ABSTRACT
This chapter discusses to some applications of stochastic processes in gambling theory and in operations research. Internet search engines are based on ranking algorithms. They rank the pages of the Web and display them on the screen according to the order of their relative importance. The Google page rank model is based on two natural principles. In probability theory, martingales refer to fair games in the sense that the average gain given the information is always null for all gambling strategies use. This terminology was introduced in 1939 by Jean Ville, but its literal origin comes from the early ages of casino gambling in the 18th century in France. The D'Alembert martingale is sometimes called the pyramid betting system. The name originates from the famous French 18th century mathematician Jean le Rond D'Alembert. The betting strategy is very simple.
