Animals return to rewarded locations. An example of this is Conditioned Place Preference (CPP) which is widely used in studies of drug reward. Although CPP is expressed as increased time spent in a previously rewarded location, the behavioral strategy underlying this change is unknown. We continuously monitored rats (n = 22) in a three room in-line configuration, before and after morphine conditioning in one end room. Although sequential room visit durations were variable, their probability distribution was exponential, indicating that the processes controlling visit durations can be modeled by instantaneous room exit probabilities. Further analysis of room transitions and computer simulations of probabilistic models revealed that the exploratory bias toward the morphine room is best explained by an increase in the probability of a subset of rapid, direct transitions from the saline to the morphine paired room via the central room. This finding sharply delineates and constrains possible neural mechanisms for a class of self initiated, goal directed behaviors toward previously rewarded locations.