Jane Street–styleTrader InternTrader InternQuestion #620

Two people each bid a number before rolling a 30-sided die. Whoever bids closer to the number the die shows wins, and wins an amount of money equal to the number rolled. For example, if I bid 15 and you bid 16, and the die lands on 10, then I win 10 from you. What is the optimal bidding strategy and the expected payoff?

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