  Consider concurrent, infinite duration, two-player win/lose games played on
graphs. If the winning condition satisfies some simple requirement, the
existence of Player 1 winning (finite-memory) strategies is equivalent to the
existence of winning (finite-memory) strategies in finitely many derived
one-player games. Several classical winning conditions satisfy this simple
requirement.
  Under an additional requirement on the winning condition, the non-existence
of Player 1 winning strategies from all vertices is equivalent to the existence
of Player 2 stochastic strategies winning almost surely from all vertices. Only
few classical winning conditions satisfy this additional requirement, but a
fairness variant of o
