What pair of teams have played the most often and either one or both of them have never played at the other team's home stadium?

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The original was posted on /r/cfb by /u/e8odie on 2024-08-16 19:10:31+00:00.

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For example, LSU and Oklahoma will play for the 4th time this year but will be the first time in either Norman or Baton Rouge.

For just one-sided ones, Notre Dame/Navy comes so close as they’ve played 94 times and only once in Annapolis and even that was only 10 years ago.

EDIT: Sigh. Yes, I forgot to exclude situations like Red River Shootout or World’s Largest Outdoor Cocktail Party