Logic Problem for GoT

[Ulysses]

[ QUOTE ]
I understand how choosing to switch makes no difference from a common sense and Bayesian perspective, but I don't understand how that overrules EV calcs.

[/ QUOTE ]

A few people have posted good questions that perhaps will help you think about this problem.

The links I posted provide mathematical/probability analysis of this problem that is relatively easy to grasp even if you don't understand all of the math behind some of their statements.

As for your EV issue, perhaps thinking about it like this will help you see where you're going wrong.

You said that the envelope you pick has x. Thus the other one has either 2x or .5x. So, switching gives you 2.5x/2 = 1.25x.

OK. But what if we define the amount in the other envelope as y? Now, what does x equal? Well, 50% of the time x=2y and 50% of the time x=.5y, right? So, the first envelope gives us 2.5y/2 = 1.25y and switching gets us y.

Anyway, the main reason I entered this thread was that I think if you're going to make smug comments like "It can and it is" and follow up with patronizing comments like your one regarding the game shows, you better get your answers right, else you come off looking very foolish.

[Zeno]

From the website posted by El:

"To summarize: the paradox arises because you use the prior probabilities to calculate the expected gain rather than the posterior probabilities. As we have seen, it is not possible to choose a prior distribution which results in a posterior distribution for which the original argument holds; there simply are no circumstances in which it would be valid to always use probabilities of 0.5. '


-Zeno

[Zeno]

The common sense answer to this 'problem' is one of simplicity, a Gordian Knot. Alexander the Great used it long ago. Interesting side bar Choose your knots wisely


The REAL SOLUTION:

There are two boxes with money. Obviously having the money in both boxes is more advantageous that having the money in only one box. So when asked if you want to switch you say , No - I'll just take both boxes' as you aim a 12-gauge pump action shotgun at the hosts head.

I certainly hope this ends all the silly math logic stuff.

-Zeno, Cutting to the chase once again.