Optimal Stopping in a Blue-Red Ball Draw
A box contains 4 blue balls and 3 red balls. You draw balls one at a time without replacement. Each blue ball earns you $\
$ and each red ball costs you $\
$. After each draw you see the ball's color, collect (or pay) the dollar, and then decide: stop and keep your running total, or draw again.
You may stop at any point -- including before drawing at all (locking in $\$0$). What is the optimal stopping strategy, and what is the expected profit under that strategy?
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