As AlphaZero has revolutionized the AI of planning when the number of possible futures is combinatorially large, our lack of understanding of how humans plan in such situations has come into stark contrast. The psychology of reasoning in chess once seemed promising but is now virtually extinct. Instead, most cognitive scientists favor planning tasks that don’t require much thinking ahead. I will show that it is possible to study human planning in tasks of intermediate complexity while maintaining experimental tractability and computational modelability. I will describe a series of experiments on a game that we call four-in-a-row -- a variant of tic-tac-toe and Go Moku. I will describe a heuristic computational model of human play, inspired by best-first search and fitted to human moves using inverse binomial sampling and Bayesian Adaptive Direct Search. This model predicts moves in unseen positions, decisions in unseen tasks, eye fixation patterns, mouse movements, and response times. The model allows us to computationally characterize the effects of expertise and time pressure. I will describe parallel results from a very large online data set. I will discuss two ways in which the AI and the cognitive science of complex planning could converge.