Links

Solving the Monty Hall Problem using Information Theory

Also includes a refresher on information theory basics like entropy and information gain. “Information gain” is central to the explanation

Since Monty Hall knows where the car is located, he opens one of the remaining two doors that always contains a goat. In opening the door Monty Hall provides information given by -ln (2), since he has a choice of two doors.

There is no shortage of excellent articles and YouTube videos discussing this problem but the two explanations that have resonated the most with me are the (1) information theory approach as described in the link and (2) extending the problem to 10,000 doors as opposed to 3 doors.