A new government lottery has been announced. Each person who buys a ticket submits an integer number between 0 and 100. The winner is the person whose submission is closest to 2 / 3 of the average of all submissions. If ties occur, the prize will be shared. If Chloe expects other players to select numbers randomly, what number should she choose? If you expect all other players to exhibit the same depth of reasoning as Chloe, what number would you choose?
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