they produce said randomized result. 
     
     
         6 . The method from  claim 1  wherein said predetermined probability distribution is the D20 With Advantage probability distribution that results from rolling two 20-sided dice each numbered 1-20 and choosing the greater value as the result. 
     
     
         7 . The method from  claim 1  wherein said predetermined probability distribution is an approximation of the D20 With Advantage probability distribution that results from rolling two 20-sided dice each numbered 1-20 and choosing the greater value as the result. 
     
     
         8 . The method from  claim 1  wherein said predetermined probability distribution is the D20 With Disadvantage probability distribution that results from rolling two 20-sided dice each numbered 1-20 and choosing the lesser value as the result. 
     
     
         9 . The method from  claim 1  wherein said predetermined probability distribution is an approximation of the D20 With Disadvantage probability distribution that results from rolling two 20-sided dice each numbered 1-20 and choosing the lesser value as the result. 
     
     
         10 . The method from  claim 1  wherein said predetermined probability distribution is an approximation of the 4D6 Drop Lowest probability distribution that results from rolling four 6-sided dice each numbered 1-6 and summing the three greatest values to come to the result. 
     
     
         11 . A plurality of dice for producing a randomized result conforming to a predetermined probability distribution, comprising:
 a. a primary die with a predetermined number of primary faces, and   b. a secondary die with a predetermined number of secondary faces, and   c. a plurality of primary markings that appear on said primary faces and are selected from the group consisting of result markings and markings directing a user to roll said secondary die, and   d. a plurality of secondary markings that appear on said secondary faces and indicate a result,   
       wherein when a user starts by rolling said primary die and follows any potential directions given by said primary die to roll additional members of said plurality of dice, said randomized result is eventually produced by a member of said plurality of dice. 
     
     
         12 . The plurality of dice from  claim 11  wherein said primary die has an insufficient quantity of said primary faces to produce said randomized result when used in isolation because said predetermined probability distribution includes results which are less probable than the probability of rolling any individual example of said primary faces. 
     
     
         13 . The plurality of dice from  claim 11  wherein said predetermined number of primary faces is selected from the group consisting of 120 and 60. 
     
     
         14 . The plurality of dice from  claim 11  wherein said predetermined number of secondary faces is selected from the group consisting of 120, 100, 60, 50, 48, 30, 24, 20, 12, 10, 8, 6 and 4. 
     
     
         15 . The plurality of dice from  claim 11  wherein said plurality of dice includes a tertiary die and said plurality of secondary markings includes markings directing said user to roll said tertiary die and when said user starts by rolling said primary die and follows any potential directions given by said primary die to roll said secondary die and follows any potential directions given by said secondary die to roll said tertiary die, said randomized result is eventually produced by a member of said plurality of dice. 
     
     
         16 . The plurality of dice from  claim 11  wherein said predetermined probability distribution is the D20 With Advantage probability distribution that results from rolling two 20-sided dice each numbered 1-20 and choosing the greater value as the result. 
     
     
         17 . The plurality of dice from  claim 11  wherein said predetermined probability distribution is an approximation of the D20 With Advantage probability distribution that results from rolling two 20-sided dice each numbered 1-20 and choosing the greater value as the result. 
     
     
         18 . The plurality of dice from  claim 11  wherein said predetermined probability distribution is the D20 With Disadvantage probability distribution that results from rolling two 20-sided dice each numbered 1-20 and choosing the lesser value as the result. 
     
     
         19 . The plurality of dice from  claim 11  wherein said predetermined probability distribution is an approximation of the D20 With Disadvantage probability distribution that results from rolling two 20-sided dice each numbered 1-20 and choosing the lesser value as the result. 
     
     
         20 . The plurality of dice from  claim 11  wherein said predetermined probability distribution is an approximation of the 4D6 Drop Lowest probability distribution that results from rolling four 6-sided dice each numbered 1-6 and summing the three greatest values to come to the result.