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So his payoff, the attacker's payoff,
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is how many battalions does he get to bring into your country?
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He only has two to start with and for you,
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it's how many battalions of his get destroyed?
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So just to give an example,
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if he goes through the hard pass and you defend the hard pass,
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he loses one of those battalions going over the mountains
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and the other one because he meets you.
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So he has none left and you've managed to destroy two of them.
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Conversely, if he goes on the hard pass
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and you defend the easy pass,
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he's going to lose one of those battalions.