  In this paper we revisit an open problem posed by Aldous on the max-entropy
win-probability martingale: given two players of equal strength, such that the
win-probability is a martingale diffusion, which of these processes has maximum
entropy and hence gives the most excitement for the spectators? We study a
terminal-boundary value problem for the nonlinear parabolic PDE
$2\partial_te(t,x)=\log(-\partial_{xx}e(t,x))$ derived by Aldous and prove its
wellposedness and regularity of its solution by combining PDE analysis and
probabilistic tools, in particular the reformulation as a stochastic control
problem with restricted control set, which allows us to deduce strict
ellipticity. We establish key qualitative properties of the solution including
concavity, monotonicity, convergence to a steady state for long remaining time
and the asymptotic behaviour shortly before the terminal time. Moreover, we
construct convergent numerical approximations. The analytical and numerical
results allow us to highlight the behaviour of the win-probability process in
the present case where the match may end early, in contrast to recent work by
Backhoff-Veraguas and Beiglb\"ock where the match always runs the full length.
