Compared to the gambler’s fallacy in which one makes predictions negatively dependent on the past information, in the hot hand belief, one makes predictions positively dependent on the past information. Both phenomena have been attributed to people’s misperception of randomness. The present study examines an alternative explanation that the positive dependency in the hot hand belief may be due to people’s effort to reduce uncertainty by estimating the unknown probability (common probability estimation), a result known as the Laplace’s rule of succession. We report an experiment to demonstrate that the dependency on the history can be reversed from negative to positive by manipulating the participants’ assumptions about the unknown probability.