Inferring the Host: A Bayesian Look at the Monty Hall Problem

The classic Monty Hall problem's "always switch" solution is re-examined through a Bayesian lens, revealing its dependence on a specific model of the host's behavior. Different host scenarios are explored, such as an ignorant host or one with a preference for opening a particular door, which significantly alters the probability of winning. By observing the host over several games, one can infer their habits and create a more accurate model for making the switching decision. This approach uses Bayesian inference and Python code to estimate the host's bias from data and propagate that uncertainty into the final win probability. The analysis also extends to comparing different models, like determining if the host even knows where the car is based on a series of episodes.