# Should I switch?

#### Jomo

##### Elite Member
Suppose someone has two envelopes. One has twice as much money as the other. I am given an envelope and I have the change to switch to the other envelope. Should I switch?
Please note, that each envelope has a positive amount!

#### Harry_the_cat

##### Senior Member
It could depend on whether the person who gave them to you knows what's inside, especially if they get to keep the contents of the other one. Would they use reverse psychology and give you the one with more money, expecting you to swap?

#### Jomo

##### Elite Member
I always leave something out! The person randomly gives you one of the envelopes. Should you switch?

#### lev888

##### Full Member
I don't see how switching would help. Would turning a coin over increase the chances of getting the result you prefer?

#### Subhotosh Khan

##### Super Moderator
Staff member
Suppose someone has two envelopes. One has twice as much money as the other. I am given an envelope and I have the change to switch to the other envelope. Should I switch?
Please note, that each envelope has a positive amount!
Remember this is NOT "Monty Hall Problem"!!

#### Jomo

##### Elite Member
Any other responses?

#### Dr.Peterson

##### Elite Member
The basic issue in this "two envelope paradox" is that you can work out expected values and convince yourself that it's better to switch, but then you can repeat the same argument and convince yourself to switch back. On the other hand, if you start with the observation that you are equally likely to have either envelope, it's obvious there's no benefit in switching. A lot has been said about it.

#### Jomo

##### Elite Member
I would choose to switch indefinitely!

#### Jomo

##### Elite Member
Dr Peterson, I truly see why if you switch then you should switch back. I looked at the link you provided and was surprised that the expected value showed that you should switch. It seems that this expected value is being less than truthful? How can that be?

#### Subhotosh Khan

##### Super Moderator
Staff member
Dr Peterson, I truly see why if you switch then you should switch back. I looked at the link you provided and was surprised that the expected value showed that you should switch. It seems that this expected value is being less than truthful? How can that be?
If you read the "work" carefully (where they show the expected value showed that you should switch) - they indicate that there is an "intentional" flaw in the logic and they "challenge" you to find it.

#### Dr.Peterson

##### Elite Member
If you read the "work" carefully (where they show the expected value showed that you should switch) - they indicate that there is an "intentional" flaw in the logic and they "challenge" you to find it.
... which is why I said "you can work out the expected values and convince yourself ..."!

I didn't say you'd be right.

#### Jomo

##### Elite Member
But to Dr P and SK, how can the EV be wrong? don't mean in this particular case, I mean in any case.

#### Dr.Peterson

##### Elite Member
The article gives answers, though I'm not sure it's the best explanation. Here's a shorter version: https://www.math.hmc.edu/funfacts/ffiles/20001.6-8.shtml

As far as I'm concerned (and I can't say I've studied this deeply), the problem with the argument comes down to the fact that you don't know how much is actually in your envelope, so the claim to have found the expected value is bogus. The "A" in terms of which it is stated is not a number, but a random variable, and we know nothing about it.

#### Jomo

##### Elite Member
The article gives answers, though I'm not sure it's the best explanation. Here's a shorter version: https://www.math.hmc.edu/funfacts/ffiles/20001.6-8.shtml

As far as I'm concerned (and I can't say I've studied this deeply), the problem with the argument comes down to the fact that you don't know how much is actually in your envelope, so the claim to have found the expected value is bogus. The "A" in terms of which it is stated is not a number, but a random variable, and we know nothing about it.
I read the new link and have to absord all this. It usually takes me time to see things but when i do, I have a good solid understanding of it.
If only I was allowed to take my finals a year later!