Batesian mimicry is one of the most popular topics in biology.  Three players are involved in Batesian mimicry: a mimic, a model, and a predator. Specifically, the palatable mimic benefits from having a phenotype similar to that of the unpalatable model, and the predator's ability to distinguish between the mimic and the model depends on the similarity between the two prey items. This similarity could also be seen as the predator's decision accuracy. Intuitively, mimics are thought to gain the most benefit if they are highly similar to the models. However, empirical evidence has shown that imperfect mimicry exists in nature (i.e., mimics that do not show high similarity with the models). Here, we use a theoretical framework to study how the accuracy of predator decisions influences the stability and dynamics of the mimicry system. Our results suggest that systems with intermediate similarity between the model and the mimic exhibit the most stable dynamics and have the highest total population density. Therefore, we conclude that imperfect mimicry is a beneficial property of the mimicry system, rather than an insufficient of the mimicry system.