A generalization of the car versus billy-goat problem

Abstract

This paper is a generalization of the famous and counter intuitive problem of car versus billy-goat, known as the Monty Hall problem. With the hypothesis that the number of cars plus the number of billy-goats is equal to the number of doors, and the TV host may open more than one door, we prove that the best strategy is always to switch the door. To obtain the analytical results we use only simple calculations of probability. We also did some numerical simulations that illustrate the obtained results. The programming code is included in the paper.