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 Quit as a winner (Posted on 2015-09-24)
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.

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 further fine tuning | Comment 5 of 8 |
(In reply to re: computer exploration by Charlie)

Starting with a stop value of 5 and then changing it as the deck progresses:

If draw = 17 Then v = 4
If draw = 34 Then v = 3
If draw = 40 Then v = 2
If draw = 48 Then v = 1

produces an expected value of about \$2.60.

79750    0.7975 2.59698

A value of 2.61 can be achieved by starting with a cutoff of 6 and switching to 5 at the 8th draw, in addition to the above switches.

 Posted by Charlie on 2015-09-24 15:47:31

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