My brain asplodes!

[elfs]

I've been trying to figure out The Monty Hall Paradox. So far, the Bayes Theorem explanation holds the most weight and makes the most sense, but moving out of the purely mathematical aspects of Bayesian math to the real world makes my brain asplode.

There's a lovely simulator with tallies on-line as well.

Comments

[ewhac.livejournal.com]

Yes, discussing ten doors makes the issue clearer than talking about three.

You pick one door; you have a 1/10 chance of winning. Monty has a 9/10 chance of winning.

Then Monty opens 8 doors with nothing behind them. The odds have not changed; You still have a 1/10 chance of winning and Monty 9/10. Then he asks if you want to change your choice.

You could pick any one of the other nine doors. But, having opened eight of the losing ones, you know which ones not to pick. In other words, Monty's overwhelming 9/10 chance has been conflated to a single door, making your choice obvious.