Jane Street–styleTraderAssistant TraderQuestion #269

You have a box filled with cash, where the cash value is uniformly distributed between 1 and 1000. You participate in an auction: you win the box if you bid at least the value of the cash inside; you win nothing and lose nothing otherwise. If you win, you can resell the box for 150% of its value. How much should you bid to maximize the expected value of your profit (resale value minus bid)?

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