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?

(In reply to solution--I think by Charlie)

I think that your solution simplifies the answer too much. 

 If A=2 and B=3 there is a 40% chance of winning $1, a 40% chance of breaking even and a 20% chance of losing $1.

I don't have an answer yet, but with the choice of stopping at any point, the odds shift.

Posted by Leming on 2008-03-11 15:16:43