  We show open games cover extensive form games with both perfect and imperfect
information. Doing so forces us to address two current weaknesses in open
games: the lack of a notion of player and their agency within open games, and
the lack of choice operators. Using the former we construct the latter, and
these choice operators subsume previous proposed operators for open games,
thereby making progress towards a core, canonical and ergonomic calculus of
game operators. Collectively these innovations increase the level of
compositionality of open games, and demonstrate their expressiveness.
