Performing conditional strategies in strategic STIT theory

We introduce a formalization of conditional strategies in strategic STIT theory. This will turn out to have unexpected consequences, in particular it turns out that performing a strategy conditional on c is equivalent to performing that strategy conditional on a logically weaker condition. Hence it will turn out that performance of a strategy conditional on c can already commit you to performing that strategy if c is not the case. We will argue in favour of our formalization, this result and some further consequences. Our investigation points to a misunderstanding that the conditions in the conditional strategies are moment-determinate.