Every day, billions of human beings are making dozens of decisions that do not appear based on the same, seemingly sound mathematical principles they would apply to a gambling or investing situation. Yet these decisions are not irrational, rather they are the product of an innate sense pertaining to risk and opportunity. This Third Edition is presented for the non-mathematician (though the underlying math is provided for those who are interested), and not only gives reason to reconsider the bases we assess gambling and investing situations, but reveals this magnificent, innate ability we possess.For decades various mathematical notions have presented themselves which, though applicable to domains such as probability, game theory, operations research, and quantitative finance, have fallen essentially outside the purview of these various disciplines. Yet the concepts detailed in this text are all related, and taken together comprise their own niche-discipline, introduced here as Risk-Opportunity Analysis.