How do people plan ahead in sequential decision-making tasks? In this article, we compare computational models of human behavior in a challenging variant of tic-tac-toe, to investigate the cognitive processes underlying sequential planning. We validate the most successful model by predicting choices during games, two-alternative forced choices and board evaluations. We then use this model to study individual skill differences, the effects of time pressure and the nature of expertise. Our findings suggest that people perform less tree search under time pressure, and that players search more as they improve during learning.