Anyone who considers arithmetical methods of producing random digits is, of course, in a state of sin.-- John von Neumann (1951)

Anyone who has not seen the above quotation in at least 100 places is probably not very old.-- D. V. Pryor (1993)

In this section, we shall explore possible reasons for von Neumann's curious statement. This statement is curious for two particular reasons: (1) arithmetic methods are widely used on all computers to generate random numbers, and (2) John von Neumann himself devised such methods for generating random numbers. Von Neumann probably made the above statement in reference to the fact that there are many ways to go amiss when so doing. Our goal in this section is, through a series of example problems, to illustrate various properties of random number generators. With a visceral understanding of the generation process and a solid foundation of cause and effect illustrated through examples, it is our hope that this may help prevent ``straying'' into unacceptable techniques.