  The mu-calculus is a powerful tool for specifying and verifying transition
systems, including those with both demonic and angelic choice; its quantitative
generalisation qMu extends that to probabilistic choice.
  We show that for a finite-state system the logical interpretation of qMu, via
fixed-points in a domain of real-valued functions into [0,1], is equivalent to
an operational interpretation given as a turn-based gambling game between two
players.
  The logical interpretation provides direct access to axioms, laws and
meta-theorems. The operational, game- based interpretation aids the intuition
and continues in the more general context to provide a surprisingly practical
specification tool.
  A corollary of our proofs is an extension of Everett's singly-nested games
result in the finite turn-based case: we prove well-definedness of the minimax
value, and existence of fixed memoriless strategies, for all qMu
games/formulae, of arbitrary (including alternating) nesting structure.
