Zelaron Gaming Forum  
Stats Arcade Portal Forum FAQ Members List Social Groups Calendar Search Today's Posts Mark Forums Read
Go Back   Zelaron Gaming Forum > The Zelaron Nexus > Science and Art > Principia Mathematica

 
 
Thread Tools Display Modes

 
The two envelope problem
Reply
Posted 2019-12-16, 10:06 AM
This one is fun to think about:

The two envelope problem is a famous paradox from probability theory (which we first presented on Plus back in September). Imagine you are given two envelopes, one of which contains twice as much money as the other. You're allowed to pick one envelope and keep the money inside. But just before you open your chosen envelope you are given the chance to change your mind. Should you stick with the envelope you picked first or switch?

To find out write for the amount that's in your chosen envelope. This means that the amount of money in the other envelope is either or . The probability that it's is and so is the probability that it's . So the expected amount you'll get for switching is



Since that’s bigger than . But it's intuitively obvious that switching shouldn't increase your expected value, since you haven't been given any new information. Furthermore, after switching you could make the exact same argument and conclude you should switch again, ad infinitum. So there's a paradox here and the problem is to resolve it.

Last edited by Demosthenes; 2019-12-16 at 10:09 AM.
Old
Profile PM WWW Search
Demosthenes seldom sees opportunities until they cease to beDemosthenes seldom sees opportunities until they cease to beDemosthenes seldom sees opportunities until they cease to beDemosthenes seldom sees opportunities until they cease to be
 
Demosthenes
 



 
Reply
Posted 2019-12-17, 06:14 AM in reply to Demosthenes's post "The two envelope problem"
The amount of money is not dependent upon what’s in your envelope. 2/3 of it is in one and 1/3 in the other. The expected value of the other envelope is 1/2*(1/3x+2/3x)=.5x, which is the same as the one you hold.
Old
Profile PM WWW Search
WetWired read his obituary with confusionWetWired read his obituary with confusionWetWired read his obituary with confusionWetWired read his obituary with confusion
 
 
WetWired
 



 
Reply
Posted 2020-07-15, 06:17 PM in reply to Demosthenes's post "The two envelope problem"
Still haven't been able to get my mind around this thing :-(
Old
Profile PM WWW Search
Demosthenes seldom sees opportunities until they cease to beDemosthenes seldom sees opportunities until they cease to beDemosthenes seldom sees opportunities until they cease to beDemosthenes seldom sees opportunities until they cease to be
 
Demosthenes
 
 

Bookmarks

« Previous Thread | Next Thread »

Currently Active Users Viewing This Thread: 1 (0 members and 1 guests)
 
Thread Tools
Display Modes

Posting Rules [Forum Rules]
You may not post new threads
You may not post replies
You may not post attachments
You may not edit your posts
BB code is On
Smilies are On
[IMG] code is On
HTML code is Off
Forum Jump

Similar Threads
Thread Thread Starter Forum Replies Last Post
complaining about stupid guy problem talentedhamster Life Discussion 23 2008-12-15 07:11 AM
problem switching patches ask_rabber General Gaming 7 2002-04-15 01:15 PM
Avatar Problem Bezier General Discussion 2 2002-03-28 05:47 PM
guys we have a problem Killah Forum News, Suggestions and Discussion 4 2002-02-11 07:38 PM


All times are GMT -6. The time now is 12:09 AM.
'Synthesis 2' vBulletin 3.x styles and 'x79' derivative
by WetWired the Unbound and Chruser
Copyright ©2002-2008 zelaron.com
Powered by vBulletin® Version 3.8.2
Copyright ©2000 - 2024, Jelsoft Enterprises Ltd.
This site is best seen with your eyes open.