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
computer exploration by Charlie)
Setting the stop value at 5 while still in the first third of the deck, at 4 while in the middle third of the deck and 3 in the last third of the deck increases the expected value to about 2.40.
wins win fract exp value
59046 0.59046 2.3965
DefDbl AZ
Dim crlf$
Private Sub Form_Load()
Form1.Visible = True
Text1.Text = ""
crlf = Chr$(13) + Chr$(10)
wins = 0
For tr = 1 To 100000
If tr Mod 10000 = 0 Then Randomize Timer
DoEvents
red = 26: black = 26
posn = 0
v = 5
For draw = 1 To 52
If draw = 17 Then v = 4
If draw = 34 Then v = 3
r = Rnd(1)
If r < black / (black + red) Then
black = black  1
posn = posn  1
Else
red = red  1
posn = posn + 1
If posn >= v Then wins = wins + 1: ev = ev + posn: Exit For
End If
Next
If tr = 100000 Then
Text1.Text = Text1.Text & Str(v) & " " & wins & " " & wins / tr & Str(ev / tr) & crlf
End If
Next tr
Text1.Text = Text1.Text & crlf & " done"
End Sub

Posted by Charlie
on 20150924 15:38:36 