Thompson's story is one of the most notable in this year's class. He was selected in the same draft as his identical twin brother, Ausar, who was selected fifth overall right after his sibling.
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They are the first twins in NBA history to be drafted within the first five selections.
Thompson was selected after Victor Wembanyama went to San Antonio first overall, Brandon Miller to Charlotte at No. 2, and Scoot Henderson to Portland at No. 3.
The 19-year-old Wembanyama was the rare can't-miss prospect of this year's festivities.
Houston also may have came away with the steal of the draft when it took Villanova small forward Cam Whitmore at No. 20. Whitmore, the best available player at that point, was ranked second at his position and projected by ESPN to go no higher than the sixth pick.
There was more celebrating for H-Town in the first round. University of Houston Cougars forward Jarace Walker is officially a top-eight draft pick. His teammate, Marcus Sasser, went 17 picks later at No. 25.
Houston gets blessed at No. 4
Not since the fictional recruit Jesus Shuttlesworth has a name gotten much buzz when it comes to ascending to the next level of basketball.
Amen Thompson's name caught on as the primary choice of the Rockets, based on numerous draft projections days out from the event.
Thompson, 20, wasn't the only one of his name and look who got picked this year. His identical twin brother, Ausar, was selected to the Detroit Pistons at No. 5.
So, what's so catchy about Amen Thompson? The 6-foot-7-inch guard is primarily a raw prospect, but someone that a team loaded with Jalen Green, Jabari Smith Jr., and Alperen Sengun can afford to develop.
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"All signs point to Thompson being the choice for Houston at No. 4, with the Rockets weighing a big upside swing on the hope that he can become the type of connective guard their roster needs," ESPN's Jeremy Woo wrote on Wednesday. "While it may take him some time to adjust to the speed of the NBA game, his unique athleticism and passing vision should allow him to create advantages in the open floor."
The brothers Thompson also have a tie to southeast Texas. Their older sibling was a member of the Prairie View A&M men's basketball team.
While a pick like this can certainly pay off, it's hard to ignore that Houston has earned high-draft positions in the last three losing seasons.
SEE MORE: The Rockets are ready to move past their rebuild
Rockets get value selection at No. 20
Houston may have committed theft on Thursday night. Sixteen spots after taking Amen Thompson, the Rockets went with the best player available: Villanova small forward Cam Whitmore.
Whitmore was projected by ESPN to go as high as the sixth overall pick but started to fall from that position.
There's a risk with the 6-foot-7, 232-pound prospect. He suffered a broken thumb before the start of the past season, causing him to miss seven games.
Still, the injury and the resulting falloff for the Big East preseason freshman of the year didn't scare Rafael Stone and company.
Rockets trade rumors
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Needless to say, nothing has been substantiated yet, but that hasn't stopped folks like ESPN's Adrian Wojnarowski and others to throw out Houston's trade possibilities.
Dedicated Houston Rockets blog, The Dream Shake, mentioned on Wednesday a potential trade with the Los Angeles Clippers to acquire Paul George, though a convoluted scenario would need to take place to make it happen.
There's also drafting to accommodate a looming free-agent signing, like Kyle Kuzma, Draymond Green, or prodigal star, James Harden.
2 UH Cougars selected in first round
The University of Houston Cougars have a couple of prospects in the draft: freshman forward Jarace Walker and senior guard Marcus Sasser.
Walker, who was ESPN's top power forward available going into the event, was selected eighth overall to the Washington Wizards, who are trading him to the Indiana Pacers.
The freshman represents UH's highest draft pick in 39 years when Hakeem Olajuwon went first overall to the Rockets.
Seventeen picks after his teammate, Sasser was selected 25th overall to the Memphis Grizzlies, who, like Walker's drafting team, are trading him to the Detroit Pistons.
SEE MORE: Houston Cougars star Marcus Sasser on pre-draft Nuggets visit: 'It was fun for sure'
UH star Sasser expects to be drafted in late-1st or early-2nd round