Shafer (management, Rutgers U.) and Vovk (computer science, U. of London) explain how probability can be based on game theory rather than measure theory, and how doing so allows it to be used in finance without a lot of distracting and confusing assumptions about randomness. Where necessary, they have chosen clarity and simplicity over completeness and generality, and invite readers to participate in developing the idea rather than aspiring to a comprehensive treatise. After setting out the principles, they look first at probability without measure, and then at finance without probability. Annotation c. Book News, Inc., Portland, OR (booknews.com)