INTRODUCTION

The concepts of chance and uncertainty are as old as civilization. People have always had to cope with weather uncertainty, health hazards, food insecurity, and other risky aspects of their environment. As a result, they have devised risk-management schemes that reduce uncertainty and improve the chances for their own survival. Interestingly, early risk-management strategies were developed without formal logical structures. An example is the decision rule: Do not all put your eggs in the same basket. This simple decision rule does not require any specific assessment of risk. This indicates that modern probability and statistics are not absolutely necessary for risk management. Yet, in many situations, there is much to gain from imposing some structure on what is not known. This includes gambling games.

Games of chance have a long history. Gambling with dice has been popular for many centuries. The precursors of dice have been found in Egypt and elsewhere by 3500 B.C. Interestingly, because they are relatively simple, gambling games provided the impetus for the development of probability theory in the sixteenth and seventeenth century. Girolamo Cardano (1501 1576) and Galileo Galilei (1564 1642) calculated numerical probabilities for certain dice combinations. Blaise Pascal (1623 1662) and Pierre Fermat (1601 1665) started the mathematical theory of probability by deriving the probabilities for certain gambling problems involving dice. Since then the theory of probability has been developed and refined, with applications to engineering, science, and management.

The main motivation for probability theory is to impose a structure on what is not known. While...