This paper reports an experiment involving an ultimatum bargaining game, played in the Slovak Republic. Financial stakes were varied by a factor of 25, and behavior was observed both when players were inexperienced and as they gained experience. Consistent with prior results, changes in stakes had only a small effect on play for inexperienced players. But the present experimental design allows us to observe that rejections were less frequent the higher the stakes, and proposals in the high stakes conditions declined slowly as subjects gained experience. This Slovak experiment is the first to detect a lower frequency of rejection when stakes are higher and this can be explained by the added power due to multiple observations per subject in the experimental design. A model of learning suggests that the lower rejection frequency is the reason that the proposers in the higher stakes conditions of the ultimatum game learn to make lower offers.