Faking Probabilities: Computer Simulation
MAHOGANY DICE AND MODULAR ARITHMETIC
Simulation is one of the most commonly used techniques to gain information about complicated systems, but the term “simulation” is used to convey many different meanings. According to the Merriam-Webster online dictionary, simulation is “the imitative representation of the functioning of one system or process by means of the functioning of another.” We probably think of simulation as something involving computers, but it does not have to be so. For example, airplanes flying in specific parabolic patterns are used in astronaut training to simulate weightless conditions in space. Even when we restrict our attention to computer simulation, there are many different meanings. An airline pilot in training sits in a flight simulator, a nurse in training may use a medical simulator that imitates reactions of a real patient, and the Weather Channel may run a computer simulation with graphics to illustrate how a hurricane can affect coastal areas. For probabilists, however, simulation means “imitating randomness” and the term “Monte Carlo simulation” is sometimes used to emphasize this when we talk to outsiders.
The main use of simulation is to approximate quantities that are difficult to compute exactly. For example, compare roulette and blackjack. In roulette, it is easy to compute probabilities and expected gains, but in blackjack with its more complicated rules and choice of strategies, exact probability ...