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If he's using Fact A,
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he should not shoot.
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Alternatively, he could think that Chevy is going to shoot tomorrow,
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in which case he uses Fact B,
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and what does he do?
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He adds up his probability, Patrick's probability of hitting today
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plus Chevy's probability of hitting tomorrow:
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he asks is that sum bigger than 1, and he concludes, no.
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So we have no shot here and no shot here,
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and notice that both of those arguments were dominance arguments.
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In each case, whether Chevy thought
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that Patrick was going to shoot tomorrow