Maths Paradox

dinjo99

Hi folks,
New to this forum so apologies if this has been asked before.

I love Maths puzzles but this apparent paradox has confused me for years.
The scenario is as follows.

There are two unmarked envelopes containing random sums of money.
We know that if we open one of the envelopes the other will contain either double or half the amount of money. When you open an envelope, you will have a choice, take that amount of money or gamble and open the other envelope and get that amount.

You pick an envelope. It contains €100. Should you keep that amount or gamble.
Now obviously the other envelope contains either €50 or €200 so you should definitely gamble and open the other envelope as you will either win an extra €100 or lose €50.
Therefore it is always +EV to gamble and open the other envelope, which begs the question,

If it is always correct to open the other envelope, why not just open the other envelope first?

What am I missing?

purplefields

Is this the Monty Hall problem?

I believe that there are three envelopes, if it is.
https://en.wikipedia.org/wiki/Monty_Hall_problem

dinjo99

No, totally different. The Monty Hall, I can understand and makes sense to me from a maths point of view.

This one doesn't.

purplefields

I don't know if you've seen the wikipedia explanation. The resolutions seem insane for what appears to a simple conundrum.

https://en.wikipedia.org/wiki/Two_envelopes_problem

dinjo99

Cheers Purplefields,

I hadn't seen that.
I will spend the weekend trying to make sense of it!

Potatoeman

dinjo99 wrote: »

Hi folks,
New to this forum so apologies if this has been asked before.

I love Maths puzzles but this apparent paradox has confused me for years.
The scenario is as follows.

There are two unmarked envelopes containing random sums of money.
We know that if we open one of the envelopes the other will contain either double or half the amount of money. When you open an envelope, you will have a choice, take that amount of money or gamble and open the other envelope and get that amount.

You pick an envelope. It contains €100. Should you keep that amount or gamble.
Now obviously the other envelope contains either €50 or €200 so you should definitely gamble and open the other envelope as you will either win an extra €100 or lose €50.
Therefore it is always +EV to gamble and open the other envelope, which begs the question,

If it is always correct to open the other envelope, why not just open the other envelope first?

What am I missing?

It doesn’t matter which envelope you open first, the second envelope is always the second envelope and should always be opened as you always have a chance of doubling your money.

GreeBo

I think its nothing to do with first or second, you should always open both envelopes as you can always win more than you can lose.

Elwood_Blues

Pretty simple answer really. Take both envelopes and do a legger.