In many situations encountered in our daily lives where we have several options to choose from, we need to balance the amount of planning into the future with the number of alternatives we want to consider to achieve our long-term goals. A popular way to study these planning problems in controlled environments is maze-solving tasks, since they can be precisely defined and controlled in terms of their topology. In our study, participants solved mazes that differed systematically in topological properties regulating the number of alternatives and depth of paths. Replicating previous results, we show the influence of these spatial features on performance and stopping times. Longer and more branched solution paths lead to more planning effort and longer solution times. Additionally, we measured subjects’ eye movements to investigate their planning horizon. Our results suggest that people decrease their planning depth with increasing number of alternatives.