Dealing With Monte Hall.

A friend and I were talking about Deal or No Deal at work the other day, and he was insistant that if offered the Dealer's swap at the end of the game, you should always swap, in the same way you should swap when offered in the Monte Hall problem.

Is he right?

No.

Different problem, discussed somewhere on the wizardofodds site.

See my mathproblems.info site, problem 186.

I first came across the 'Monty Hall' problem (didn't know it was called that until now) when at college 5 years ago when my maths lecturer (and avid poker player) brought it up. I thought it was the most ridiculous thing I'd ever heard and immediately set about proving it was b****cks. I was quite shocked when I ended up proving it to be correct.

This is a different problem because in the Monty Hall problem, Monty knows where the prize is, and uses that info when he picks which of the other doors to open. (More likely, to prevent Monty from having a 'poker tell', the stage director knows, and tells Monty which door to open after the contestant chooses. It's the same thing.)


On Deal or No Deal, the player picks the first suitcase, and also picks which suitcases to open as they get down to the last suitcase.

I.E. No knowledge of the suitcase contents is used when selecting cases to open. Everything remains completely random.

No matter which two amounts are left, even in the very unlikely case where the two suitcases left have the lowest and highest amounts, both have an equal chance of having the bigger prize.

The Monty Hall problem is usually framed badly, especially by Marilyn Vos Savant, which is the reason for much the confusion. As was noted above, the problems are different because Monty knew where the big prize was, and Howie did not.