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Why may an optimal strategy in an imperfect information game be randomised?

  • A.Random play is optimal whenever the state is not fully known
  • B.A predictable strategy can be exploited by the opponent
  • C.Randomisation reduces the computation the player must do
  • D.The rules of such games usually require a random element

Answer: B

If a player always bluffs with the same hands, the opponent learns to call, so mixing between actions with the right probabilities is necessary to be unexploitable. That is the content of a mixed strategy equilibrium. Computation, rules and general ignorance are not the reason, and random play is certainly not optimal in itself. That deliberate unpredictability can be part of an optimal policy is a genuine departure from everything in the perfect information case.

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