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5920概率中等derivationmedium

Clairvoyance Across Three States

题目

The state is High, Mid, or Low with probabilities 12,13,16\frac12,\frac13,\frac16. You pick action Long or Flat once. Long pays 12, 3, 912,\ -3,\ -9 in High, Mid, Low respectively; Flat pays 00 in every state. A clairvoyant will tell you the exact state before you choose. What is the difference between your expected payoff acting on the clairvoyant's report and your expected payoff using the single best action chosen in advance?

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