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 re(2): .. what went wrong .. by Charlie)

I concur with the entire substance of your comment.

It occurs to me that the (modified) recurrence relation is itself a function specification, i.e., it provides a procedure for calculating W(A,B) for any non-negative integers A and B. In a sense, it is then just as good as an expression in closed form, even if it requires more work to calculate, especially for large A,B.

Still, I am unsatisfied. I know you are a fan of spread sheet solutions. Still, I'd like to ask, can you extract a closed form solution?

Posted by FrankM on 2008-03-25 15:15:57