Some rivalries are defined by a "big brother vs. little brother" dynamic -- the more successful team vs. the team that lives to destroy the more successful team's season. In the Red River Rivalry, the programs have traded who gets to play each role.
Some rivalries are nonconference affairs between schools who enjoy massive geographic overlap and recruit the same prospects but have never been in the same league. Red River was that ... until it wasn't.
At one point or another, Oklahoma-Texas has been pretty much everything. The schools have met 117 times; since 1929, the only time they didn't play at Dallas' Cotton Bowl was in 2018, when they also played in nearby Arlington in the Big 12 championship game.