When people on the first interesting logic problem googled "Monty Hall problem", they found a Wikipedia article that tried to make the argument clearer by considering a scenario with more than three doors.

For the longest while, probabilists thought that the three-door problem was the simplest. Finally, someone developed a proper, two-door problem. Here it is:

The game-show host has two identical envelopes, and tells the contestant that one envelope contains twice as much money as the other. The contestant chooses one envelope, and the host opens it to reveal, say, $200. He then offers the contestant the option of keeping his $200 envelope or trading it for the other envelope.

What should the contestant do?

 

I'd trade it, why not? Winning an additional $200 is worth risking only $100 for.

Basically it's like winning $200 and betting $100 of it on winning $300.

Worse comes to worse you have $100 best case you have $400

 

 

This isn't a logic question its a question of greed

But seriously, you should change it (well, whoever wrote it originally) so that one envelope has a certain amount and the other has 10x that amount.

So in this case the man has an envelope with $200 but a "choice" of an envelope with eiter $20 or $2000. People would stop to think more about the question, mainly because $20 isn't much, $200 is a nice bonus, but $2000 is really nice.

No one wants to give up $180 dollars to get $20, but in the original question you can give up $100 (at most, $200 - 50%) to chance a total income of $400. Thats almost worth doing, because you still walk away with $100.

 

While you're correct that a larger multiplier will make the choice clearer, that's not the point of the problem.

There is a very subtle, paradoxical quality to this situation.

The question is: can you spot it?

 

yes

 

Choosing the envelope, not opening it and then switching vs. choosing an envelope, opening it and then switching.

 

Almost.

It's subtler than that.

 

Where's the option for "Punch the game show host and take both" ?

 

ok math minor here(comp sci major ), and i dont see how there is any advantage either way.

http://mathforum.org/dr.math/faq/faq.monty.hall.html

This website claims that there are only three possible methods of choosing. This is incorrect. There are four, which again makes the ratio 2/4.