[E. Pluribus Unum]

Same thing as the Monty Hall 3-door problem.

[shibumi]

Option 3:

Pass on the bait offered by the guy pimping wmbriggs.com and move on to the next legitimate article.

[tacticalogic]

If you get to look first, then if the first envelope contains an odd amount, you probably want to switch.

[Jack Hammer]

The solution, of course, is to ‘cut the Gordian knot’ - that is, you grab both envelopes, slug the guy playing the silly probability game, and walk away.

[Zeppelin]

He’s right in that you SHOULD switch.

The expected value of 5/4X is not illogical.

Think of it like this. Let’s say you choose an envelope and it contain’s $100. According to the riddle, you have a 50% chance of it being $200 and a 50% chance of it being $50.

I would say to switch b/c if you get the $50, then you’ve only “lost” $50, whereas if you get the $200, you’ve “gained” $100. And if you have an equal chance of gaining $100 as you do of losing $50, then go for it!

If the issue was such that you had a 50/50 chance of doubling or losing it all, then the expected value would be 1X and it wouldnt matter which you chose (from a probability standpoint).

[frithguild]

Sounds like what we all do in an voting booth.

[Amagi]

Man in Black: All right. Where is the poison? The battle of wits has begun. It ends when you decide and we both drink, and find out who is right... and who is dead.
Vizzini: But it's so simple. All I have to do is divine from what I know of you: are you the sort of man who would put the poison into his own goblet or his enemy's? Now, a clever man would put the poison into his own goblet, because he would know that only a great fool would reach for what he was given. I am not a great fool, so I can clearly not choose the wine in front of you. But you must have known I was not a great fool, you would have counted on it, so I can clearly not choose the wine in front of me.
Man in Black: You've made your decision then?
Vizzini: Not remotely. Because iocane comes from Australia, as everyone knows, and Australia is entirely peopled with criminals, and criminals are used to having people not trust them, as you are not trusted by me, so I can clearly not choose the wine in front of you.
Man in Black: Truly, you have a dizzying intellect.
Vizzini: Wait til I get going! Now, where was I?
Man in Black: Australia.
Vizzini: Yes, Australia. And you must have suspected I would have known the powder's origin, so I can clearly not choose the wine in front of me.
Man in Black: You're just stalling now.
Vizzini: You'd like to think that, wouldn't you? You've beaten my giant, which means you're exceptionally strong, so you could've put the poison in your own goblet, trusting on your strength to save you, so I can clearly not choose the wine in front of you. But, you've also bested my Spaniard, which means you must have studied, and in studying you must have learned that man is mortal, so you would have put the poison as far from yourself as possible, so I can clearly not choose the wine in front of me.
Man in Black: You're trying to trick me into giving away something. It won't work.
Vizzini: IT HAS WORKED! YOU'VE GIVEN EVERYTHING AWAY! I KNOW WHERE THE POISON IS!
Man in Black: Then make your choice.
Vizzini: I will, and I choose - What in the world can that be?
Vizzini: [Vizzini gestures up and away from the table. Roberts looks. Vizzini swaps the goblets]
Man in Black: What? Where? I don't see anything.
Vizzini: Well, I- I could have sworn I saw something. No matter.First, let's drink. Me from my glass, and you from yours.
Man in Black, Vizzini: [Vizzini and the Man in Black drink ]
Man in Black: You guessed wrong.
Vizzini: You only think I guessed wrong! That's what's so funny! I switched glasses when your back was turned! Ha ha! You fool! You fell victim to one of the classic blunders - The most famous of which is "never get involved in a land war in Asia" - but only slightly less well-known is this: "Never go against a Sicilian when death is on the line"! Ha ha ha ha ha ha ha! Ha ha ha ha ha ha ha! Ha ha ha...
Vizzini: [Vizzini stops suddenly,his smile frozen on his face and falls to the right out of camera dead]
Buttercup: And to think, all that time it was your cup that was poisoned.
Man in Black: They were both poisoned. I spent the last few years building up an immunity to iocane powder.

[Fresh Wind]

Pull out your gun and take both envelopes.

[matt1234]

No one is going to offer me free money because I’m a middle aged white guy.