Many Faces of the Gambler's Fallacy: Subjective Randomness and Its Diverse Manifestations

The series of heads and tails obtained when tossing a fair coin exemplifies a random sequence. Randomness defies a strict definition, yet it is widely used in daily and scientific discourse. When perceiving or producing randomness, people err by exaggeratedly expecting a change after a few identical symbols. This is the gambler's fallacy (GF). Diverse real manifestations of GF, in casino or lottery decisions, expressions in fiction and art, and uses in deciphering codes, are all described, interwoven with stories and anecdotes. The roots of GF are presumably ascribed to one's inability to forget or ignore previous stimuli in a sequence. Students, not only of psychology, and other inquisitive readers may find the GF issue challenging.

Ruma Falk, nee Oren-Aharonovich, born in Jerusalem in 1932, is professor emeritus of psychology at the Hebrew University of Jerusalem. She studied mathematics, statistics and psychology at the Hebrew University, including one (rewarding) academic year (1954/5) at Stockholm's University (then Högskola) in Sweden, and spent sabbaticals at Decision Research in Eugene, Oregon, Berlin's Institute for Advanced Studies, University of Massachusetts, Amherst, and Harvard University. R. F. had been teaching courses in statistics, probability, the psychology of chance, and problem solving in several departments of the Hebrew University (psychology, school of education, and others) for many years. Her research deals with the perception of randomness (PhD dissertation supervised by Amos Tversky), and with the surprisingness of coincidences. She published articles on probabilistic and mathematical issues as well as on her research concerning the development of the concept of probability and the notion of the infinity of numbers in children. One book in English and two in Hebrew were devoted to problems, puzzles and their analyses. Ruma has been cooperating through all the stages with her husband (since 1953), Raphael, a geneticist who specialized in the history and philosophy of science. They have two children, four grandchildren and two great-grandchildren.