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: Table of Fair Amount by Charlie)

For A=2 and B=2 The worst one should complete the sequence is at 0.  So continue until above 0.

++-- One card - Stop +1
+-+- One card Stop +1      { A = 1 B = 2
+--+ One card Stop +1     
-++- Three cards Stop +1  { A = 0 B = 1
-+-+ Four cards Stop 0
--++ Four cards Stop 0

Using the matrix from my previous posts . . . continue until the A vs B put you at a zero value.

Posted by Leming on 2008-03-11 19:33:11