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?
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