The tendency for people to believe that an outcome is less likely to occur the more often it has recently occurred is known as the Gambler’s Fallacy belief. In many situations, such as casino gambling, the belief is an error. We show that the Gambler’s Fallacy is unlikely to be corrected for with increased experience with random events. We develop a simple model of how people learn about the probability of success given recent success via repeated exposure to random sequences. For each sequence people observe the proportion of success given recent success and then update their beliefs, but (partially) neglect sample size. In the limit subjects never learn the true probability. The model has novel predictions for behavior. We propose some simple experimental tests.