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 20080311 15:33:36 