Project 4: The Discrepant Dice Company

The Discrepant Dice Company is a start-up devoted to solving the following critical problem plaguing modern society: too many die rolls are needed to determine an outcome. For example, suppose that you wanted to specify a random event with an arbitrary probability, say 57.5%. With a regular 6-sided die, you could get outcomes with 50% probability (e.g., roll an even number) or 67% probability (e.g., roll a number less than 5). But to get closer to the desired probability you'd need to either roll the die multiple times, or use a die with more faces. But even a regular 20-sided die will still not be able to get closer than 55% or 60% with one roll.

Your job is to design a die that allows you to get as close as possible to any specified outcome probability.