Logical Omniscience at the Laboratory

•We experimentally measure how many steps of counterfactual reasoning humans can do.•In order to separate cognitive ability from other behavioural influence factors in games we use a novel computerized version of the Dirty Faces Game.•We find that on average our subjects can perform two to three steps of iterative reasoning.•This shows that subjects are better at iterative reasoning than suggested by studies that do not control for subjects’ beliefs about the rationality of others or social preferences.