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 What's the catch? by ed bottemiller)

More details:  The question also includes what is the fair amount . . . if A=2 and B=3 the fair amount is $0.20

A=2 B=3

First Draw

40% A = Profit $1 Stop (40% Profit $1)

60% B = Loss $1 Continue

2nd Draw

  50% A = Profit $0 Stop (30% Profit $0)

  50% B = Loss $2 Continue

3rd Draw

    66% A = Loss $1 Continue

4th Draw

      50% A = Profit $0 Stop (10% Profit $0)

      50% B = Loss $2 Continue

5th Draw

        100% A = Loss $1 Out of cards (10% Loss $1)

Alternate 3rd Draw

    33% B = Loss $3 Continue

      100% A = Loss $2 Continue

        100% A = Loss $1 Out of cards (10% Loss $1)

Summation (40% $1 profit, 40% no profit, 20% $1 loss).

If the bet was less than $0.20, then one stands to make a profit in the long run.

Edited on March 11, 2008, 4:41 pm

Posted by Leming on 2008-03-11 15:33:36