Successful innovation hinges on balancing exploring new ideas and exploiting existing ones. A rational innovator should be state-sensitive, effectively switching to exploitation when the best available idea reaches some standard. We tackle innovation with a discovery-by-recombination game under additive reward growth, and compare the optimal state-dependent policy with a state-independent policy. Our experiment reveals that participants made state-dependent decisions, exploring more in rounds with early successes, albeit being told of the same true success probability. In contrast, the optimal state-dependent policy switches to exploitation earlier. This suggests that participants' state-sensitivity may be driven by ad-hoc subjective probabilities. Participants also deviated from optimality through excessive exploration, switching multiple times between exploration and exploitation, and their switching points also differed from the theoretical optimum.