My brother and our mate spent about four hours on Monday night running through the Monty Hall Problem trying to wrap our heads around the numbers. My brother was convinced that Deal or No Deal was the same problem as Monty Hall. Our mate was convinced otherwise; I tended to agree with him based on my initial thoughts, but having some experience with the weird unintuitive nature of the Monty Hall Problem I deferred a decision until I’d thought about it some more.
This culminated in the creation of some PHP scripts to run a few zillion trials of both problems. The one for Deal or No Deal was quite simple to conceive and it seemed pretty clear almost straight away that it was not the same thing, especially after I started working on the Monty Hall version. Fortunately I found someone else had already done it in PHP so I just played with that.
Anyway, it’s probably obvious to anyone that knows a lot about conditional probability, but they’re not the same problem.
If anyone cares, the PHP script for the Deal or No Deal stuff is up here.