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All right, the running game and the passing game.
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So a very simple idea whether to run or whether to pass
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when you have the ball
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is likely to end up as a mixed-strategy equilibrium.
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The defense is also randomizing between, for example,
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rushing the passer or playing a run defense.
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Is that right? This is not exactly a game I know a lot about,
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but I'm hoping I'm getting close enough here.
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It couldn't possibly be a pure-strategy equilibrium,
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other than very extreme parts of the game,
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like at the end of the game perhaps,
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but for most of the game,