Stick or Swap for the Second Bill

Akuna Capital

A magician's cabinet has two drawers. The left drawer holds a $1\$1 bill together with a $100\$100 bill; the right drawer holds two $100\$100 bills. You open one drawer at random, blindly pull out one bill, and see that it is $100\$100. You now get to draw exactly one more bill — from the same drawer, or from the other one. Does switching drawers improve your expected haul?

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