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We consider games with two antagonistic players --- \'Elo\"ise (modelling aprogram) and Ab\'elard (modelling a byzantine environment) --- and a third,unpredictable and uncontrollable player, that we call Nature. Motivated by thefact that the usual probabilistic semantics very quickly leads toundecidability when considering either infinite game graphs orimperfect-information, we propose two alternative semantics that leads todecidability where the probabilistic one fails: one based on counting and onebased on topology.

How Good Is a Strategy in a Game With Nature?