We here present both experimental and theoretical results for an Anticipation Game, a two-stage game wherein the standard Dictator Game is played after a matching phase wherein receivers use the past actions of dictators to decide whether to interact with them. The experimental results for three different treatments show that partner choice induces dictators to adjust their donations towards the expectations of the receivers, giving significantly more than expected in the standard Dictator Game. Adding noise to the dictators' reputation lowers the donations, underlining that their actions are determined by the knowledge provided to receivers. Secondly, we show that the recently proposed stochastic evolutionary model where payoff only weakly drives evolution and individuals can make mistakes requires some adaptations to explain the experimental results. We observe that the model fails in reproducing the heterogeneous strategy distributions. We show here that by explicitly modelling the dictators' probability of acceptance by receivers and introducing a parameter that reflects the dictators' capacity to anticipate future gains produces a closer fit to the aforementioned strategy distributions. This new parameter has the important advantage that it explains where the dictators' generosity comes from, revealing that anticipating future acceptance is the key to success.