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We introduce a class of extensive form games whereplayers might not be able to foresee the possible consequences of their decisions and form a model of theiropponents which they exploit to achieve a more profitable outcome. We improve upon existing models ofgames with limited foresight, endowing players with theability of higher order reasoning and proposing a novelsolution concept to address intuitions coming from realgame play. We analyse the resulting equilibria, devisingan effective procedure to compute them.