538 Riddler: Ghostbusters

A solution to the riddle on page 71 of The Riddler and also in the weekly column: Will You Be A Ghostbuster Or A World Destroyer?

There is a simple closed form solution, but I wanted to do a brute force Monte Carlo simulation. I randomly assigned two spots on the circle for the two ghostbusters (Abe and Betty) and then assigned two spots for the ghosts (Dan and Candace). Then ran multiple simulations and tracked of the streams crossed or not.

The convergence plot below shows how ~1k sims convergence to the solution of 33% chance that they cross streams.

See the Jupyter Notebook.