A Toolbox for Quasirandom Simulation

Abstract

In the eighteenth century, Georges-Louis Leclerc, Comte de Buffon, proposed a novel method to estimate p—dropping a needle over and over again onto a wooden floor of parallel planks. The probability of a needle crossing a join in the floor is related to p. By counting the number of crosses, one can estimate this probability, and hence compute a value for p (see [1]). Buffon is said to have tried the method by tossing baguettes over his shoulder. A more direct way of estimating p is to throw darts randomly at a circular target inscribed in a square, and count the proportion that land inside the circle. These are simple examples of numerical integration by simulation.