The money in 2 evelopes "paradox"

[bantam222]

:wall: my friend gave me this and i can't figure it out :wall:

 

both arguments seem valid

 

 

 

here's the paradox ...

 

 

 

Suppose you're given 2 envelopes with money in them and you are told that one contains twice as much as the other (let's say they're cheques and therefore weight is not an issue). You pick one and open it up to reveal a $100 cheque. You are now offered the opportunity to switch envelopes.

 

 

 

Is switching profitable?

 

 

 

Argument 1: It's profitable to switch. You had a 50/50 chance of picking the high or low envelope so there's a 50% chance that the other envelope is the high and a 50% chance it's the low. Therefore, the profitablity of the switch = 0.5*(+100) + 0.5*(-50) = +25.

 

 

 

Argument 2: It doesn't matter, switching isn't profitable or non-profitable. If always switching was a +EV strategy then it would be more profitable to choose envelope A first and then switch to B then to just choose envelope B and not switch.

 

 

 

Who's right? Can anyone give a good answer explaining why one doesn't work?

[Bob_LMS]

I have to say that it has a 50 50 chance of being profitable you could be the highest or the lowest personally i wouldldnt switch but 100 bucks is alot to someone w/o a job that has to pay 345 for drivers ed:cry: in less than 2 months lol

[bantam222]

i think you don't understand the question...

 

its not asking what percentage of the time you gain money, and what percentage of the time you lose money. that is 1/2.

 

 

 

we see 100$, and there is a 1/2 chance we picked the envolope with the larger amount, and a 1/2 chance we picked the envolope with the smaller amout. So if we switch, half the time we will get 50$, and half the time we will get 200$. 50$ + 200$ = 250$ / 2 = 125$, so a 25$ profit on average from switching

 

 

 

 

 

the problem is that the above can't be true. That is saying that if we pick envolope A, look at the amount of money in it and switch to envolope B, is more profitable then just picking envolope B the first time, and not switching...

[Random]

what's the point? free money either way :lol:

[jiyuueno20]

what's the point? free money either way :lol:

 

 

 

:lol: :lol: :lol: :lol: yay free money!!!! :lol: :lol: :lol: :lol:

 

 

 

p.s. my first post yay!!!!!!! \

[Doomster]

This is making my brain hurt!

 

 

 

So if you see a ÃÆââ¬Å¡Ãâã100, then it is the higher of a ÃÆââ¬Å¡Ãâã100 / ÃÆââ¬Å¡Ãâã50 pair, or the lower of a ÃÆââ¬Å¡Ãâã100 / ÃÆââ¬Å¡Ãâã200

 

 

 

So by switching, it seems that there is a 50:50 chance to double or halve it, with an average increase if you gamble on the switch - seems wrong.

 

 

 

Ok, lets take all 4 possible outcomes of 2x 50/100 and 2x 100/200

 

 

 

Start & switch

 

1. Draw 50, take 100

 

2. Draw 100, take 50

 

3. Draw 100, take 200

 

4. Draw 200, take 100

 

 

 

In each case, the result is one 50, rwo 100's and one 200.

 

 

 

Now I'm more confused than ever!

[katha610]

take the money you have.. the other envelpoe might be the one with 50 bucks... be happy with what you got and dont be greedy

[darkmage099]

no clue but i have another one:

 

 

 

Suppose you went back in time and met your grandpa. And you killed him (may be accidental). But then if your grandpa wasnt born you wouldn't have been born...to kill him therefore he'd be alive and so would you and you would kill him bit then your grandpa wasnt born so you wouldnt havebeen born to kill him therefore he'd be alive.... :?: :?: :?: :?: :?: :?: :?:

[vladmoney]

It doesn't matter, because you have to look at proportions i think:

 

 

 

Lets take the worst scenerio

 

The set up is 100-50, and you switch to 50. You just lost 50% of cash you could have had.

 

Let say the set up is 200-100, and you stay. You just lost 50% of cash you could have had.

 

 

 

But lets go the other way:

 

The set up could be 100-50, and you stay. You just 200% the money you could have had if you switched.

 

Let say the set up is 200-100, and you swtich to 200. You just gained 200% of cash you could have if you stayed.

 

 

 

As you see no matter what you do you always lose/gain the same proportion. And thats what really matters because there is no way you can change what set up you have.

[Mercifull]

Its not really a paradox is it? Its far too simple

[unknownmasterofnothing]

Depends if you're a risk taker. You can either gain 100 dollars or lose 50 dollars if you take the risk. If you play it safe, you stay with 100 dollars.

[Anesthesia]

Similar to the gameshow with the goat/goat/car choice.

[Mercifull]

Similar to the gameshow with the goat/goat/car choice.

Now THATS a better thing to discuss than a simple 50/50

[bantam222]

I dont think most of you fully understand the question. The answer is not, you make money half the time if you switch.

 

 

 

Its not really a paradox is it? Its far too simple

 

 

 

here is wikipedia's answer...does that look simple?

 

 

 

http://en.wikipedia.org/wiki/Two_envelope_paradox

[katha610]

thats what they do... put simple things in formulas that do not look simple.. if you read through its not that hard

[malo2]

its all your opinion. I personally am not a person with alot of money, so id keep the chance of owning $100. For a person with more money, (S)he would not really care much wether its 50 or $100, since $50 isnt a big difference, but $200 would be a worthwille difference.

 

 

 

So in conclusion, its all in your opinion.

[darkmage099]

http://en.wikipedia.org/wiki/Time_paradox

 

 

 

the sort of answer to the paradox i said

[magictv]

Dunno if it's been posted but here is what I think. If you switch then half the time you will get ÃÆââ¬Å¡Ãâã200 which is a gain of ÃÆââ¬Å¡Ãâã100 and the other half of the time you will get ÃÆââ¬Å¡Ãâã50 and so you will lose ÃÆââ¬Å¡Ãâã50 so it makes sense to switch as the average of ÃÆââ¬Å¡Ãâã50 and ÃÆââ¬Å¡Ãâã200 is ÃÆââ¬Å¡Ãâã125 which is higher than ÃÆââ¬Å¡Ãâã100.

 

 

 

I hope that makes sense.

[bantam222]

Dunno if it's been posted but here is what I think. If you switch then half the time you will get ÃÆââ¬Å¡Ãâã200 which is a gain of ÃÆââ¬Å¡Ãâã100 and the other half of the time you will get ÃÆââ¬Å¡Ãâã50 and so you will lose ÃÆââ¬Å¡Ãâã50 so it makes sense to switch as the average of ÃÆââ¬Å¡Ãâã50 and ÃÆââ¬Å¡Ãâã200 is ÃÆââ¬Å¡Ãâã125 which is higher than ÃÆââ¬Å¡Ãâã100.

 

 

 

I hope that makes sense.

 

 

 

 

 

 

 

so what you are saying is no matter what i open in the envolope it is profitable to switch to the other one? how is that possible? Is opening envolope A, and switching to B more profitable then opening envolope B and just staying? It can't be...

 

 

 

 

 

thats the problem with this paradox, there are two "right" solusions but they have different answers...one saying its profitable to switch, the other saying its not.

[Guest GhostRanger]

This thread is ridiculous. The problem presented isn't a paradox at all, and the solution proposed by the author doesn't make any sense.

 

 

 

First off, it's not a paradox because there's nothing self-contradictory about it. It's just a matter of probability.

 

 

 

Second off, after picking the first envelope, deciding whether or not you change is a new 50-50 chance in itself. You don't factor in the fact that you've already randomly selected one. It's a 50-50 chance you will lose or gain money. Period.

 

 

 

Even if you did factor in the first choice (which you don't), you still can't solve the problem like that. There is 0% chance that you will gain $25 so that is completely ridiculous to suggest that kind of way to solve the problem. Once again, it's a 50-50 chance you will gain money and a 50-50 chance you will lose money. That's it. No paradox, just a simple problem of probability.

[darkmage099]

This thread is ridiculous. The problem presented isn't a paradox at all, and the solution proposed by the author doesn't make any sense.

 

 

 

First off, it's not a paradox because there's nothing self-contradictory about it. It's just a matter of probability.

 

 

 

Second off, after picking the first envelope, deciding whether or not you change is a new 50-50 chance in itself. You don't factor in the fact that you've already randomly selected one. It's a 50-50 chance you will lose or gain money. Period.

 

 

 

Even if you did factor in the first choice (which you don't), you still can't solve the problem like that. There is 0% chance that you will gain $25 so that is completely ridiculous to suggest that kind of way to solve the problem. Once again, it's a 50-50 chance you will gain money and a 50-50 chance you will lose money. That's it. No paradox, just a simple problem of probability.

 

=D> =D> =D>

[Nadril]

This thread is ridiculous. The problem presented isn't a paradox at all, and the solution proposed by the author doesn't make any sense.

 

 

 

First off, it's not a paradox because there's nothing self-contradictory about it. It's just a matter of probability.

 

 

 

Second off, after picking the first envelope, deciding whether or not you change is a new 50-50 chance in itself. You don't factor in the fact that you've already randomly selected one. It's a 50-50 chance you will lose or gain money. Period.

 

 

 

Even if you did factor in the first choice (which you don't), you still can't solve the problem like that. There is 0% chance that you will gain $25 so that is completely ridiculous to suggest that kind of way to solve the problem. Once again, it's a 50-50 chance you will gain money and a 50-50 chance you will lose money. That's it. No paradox, just a simple problem of probability.

 

 

 

Thank you =D> .

 

 

 

When I saw this my eye's boggled a bit. I tried thinking about it "paradox-like" but I just kept thinking...but... it's like a half chance to get that / half chance to get the other.

 

 

 

It's nothing complicated realy...

 

 

 

And anyways, say you chose Envelope A. You than look, it has 100$ in it. You think "ok, i'll try B than" you go for B. It's the same exact outcome and choice as if you went with B first...

[magictv]

What I mean is althuogh it is a 50/50 chance whether you gain or lose money, if you do gain money you will gain more money than you would lose if you lost money. So it is more profitable to switch.

 

 

 

Do y'see what I mean?

[Not]

It is not more profitable to switch, the only 50/50 chance that matters is where you pick the original envelope. Either is has a certain amount of money or is has double the amount.

 

 

 

You are not aware of this outcome when you make your next decision.

 

 

 

Assume the envelopes contain $1 and $2, 50% of the time a swich will win you $1 and 50% of the time a swich will cost you $1. You aren't aware that the other envelope can't contain $.50 or $4.

[Guest XplsvBam]

Its not really a hard choice at all. Let's say you open the first check and its $100.00. Then the only thing left to do is to open the second one. If its $50.00 no worries the $100.00 wasn't yours in the first place. If its $200.00 cool. But either way, gain or loss you will know and there is no price on knowledge.

 

 

 

If you don't open both envolopes you will always try to figure out the logical option and never be able to figure it out.