@poetryandwine I'm neither a mathematician nor a psychologist, but I think MHP is not easy and not just a probability problem.
You will be familiar with this from Gill 2009, "The Monty Hall Problem is not a Probability Puzzle (It’s a challenge in mathematical modelling)."
"The Monty Hall Problem offers much more to the student than a mindless exercise in conditional probability. It also offers a challenging exercise in mathematical modelling. I notice three important lessons. (1) The more you assume, the more you can conclude, but the more limited are your conclusions. The honest answer is not one mathematical solution but a range of solutions. (2) Whether you are a subjectivist or a frequentist affects the ease with which you might make probabilistic assumptions but simultaneously affects the meaning of the conclusions. (3). Think out of the box. Vos Savant asks for an action, not for a probability. The player has two decision moments during the show, not one."
But at no point does Gill discuss heuristics, regret theory, and equiprobability bias, which explain why subjects make the wrong choice.
Equiprobability bias increases with formal statistical education. Isn't MHP included in maths teaching now, to avoid this and because it is distinct from probability?
For equiprobability bias see Saenen, L., Heyvaert, M., Van Dooren, W., & Onghena, P. (2015). Inhibitory control in a notorious brain teaser: The Monty Hall dilemma. ZDM Mathematics Education, 47(5), 837 848. doi:10.1007/s11858-015-0667-6
Again, I would be grateful if you could explain the probability approach to the Thog Problem because I don't get it.