You have a normal deck of 52 playing cards You draw cards one by one (Cards drawn are not returned to the deck).
A red card pays you a dollar. A black one fines you a dollar.
You can stop any time you want.

a. What is the optimal stopping rule in terms of maximizing expected payoff?
b. What is the expected payoff following this optimal rule?
c. What amount in dollars (integer values only ) are you willing to pay for one session (i.e. playing as long as you wish, not exceeding the deck), using your strategy?

Source will be disclosed after the solution is published.

(In reply to First Thoughts by Steve Herman)

These were my thoughts as well.  It is possible that a "Quit if ever ahead" strategy may well be optimal.

My strategies so far:
A: Quit if ever 1 ahead
B: Quit if ever 2 ahead
C: At halfway point, quit if ahead, otherwise wait to break even then revert to rule A.

I tried these different strategies with a 2, 4 and 6 card deck and noticed the following:
If there's a recursive way of solving this I don't see it.
A and C perform the same in all cases and both outperform B.

My guess is a rule like C but involving e will arise.

Posted by Jer on 2015-09-24 12:57:54