We introduce a class of extensive form games where players might not be able
to foresee the possible consequences of their decisions and form a model of
their opponents which they exploit to achieve a more profitable outcome. We
improve upon existing models of games with limited foresight, endowing players
with the ability of higher-order reasoning and proposing a novel solution
concept to address intuitions coming from real game play. We analyse the
resulting equilibria, devising an effective procedure to compute them.