The proneness of stated preference choice experiments to hypothetical bias has increased the popularity of incentivized or real discrete choice experiments (RDCE). One challenge that practitioners face when designing RDCE is that some of the product alternatives may not be available for the study. To avoid deception, researchers should truthfully inform respondents that only a certain percentage of the product alternatives is available for the experiment. But would the proportion of available products influence the results of the RDCE? Using an induced value choice experiment, we varied the number of potentially binding alternatives in four treatments: 0%, 33%, 66%, and 100% to assess the effect of availability of product alternatives on choice behavior. We designed the induced value experiment with a profit maximization optimal strategy for agents (i.e., with a unique known profit-maximizing alternative). Our results suggest that incentives matter in that the percentage of optimal choices was lowest in the 0% treatment. Interestingly, however, we did not find statistically significant differences in amount of optimal choices in the 33%, 66%, and 100% treatments, suggesting that one could conduct an incentivized RDCE without the need to have all the product alternatives be made available in the study.