Three players roll 50-sided dice and you pick any number from 1 to 50. The highest and lowest play the middle two. Which number do you pick?
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Three players each roll a 50-sided die. As the fourth player you instead choose any integer from 1 to 50. The highest and lowest numbers form one team and the two middle numbers form the other; the team with the larger sum pays the team with the smaller sum the difference. Which number do you choose to maximise your expected value, and what is that value?
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