For March’s puzzle, you had to determine the Nash equilibrium of a tricky probabilistic model of Robot Long Jump. It turned out the optimal play involved waiting until a robot’s position was at least some threshold x and then jumping, where x satisfies the equation

(x³ - 3x + 2)e^x = 3x.

This threshold comes to ~0.416195355. Given that, the chance of any given round scoring a positive number is (1-x)e^x, and so the final answer is (1-(1-x)e^x) ~ 0.114845886…

Congrats to the solvers that successfully computed the strategy and this probability!