309.Marbles in Two Bags
★★★classical probabilityJane Street
You have 100 green and 100 red marbles and must divide all 200 between two bags, each containing at least one marble. A player then picks a bag uniformly at random and draws one marble from it; they win if it is green and nothing if it is red. Arranging the marbles to maximise the payout, what is the fair price of this game in dollars?
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You control both bags. Make one of them as close to a certain win as possible, and dump everything else in the other.
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