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If she puts in 0 she gets 0,
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if she puts in 1 she knows II will match
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and she'll double her money and get 1,
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and if she puts in 3,
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then she knows Player II will take the money and run,
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in which case our lender will have lost $3.
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So she's choosing between 0,1 and -3
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and she's going to choose $1,
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which is exactly what happened in the game.
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Everyone happy with how we did that?
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So this idea of starting at the last player, the player who moves last,
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solving out what they're going to and then working our way