When assessing potential mates is costly, there will be selection for copying others. Mate choice copying, which is the increased chance of mating with another individual after observing them mating with someone else (i.e., individual-based copying), has been documented in several species, including humans. It is touted as an example of the influence of culture on animal and human mating, but alone it is unlikely to lead the cultural evolution of mating. Rather, it requires mate choice copying with generalization (i.e., trait-based copying), which is the effect of immediate observations on future mating. This sort of mate choice copying has been documented in six species, including humans. Here, I extend an existing game theory model of mate choice copying to include generalization (Extension 1), a cost to immediate copying (Extension 2), and both previous extensions (Extension 3). The results show that Extensions 1 and 2 decrease the adaptive value of mate choice copying when compared to the original model. Extension 3 suggests that adding generalization to mate choice copying with a cost to immediate copying is a more likely evolutionary trajectory than adding it to mate choice copying without this cost. These results have implications for illuminating the emergence of the cultural evolution of mating preferences.