1. To evaluate the results of Seligman’s Monte Carlo experiment, first find the probability distribution of the gain x on a single $5 bet. The technique of simulating a process that contains random elements and repeating the process over and over to see how it behaves is called a Monte Carlo procedure. It is widely used in business and economics to investigate the performance of an operation that is subject to random effects such as weather, human behavior, economic climate, and so on.

For example, you could model a manufacturer’s inventory by modeling daily arrivals of materials from suppliers, production of items within the plant, and the shipping of manufactured items to buyers. Using this information, you could calculate the inventory of items on hand at the end of each day. All of this requires that you know or have a good approximation to distributions used to model the arrival of new material, the production of items in the plant and the shipment of completed goods. Varying the distributions used in the modeling could reveal changes that would result in a more profitable operation of the plant.

In an article entitled “The Road to Monte Carlo,” Daniel Seligman comments on the Monte Carlo method, noting that although the technique is widely used in business schools to study capital budgeting, inventory planning, and cash flow management, no one seems to have used the procedure to study how well we might do if we were to gamble at Monte Carlo.25 Following up on this thought, Seligman programmed his personal computer to simulate the game of American roulette. Roulette involves a wheel with its rim divided into 38 pockets. Thirty-six of the pockets are numbered 1 to 36 and are alternately colored red and black. The two remaining pockets are colored green and are marked 0 and 00. To play the game, you bet a certain amount of money on one or more pockets. The wheel is spun and turns until it stops. A ball falls into a slot on the wheel to indicate the winning number.

If you have money on that number, you win a specified amount. You can also bet on a color, on odd or even numbers, as well as other interesting betting schemes with various payouts.

If you bet on any single number, including 0 and 00, the payout is 35 to 1.