  We study two-player concurrent stochastic games on finite graphs, with
B\"uchi and co-B\"uchi objectives. The goal of the first player is to maximize
the probability of satisfying the given objective. Following Martin's
determinacy theorem for Blackwell games, we know that such games have a value.
Natural questions are then: does there exist an optimal strategy, that is, a
strategy achieving the value of the game? what is the memory required for
playing (almost-)optimally? The situation is rather simple to describe for
turn-based games, where positional pure strategies suffice to play optimally in
games with parity objectives. Concurrency makes the situation intricate and
heterogeneous. For most {\omega}-regular objectives, there do indeed not exist
optimal strategies in general. For some objectives (that we will mention),
infinite memory might also be required for playing optimally or
almost-optimally. We also provide characterizations of local interactions of
the players to ensure positionality of (almost-)optimal strategies for B\"uchi
and co-B\"uchi objectives. This characterization relies on properties of game
forms underpinning the formalism for defining local interactions of the two
players. These well-behaved game forms are like elementary bricks which, when
they behave well in isolation, can be assembled in graph games and ensure the
good property for the whole game.
