Mapache

I had somewhat of an annoying morning this morning, but the way it was annoying was so excessively Silicon Valley that the humor substantially outweighed the feelings of annoyance.

Specifically, on my commute in to work, I was delayed by a traffic jam on 101 because a Google Bus had rear-ended a Tesla on the exit ramp onto 237, and this meant that I arrived at work too late to get my free breakfast at the office cafe.

Chris Hallbeck posted a cute little short that involves the Monty Hall Paradox at https://www.youtube.com/shorts/At_LNDO1eq0, and it includes an explanation of the result that has a lot of people saying "I finally understand it!" in comments. And, after watching it and reading some comments, I think I have an even more intuitive explanation.

The paradox is this: In front of you is a game show host, and three doors. Behind one of the doors is a Shiny New Car, or some other great prize that you may win. Behind the other two doors are goats. You select a door. The host then opens one of the doors that you didn't select, revealing a goat, and then offers you an choice: Do you keep the door you selected first, or do you switch to the other door that they didn't open? If the door you select (either by keeping your first selection or switching to the other one) is the one with the prize, you win the prize!

If your door contains the goat, my understanding is that you do not actually get to keep the goat.

(A key datapoint -- often omitted from the descriptions! -- is that this is how the process always goes, and you know that fact. The host will always open a door with a goat, and will always offer the opportunity to switch. This is not a case where the host is being devious and only trying to get you to switch away if you start out choosing the prize.)

The paradoxical result is that switching will lead to the prize twice as often as not-switching, even though it looks like a random choice between two doors that you have no information about.

( Explanation behind cut.... )