fleung22 1 Posted February 18, 2006 Share Posted February 18, 2006 Okay...this thread may not be for everyone.If you're a math guy please assist if you can.Here's the scenario:- There are 3 closed envelopes that look identical.- One of these envelopes contain $1,000,000- The other two envelopes contain nothing- You will choose one of the three envelopesNow here's the question:Without opening the envelope to look inside...If you are given the choice of either keeping the envelope you have OR trading it for one of the other two which choice is better?My initial thoughts:This is a stupid question. It doesn't make a difference because everything is random anyhow. Your probability of picking the $1M winner is 33.3% regardless of choice. It's like a kid going..."I'll take envelope #1...wait, nono...I'll take #3!"...the chances are the same since you don't know what's inside the initial pick.Theorem from Mathematician:I don't know the details (and thus this post)...but it goes something like this but at a much more complex level.Let Pile A = Initially picked EnvelopeLet Pile B = Other 2 EnvelopesPile A has a 33.3% chance of having the $1MPile B has a 66.7% chance of having the $1MTherefore, there is a greater chance of the winner being in Pile B.By choosing to trade for a Pile B envelope you are getting a 50/50 scenario on picking the $1M from a more likely winning pile.Therefore it is always correct to choose to exchange your initial choice.Final thought:I have simplified the theorem and any guy that can even tackle this may flame the crap outta me for messing up the explanation.I've been told that it cannot be answered in a short manner such as the one I just made.To me...I quickly dismissed the theory I just posted because the 50/50 of Pile B in my mind is just 50% of 66.7% which is 33.3% anyhow...just like it was from the beginning.If you can give me a link or explaination for this it's greatly appreciated. My mind is working overtime trying to think of how there could actually be a big debate in the math world about this seemingly simple question. Link to post Share on other sites
chrozzo 19 Posted February 18, 2006 Share Posted February 18, 2006 just pick the one thats heavier...hehe Link to post Share on other sites
fleung22 1 Posted February 18, 2006 Author Share Posted February 18, 2006 just pick the one thats heavier...heheLOL...that's what I said!! But yeah...it's like a cheque or something...work with me here... Link to post Share on other sites
Ignition 0 Posted February 18, 2006 Share Posted February 18, 2006 Hold the three envelopes near a lightbulb to see what's inside... BONG! Link to post Share on other sites
vonteego3 0 Posted February 18, 2006 Share Posted February 18, 2006 try the search function. this question, in one form or another, has been discussed in about 11 brazillian threads. Link to post Share on other sites
vonteego3 0 Posted February 18, 2006 Share Posted February 18, 2006 in fact, I did the work for you.http://fullcontactpoker.com/poker-forums/v...ght=three+doorshttp://fullcontactpoker.com/poker-forums/v...ght=three+doorshttp://fullcontactpoker.com/poker-forums/v...ght=three+doorsyou're welcome. Link to post Share on other sites
TheSkearnel 0 Posted February 18, 2006 Share Posted February 18, 2006 just pick the one thats heavier...heheYou know, if I were to do this sort of thing, with the envelopes, I might just put a piece of paper in each one, and write on them:NOTHING1 MILLIONNOTHINGAnd then take care of things at the end. But...........that really has NOTHING to do with the OP.-Shawn K. Link to post Share on other sites
astros11ss 0 Posted February 18, 2006 Share Posted February 18, 2006 you asked a different question than the one posted earlier. your question depends on not knowing what's in the first envelope you choose, while in the previous threads, your first choice is opened and shown to reveal a goat. the way you asked it, no, you are wrong. at first, there is a 1/3 chance you picked right and a 2/3 chance you picked wrong. if you decide to switch, you are gambling 50-50 that you will be right, but there's only a 2/3 chance the check is in either of the doors, so 50% of 2/3 is 1/3, the original probability. i'm still trying to work out what you should do if you can see one of the other doors, but i just blazed so that might not happen anytime soon, or ever. good luck Link to post Share on other sites
fleung22 1 Posted February 18, 2006 Author Share Posted February 18, 2006 in fact, I did the work for you.http://fullcontactpoker.com/poker-forums/v...ght=three+doorshttp://fullcontactpoker.com/poker-forums/v...ght=three+doorshttp://fullcontactpoker.com/poker-forums/v...ght=three+doorsyou're welcome.Thanks for the post...very similar question on your links I suppose but it's kind of easier for me to see the other side in the 3-door example because more information has been given after opening one of the doors.In my example here you are never given additional info on any of the three envelopes. They are simply unknown the entire way.I feel like I'm searching for Will Hunting to get the proof. Link to post Share on other sites
Bubba83 0 Posted February 18, 2006 Share Posted February 18, 2006 If there is no extra information that one of the other 2 envelopes does not contain the check, then it doesn't matter if you switch envelopes or not. Link to post Share on other sites
HelioCentric 0 Posted February 18, 2006 Share Posted February 18, 2006 If there is no extra information of one of the other 2 envelopes being wrong, then there it doesn't matter if you switch envelopes or not. :clap: Link to post Share on other sites
No_Neck 0 Posted February 18, 2006 Share Posted February 18, 2006 If there is no extra information of one of the other 2 envelopes being wrong, then there it doesn't matter if you switch envelopes or not. :clap:ignorance is bliss. Link to post Share on other sites
nritchi3 0 Posted February 18, 2006 Share Posted February 18, 2006 Yeah maybe you should get the scenario right. It doesn't make a difference if you switch in this case. Link to post Share on other sites
sholden 0 Posted February 18, 2006 Share Posted February 18, 2006 If you can give me a link or explaination for this it's greatly appreciated. My mind is working overtime trying to think of how there could actually be a big debate in the math world about this seemingly simple question.There isn't such a debate because what you described is nothing like the paradox in question.The Envelope Paradox is completely different, though interesting especially around these parts since it's all about EV... Link to post Share on other sites
mrdannyg 274 Posted February 18, 2006 Share Posted February 18, 2006 in fact, I did the work for you.http://fullcontactpoker.com/poker-forums/v...ght=three+doorshttp://fullcontactpoker.com/poker-forums/v...ght=three+doorshttp://fullcontactpoker.com/poker-forums/v...ght=three+doorsyou're welcome.Thanks for the post...very similar question on your links I suppose but it's kind of easier for me to see the other side in the 3-door example because more information has been given after opening one of the doors.In my example here you are never given additional info on any of the three envelopes. They are simply unknown the entire way.I feel like I'm searching for Will Hunting to get the proof.with no extra information, there is no proof, that's why its called a paradox. i usually assume that people alot smarter than me have tried and failed... then have a beer. Link to post Share on other sites
blueodum 0 Posted February 18, 2006 Share Posted February 18, 2006 This is so trivially easy. There is no paradox.Assuming all three envelopes are identical it doesn't matter which one you choose and trading doesn't help you because you could be trading away the one with the million. Link to post Share on other sites
robert f 0 Posted February 18, 2006 Share Posted February 18, 2006 Shot the person running the game. Then you take all 3 envolopes and the money from the person you shot. I see no parodox here.I think it was a simple problem to solve. Link to post Share on other sites
LongLiveYorke 38 Posted February 18, 2006 Share Posted February 18, 2006 Like some have already said, you're confusing your paradoxes. The problem that you are trying to discuss is generally known as the Monty Hall Problem. Google it to find a ton of discussions, or check out some of the above links. The envelope paradox involves two envelopes, and is also a very interesting problem. But the way that you have stated it, there really is no paradox. Link to post Share on other sites
MDXS 0 Posted February 18, 2006 Share Posted February 18, 2006 If you can give me a link or explaination for this it's greatly appreciated. My mind is working overtime trying to think of how there could actually be a big debate in the math world about this seemingly simple question.There isn't such a debate because what you described is nothing like the paradox in question.The Envelope Paradox is completely different, though interesting especially around these parts since it's all about EV...Thank you. With no new information it doesn't matter if you switch.If Monty Hall's going to open a door, you switch. Link to post Share on other sites
CardWarfare 4 Posted February 18, 2006 Share Posted February 18, 2006 if you want a real paradox:http://fullcontactpoker.com/poker-forums/v...p?t=48860[/url] Link to post Share on other sites
Recommended Posts
Create an account or sign in to comment
You need to be a member in order to leave a comment
Create an account
Sign up for a new account in our community. It's easy!
Register a new accountSign in
Already have an account? Sign in here.
Sign In Now