Optimal rolling of fair dice using fair coins
Data Structures and Algorithms
2024-12-31 v1 Probability
Computation
Abstract
In 1976, Knuth and Yao presented an algorithm for sampling from a finite distribution using flips of a fair coin that on average used the optimal number of flips. Here we show how to easily run their algorithm for the special case of rolling a fair die that uses memory linear in the input. Analysis of this algorithm yields a bound on the average number of coin flips needed that is slightly better than the original Knuth-Yao bound. This can then be extended to discrete distributions in a near optimal number of flips again using memory linear in the input.
Cite
@article{arxiv.2412.20700,
title = {Optimal rolling of fair dice using fair coins},
author = {Mark Huber and Danny Vargas},
journal= {arXiv preprint arXiv:2412.20700},
year = {2024}
}
Comments
11 pages, 2 figures