  We present a sound, complete, and optimal single-pass tableau algorithm for
the alternation-free $\mu$-calculus. The algorithm supports global caching with
intermediate propagation and runs in time $2^{\mathcal{O}(n)}$. In
game-theoretic terms, our algorithm integrates the steps for constructing and
solving the B\"uchi game arising from the input tableau into a single
procedure; this is done on-the-fly, i.e. may terminate before the game has been
fully constructed. This suggests a slogan to the effect that global caching =
game solving on-the-fly. A prototypical implementation shows promising initial
results.
