I think importantly, the "Monty Hall Problem" as described is different from how any iteration of the Big Deal at the end of Let's Make a Deal is actually run.

I think importantly, the "Monty Hall Problem" as described is different from how any iteration of the Big Deal at the end of Let's Make a Deal is actually run. Hall himself recognized this and mentioned it in a NYT interview in the 90s. It's paywalled, but the excerpt is here: https://en.wikipedia.org/wiki/Monty_Hall_problem https://en.wikipedia.org/wiki/Monty_Hall_problem Hall understood the problem, giving the reporter a demonstration with car keys and explaining how actual game play on Let's Make a Deal differed from the rules of the puzzle. When I first heard about the puzzle, I struggled with the solution precisely because I kept making assumptions about the puzzle based on my knowledge of the show. It wasn't until I thoroughly read the question, setting aside those assumptions, that I realized it is materially different from the show and I was able to really understand the solution.