re: Assuming LSU goes undefeated..

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that means they have to defeat the teams on their schedule

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as one generally does when you "go undefeated"...

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Which of these teams will LSU leap frog?

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all of the above. in recent years an undefeated SEC team, or in a special case a one-loss SEC team (non SEC Champion) can play in a National Championship game.

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Will an undefeated team from SEC gain an automatic berth to the NC?

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as in recent years...yes. also see last season, one-loss Alabama wins the SEC Championship and goes on to obliterate Notre Dame in the BCSCG.