#pythagorean math wisdom of the eon

[13thpythagoras]

why it pays to be able to change your mind

see if I describe it faster than Steven pinker

The background is that you're on a game show and there are three doors. Behind two doors is nothing and behind the third door is a gold brick that you get to keep if you guess that door correctly. The catch is that after you guess, but before they show you the result of your guess, they actually open one incorrect or empty door that you didn't guess, and then they give you a chance to switch your guess, if you want to, or not switch your guess.

basically, it's kind of a potentially devastating paradox because initially your odds of being correct, and getting the gold is one out of three, and your odds of being wrong are two out of three. But after they show you that wrong door and eliminate it, and give you a chance to switch; if you actually switch guesses, then that turns your 2/3 probability of being wrong into a 2/3 probability of being correct.

so the punchline is if you switch your guess every time, or guaranteed in your one try, then you're actually going to be correct 2/3 of the time and get that gold break 2/3 of the time.

maybe my explanation clicks or doesn't maybe it's actually wrong or incomplete, it makes sense to me but I'm curious to hear the input from other statistics researchers.

bonus example for intuition borrowed from the world's smartest lady, but if there are say 100 doors, and only one gold brick, your first guess would be 1/100 chance for gold right? But after you guess and before the reveal, if 98 other doors are opened to reveal nothing, and you're given the chance to switch your guess, would you?...