What some puzzling problems teach about the theory of simulation and the use of resampling.

Simulation is simpler intellectually than the formulaic<br>method because it does not require that one calculate the<br>number of points in the entire sample space and the number<br>of points in some subset. Instead, one directly samples<br>the ratio. This article presents probabilistic problems<br>that confound even skilled statisticians when attacking the<br>problems deductively, yet are easy to handle correctly, and<br>become clear intuitively, with physical simulation. This<br>analogy demonstrates the usefulness of simulation in the<br>form of resampling methods.