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 derived by Aldous and prove its wellposedness and regularity of its solution by combining PDE analysis and probabilistic tools. We establish key qualitative properties of the solution and construct convergent numerical approximations, which 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 Beiglböck where the match always runs the full length. Joint work with Gaoyue Guo, Sam Howison, and Dylan Possamaï.