Tip of the Week #20                     Tip Index

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Why Flip a Coin: The Art and Science of Good Decisions

by H. W. (Harold Warren) Lewis (1997, John Wiley & Sons, Inc., 206 p.)

This entertaining book is light reading about misconceptions about probability. Twenty-three short chapters discuss brain-teasing problems ranging from winning the office football pool to winning a battle. Some of the paradoxes confound the intuition.

Although the book is sometimes short on substance, the examples provoke thinking and should foster interest in decision making. Many of the examples relate to the United States (certain laws and issues about voting) that may be of less interest to readers in other countries. However, the relevance for other countries should be readily apparent.

One of many interesting ideas is "Lanchester's Law," named after English engineer Frederick Lanchester.

For fun, I wrote a QuickBASIC Monte Carlo simulation (LANCHAST.BAS) to test Lanchester's Law. As with Lewis's example, one side (A) starts with 5 units, and the other side (B) with 3 units. I assumed a .01 chance of a unit hitting a unit of the opposing force on any particular volley. After 1,000 trials:

    Average ending A force: 3.54 units
    Average ending B force: 0.25 units
    P(A wins) = .874
    P(B wins) = .126
    Average ending A when A wins: 4.05 units (apparently the 4 units predicted by Lanchester's Law)
    Average ending B when B wins: 1.99 units.

A simple simulation provides much more information for decision making and can easily incorporate other details, such as comparative advantages, in the model.

Watch for future tips that discuss other interesting examples from Why Flip a Coin?

—John Schuyler, July 1997

Copyright 1997 by John R. Schuyler. All rights reserved. Permission to copy with reproduction of this notice.