180.Draw Again or Keep
★★★optimal stoppingAkuna Capital
A number is drawn uniformly at random from 1 to 12 and you are paid that many dollars. You may instead discard it and draw a second number, which you must then keep. Playing optimally, what is the expected payout?
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A fresh draw is worth the average of 1 through 12. Keep anything above that and redraw otherwise.
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