My Math Forum  

Go Back   My Math Forum > College Math Forum > Number Theory

Number Theory Number Theory Math Forum


Thanks Tree1Thanks
Reply
 
LinkBack Thread Tools Display Modes
April 20th, 2017, 12:58 PM   #11
Senior Member
 
Joined: Jun 2014
From: USA

Posts: 210
Thanks: 6

Quote:
Originally Posted by romsek View Post
you're talking nonsense.

If you know the value of your envelope then if it is $x$ you will swap, if it is $2x$ you will not. You will always end up with $2x$
You know the value, like 10 dollars, but you don't know if you have x = 10 or 2x = 10. In other words, you don't know which is which still.
AplanisTophet is offline  
 
April 20th, 2017, 01:06 PM   #12
Senior Member
 
romsek's Avatar
 
Joined: Sep 2015
From: CA

Posts: 1,111
Thanks: 580

Quote:
Originally Posted by AplanisTophet View Post
You know the value, like 10 dollars, but you don't know if you have x = 10 or 2x = 10. In other words, you don't know which is which still.
the scale of the bet having an influence on the betting behavior may well be a characteristic of the human personality.

it has nothing to do with math though.
romsek is online now  
April 20th, 2017, 01:13 PM   #13
Senior Member
 
Joined: Jun 2014
From: USA

Posts: 210
Thanks: 6

Quote:
Originally Posted by romsek View Post
the scale of the bet having an influence on the betting behavior may well be a characteristic of the human personality.

it has nothing to do with math though.
Assume that people will always do what will make them more money, independent of personality.

If you know your envelope has 10 dollars, then you'll swap because you'll have a 50% chance of getting 20 dollars and a 50% chance of getting 5 dollars.

That's where:

50%(0.5*10) + 50%(2*10) = 12.50

...comes from. You're making "25 cents on the dollar" on average for swapping.

If you don't know the value of your envelope, then independent of personality, you're indifferent.

Get it?
AplanisTophet is offline  
April 20th, 2017, 01:31 PM   #14
Senior Member
 
romsek's Avatar
 
Joined: Sep 2015
From: CA

Posts: 1,111
Thanks: 580

Quote:
Originally Posted by AplanisTophet View Post
Assume that people will always do what will make them more money, independent of personality.

If you know your envelope has 10 dollars, then you'll swap because you'll have a 50% chance of getting 20 dollars and a 50% chance of getting 5 dollars.

That's where:

50%(0.5*10) + 50%(2*10) = 12.50

...comes from. You're making "25 cents on the dollar" on average for swapping.

If you don't know the value of your envelope, then independent of personality, you're indifferent.

Get it?
you're also losing 25 cents on the dollar on average from swapping.

I'm done here.
romsek is online now  
April 20th, 2017, 01:37 PM   #15
Senior Member
 
Joined: Jun 2014
From: USA

Posts: 210
Thanks: 6

Quote:
Originally Posted by romsek View Post
you're also losing 25 cents on the dollar on average from swapping.

I'm done here.
Ok, but now you're the one talking nonsense...
AplanisTophet is offline  
April 20th, 2017, 02:35 PM   #16
Senior Member
 
romsek's Avatar
 
Joined: Sep 2015
From: CA

Posts: 1,111
Thanks: 580

Quote:
Originally Posted by AplanisTophet View Post
Ok, but now you're the one talking nonsense...
if i have two equiprobable outcomes, $x$ and $2x$

then the expected value is $\dfrac 3 2 x$

If I have the $2x$ envelope and swap for the $x$ envelope.

Then I come out $\dfrac 1 2 x$ below the expected value.

the way you are looking at this problem that is equivalent to losing $\dfrac 1 2 x$
romsek is online now  
April 20th, 2017, 03:02 PM   #17
Senior Member
 
Joined: Jun 2014
From: USA

Posts: 210
Thanks: 6

Quote:
Originally Posted by romsek View Post
if i have two equiprobable outcomes, $x$ and $2x$

then the expected value is $\dfrac 3 2 x$

If I have the $2x$ envelope and swap for the $x$ envelope.

Then I come out $\dfrac 1 2 x$ below the expected value.

the way you are looking at this problem that is equivalent to losing $\dfrac 1 2 x$
As I said in the OP, I only acknowledge an average value of 1.5x as you say.

When someone gets an envelope, they don't know if they have x or 2x. If you let them peek in the envelope and see 10 bucks, they 'correctly' assess that they have a 50% chance of getting 20 and a 50% chance of getting 5 if they swap. This is an illusion created by frame of reference in the sense that only one of those two outcomes is possible and one isn't.

Let me be clear now. Let's say X = 10 and 2X = 20. Based on what the person is given, they see 10 in the envelope, they'll get 20 every time but if they see 20 in the evelope, they'll get 10 every time. From their point of reference, they have to swap thinking it will earn them that 25 cents on the dollar, but it can't, because 5 is not an option when they see 10 in that envelope and 40 is not an option when they see 20 in that envelope. The true average value will be 15 (half the time the person will end up with 10 and the other half the person will end up with 20).

I'm saying that the notion there can be a 50%(0.5x) + 50%(2x) = 1.25x option where swapping earns you that 25 cents on the dollar is nonsense. I don't see a true paradox.

So then, by saying 1.5x is the only possible average outcome, you are agreeing with me, yes?
AplanisTophet is offline  
April 20th, 2017, 03:05 PM   #18
Senior Member
 
romsek's Avatar
 
Joined: Sep 2015
From: CA

Posts: 1,111
Thanks: 580

I'm not getting dragged into an extended discussion with you.
romsek is online now  
April 20th, 2017, 03:11 PM   #19
Senior Member
 
Joined: Jun 2014
From: USA

Posts: 210
Thanks: 6

Quote:
Originally Posted by romsek View Post
I'm not getting dragged into an extended discussion with you.
Can I get a yes or no at least? I don't think an extended discussion is necessary (maybe it is, I just don't think so).

If you can't give a yes or no, then I think you're saying that you think an extended discussion is necessary, that there is more to be discussed but that you just don't want to.
AplanisTophet is offline  
April 20th, 2017, 03:49 PM   #20
Senior Member
 
Joined: Jul 2008
From: Western Canada

Posts: 2,277
Thanks: 31

Since this was posted in the number theory section rather than the probability section, my first thought was that perhaps the amount of money in the envelopes must be an integer number of dollars. If that were the case, then there would certainly be some strategies available to maximize your gain. For example if the first envelope contains an odd amount, then obviously you should exchange it for the other envelope.
Yooklid is online now  
Reply

  My Math Forum > College Math Forum > Number Theory

Tags
envelope, paradox, solution



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Paradox zylo Topology 15 March 11th, 2016 01:03 AM
2 envelope paradox mathman Advanced Statistics 8 March 7th, 2013 01:39 PM
About Russell's Paradox dalant019 Applied Math 6 January 15th, 2011 04:22 AM
Is this a paradox? wonderboy1953 Physics 1 December 3rd, 2009 02:52 AM
Maths Paradox math-genius Algebra 19 December 13th, 2008 07:39 AM





Copyright © 2017 My Math Forum. All rights reserved.