The two fallacies of gamblers: type I and type II

The so-called "gambler's fallacy" asserts that gamblers believe mechanical randomizers (such as roulette) exhibit sequential tendencies. In this paper we introduce another false belief of gamblers, namely the tendency to bet on a winning number under the assumption that the roulette wheel is biased. We discuss the proper analysis for detecting biased numbers and demonstrate empirically that people notoriously underestimate the number of observations needed for a reliable detection of biased numbers. We label this bias as the Type II gambler's fallacy and suggest that both types of the fallacy are due to misperceptions of randomness. Implications for real life situations are briefly discussed