We examine how almost winning in roulette affects subsequent betting behavior. Our main finding is heterogeneity in gambler behavior with some gamblers less likely to bet on numbers that were near misses on the prior spin and other gamblers more likely to bet on near miss numbers. Using a unique data set from the game rapid roulette, we model the likelihood of a gambler betting on a near miss number while controlling for the favorite number bias and the likelihood of a number being a near miss. We also find no evidence that near misses in roulette leads to gamblers extending the time spent gambling or to the placing of more bets.

We examine two departures of individual perceptions of randomness fromprobability theory: the hot hand and the gambler's fallacy, and theirrespective opposites. This paper's first contribution is to use data fromthe field (individuals playing roulette in a casino) to demonstrate theexistence and impact of these biases that have been previously documented in thelab. Decisions in the field are consistent with biased beliefs, although weobserve significant individual heterogeneity in the population. A secondcontribution is to separately identify these biases within a given individual,then to examine their within-person correlation. We find a positive andsignificant correlation across individuals between hot hand and gambler'sfallacy biases, suggesting a common (root) cause of the two related errors. Wespeculate as to the source of this correlation (locus of control), and suggestfuture research which could test this speculation.

In the classic Dubins-Savage subfair primitive casino gambling problem, the gambler can stake any amount in his possession, winning (1 - r)/r times the stake with probability w and losing the stake with probability 1 - w, 0 ≤ w ≤ r ≤ 1. The gambler seeks to maximize the probability of reaching a fixed fortune by gambling repeatedly with suitably chosen stakes. This problem has been extended in several directions to account for limited playing time or future discounting. We propose a unifying framework that covers these extensions, and prove that bold play is optimal provided that w ≤ ½ ≤ r. We also show that this condition is in fact necessary for bold play to be optimal subject to the constraint of limited playing time.

The random walk arising in the game of roulette involves an absorbing barrier at the origin; at each step either a unit displacement to the left or a fixed multiple displacement to the right can occur with probabilities q and p respectively. Using generating functions and Lagrange's theorem for the expansion of a function as a power series explicit expressions are deduced for the probabilities of the player's capital at the nth step.