Neither do the teams' two experienced head coaches - UH's Kelvin Sampson and UM's Jim Larranaga.
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According to Houston's athletics department, Friday's Sweet Sixteen matchup, with an Elite Eight spot on the line, will be the first time Sampson and Larranaga will face off against each other.
Sampson's two Final Four berths - one with Oklahoma in 2002 and then 19 years later with Houston - are well-documented and likely fly under the radar with the most casual observers. But Larranaga can claim to be the man behind a sports story worthy of cinema: he led a little-lauded No. 11 George Mason University team to a dream-like run in March Madness back in 2006 when the Patriots shocked the college basketball world on the way to a Final Four berth.
Both coaches are competing for a replay of those glory days.
Houston may be in a better position as the No. 1 seed in the Midwest Regional semifinals, which start on Friday at 6:15 p.m. in Kansas City with UH's game.
Sampson should have his two star guards - Marcus Sasser and Jamal Shead - on the floor against the Atlantic Coast Conference regular season champs. Sasser is getting over a groin injury while Shead is playing through knee pain.
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The Coogs were on the floor inside T-Mobile Center on Thursday for workouts a day out from the high-stakes matchup.
The winner faces whoever comes out on top in the Xavier vs. Texas game that tips off after UH vs. Miami. There is a possibility that Houston and Texas - two of the most fearsome programs this past season - may face off in the Elite Eight with a trip to a home-state/hometown Final Four on the line.
SEE ALSO: How did the 7 Texas schools in March Madness do after 1st weekend?
As of Thursday, Caesars Sportsbook has Houston as a seven-point favorite over Miami. Meanwhile, Texas sits as a four-point favorite to win its game on Friday.
To go even further, ABC13's partners at FiveThirtyEight give Houston the best odds among remaining teams to win the whole tournament at a 27% chance.
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One last tidbit: the Midwest Region champion will face off in the Final Four with whoever comes out of the West Region, which has semifinals tipping off Thursday night. The region's remaining teams - Arkansas, UConn, Gonzaga, and UCLA - are duking it out in Las Vegas.
Eyewitness Sports is in Kansas City for the Cougars' potential bid to return to Houston as a Final Four participant. Watch ABC13 newscasts for updates from the Coogs' camp leading up to the big showdown.
SEE ALSO: Final Four preparations already underway cause road closures
Final Four preparations already underway at NRG Stadium