The ability of an individual to predict the outcome of the actions of others and to change their own behavior adaptively is called anticipation. There are many examples from mammalian species—including humans—that show anticipatory abilities in a social context, however, it is not clear to what extent fishes can anticipate the actions of their interaction partners or what the underlying mechanisms are for that anticipation. To answer these questions, we let live guppies (Poecilia reticulata) interact repeatedly with an open-loop (noninteractive) biomimetic robot that has previously been shown to be an accepted conspecific. The robot always performed the same zigzag trajectory in the experimental tank that ended in one of the corners, giving the live fish the opportunity to learn both the location of the final destination as well as the specific turning movement of the robot over three consecutive trials. The live fish’s reactions were categorized into a global anticipation, which we defined as relative time to reach the robot’s final corner, and a local anticipation which was the relative time and location of the live fish’s turns relative to robofish turns. As a proxy for global anticipation, we found that live fish in the last trial reached the robot’s destination corner significantly earlier than the robot. Overall, more than 50% of all fish arrived at the destination before the robot. This is more than a random walk model would predict and significantly more compared to all other equidistant, yet unvisited, corners. As a proxy for local anticipation, we found fish change their turning behavior in response to the robot over the course of the trials. Initially, the fish would turn after the robot, which was reversed in the end, as they began to turn slightly before the robot in the final trial. Our results indicate that live fish are able to anticipate predictably behaving social partners both in regard to final movement locations as well as movement dynamics. Given that fish have been found to exhibit consistent behavioral differences, anticipation in fish could have evolved as a mechanism to adapt to different social interaction partners.