30.When to Stop Drawing
★★★optimal stoppingJane Street
A jar holds 3 balls marked and 2 balls marked . You draw balls one at a time without replacement, accumulating their values, and may stop at any moment and keep your total. Playing optimally, what is the fair price of this game?
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Work backwards over the states given by how many of each ball remain. At each state compare stopping with drawing once more and continuing optimally.
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