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    An agent who commits to repeating a mixed strategy after ... — Carmelics
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    Challenges→It is rational for an atheist or agnostic who initially follows a mixed strategy (e.g., tossing a fair coin to decide whether to wager for God) to repeat that mixed strategy indefinitely after each tails result, because with probability 1 the coin will eventually land heads and the agent will wager for God.

    An agent who commits to repeating a mixed strategy after each tails result has effectively adopted a policy indistinguishable in practice from never wagering for God, since no finite tails sequence triggers revision of the strategy.

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    Key Terms

    Finite sequence(in logic and decision theory)
    A limited number of events or outcomes that happen one after another, rather than going on forever.
    Indistinguishable in practice(in philosophy of action and decision theory)
    So similar in actual real-world results that there's no meaningful difference between them, even if they're theoretically different.
    Policy(in decision theory and ethics)
    A general plan or principle that guides how someone will make decisions or act in similar situations.
    Revision(in epistemology and decision theory)
    A change or update to a belief, plan, or strategy based on new information or reflection.
    Wagering for God(in philosophy of religion and decision theory)

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    A reference to Pascal's Wager, an argument that you should believe in God because the potential reward (eternal life) outweighs the risk of being wrong.
    agent(Economics terminology applied to medical ethics)
    The party in a principal-agent relationship who is instructed to produce the good or service on the principal's behalf — in the medical context, the doctor
    mixed strategy(The uniform three-way randomization over bridges is the mixed strategy under analysis.)
    A strategy in which a player assigns probabilities over available actions and randomizes according to that distribution.

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    Truth & Knowledge1 linkedNatural Theology1 linked

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    It is rational for an atheist or agnostic who initially follows a mixed strategy...

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