All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Probability
Pick a card, any card.. (Posted on 2008-03-11) Difficulty: 3 of 5
You sit down with a well mixed deck containing A cards marked "+" and B cards marked "". You may draw cards from this deck as long as you want, i.e., you can stop playing at any point. Each time you draw a + card you are given $1 and each time you draw a card you have to pay $1. Cards are not replaced after having been drawn.

What would be a fair amount to pay for the right to play (i.e., what is the expected payoff) and under what circumstance should a player cease drawing?

No Solution Yet Submitted by FrankM    
Rating: 2.7500 (4 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Some Thoughts .. and on the eighth day, he began to scratch his head and wonder what went wrong .. | Comment 33 of 37 |


1. Gee, it's exciting to see the problem generate so much interest and good thinking!

2. I feel badly to have lost sight for so long, and even to have missed important requests for clarification. Maybe the site could have some facility for author notification. Perhaps a theme for the forums..


1. There is more to this problem than met my eye! As has been pointed out, the proposed solution is at fault, and will have to be corrected.

2. I would much prefer to replace it with a closed form solution. Dej Mar (comment 27) may have pointed out a way. I'll need to research this, or perhaps someone may get there before me. I would only be willing to accept a spreadsheet solution of last resort. 

3. I continue to have confidence in the published recursion relation. We can also believe that the published (and erroneous) formula fulfills the recursion relation condition. What I had overlooked was the possibility that the recursion relation could have multiple solutions. Presumably this is cause of the trouble.

  Posted by FrankM on 2008-03-24 17:06:48
Please log in:
Remember me:
Sign up! | Forgot password

Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (4)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Copyright © 2002 - 2018 by Animus Pactum Consulting. All rights reserved. Privacy Information