The bewildered novice in chess moves cautiously, recalling individual rules, whereas the experienced player absorbs a complicated situation at a glan… - William Feller

Simple methods will soon lead us to results of far reaching theoretical and practical importance. We shall encounter theoretical conclusions which not only are unexpected but actually come as a shock to intuition and common sense. They will reveal that commonly accepted notions concerning chance fluctuations are without foundation and that the implications of the law of large numbers are widely misconstrued.

When this book was first conceived (more than 25 years ago) few mathematicians outside the Soviet Union recognized probability as a legitimate branch of mathematics.

To every event defined for the original random walk there corresponds an event of equal probability in the dual random walk, and in this way almost every probability relation has its dual.