In 1953, Gale and Stewart developed the general theory of infinite games (the so-called Gale-Stewart games) which are two- player zero-sum infinite games with perfect information.  The theory of Gale-Stewart games has been deeply investigated by many logicians and it has been one of the main topics in set theory while having connections with other topics of set theory as well as model theory and computer science.

In 1969, Blackwell proved the extension of von Neumann's mini-max theorem where he introduced infinite games with imperfect information - nowadays called Blackwell games. Although Blackwell games have not been as much investigated as Gale-Stewart games, in 1998, Martin proved that the Axiom of Determinacy (AD) implies the Axiom of Blackwell Determinacy (Bl-AD) and conjectured the converse, which is still not known to be true.

In this talk, we introduce Gale-Stewart games, Blackwell games and their determinacy and talk about the connection between the determinacy of Gale-Stewart games and that of Blackwell games. A part of the work is with Benedikt Loewe & Devid de Kloet and another part is with Hugh Woodin.