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.

Hmm, what an interesting question.

Obviously, the game has a positive value, as you can always guarantee that you do not lose by just drawing all 52 cards.

Also, the stopping rule must involve both the amount that you are ahead and the number of cards remaining. For instance, if you are $1 ahead after 1 card, I imagine that it would be foolish to quit. If you are $1 ahead after 51 cards, you should definitely quit.