Blackjack is normally very easy-going and friendly, but unfortunately for him Caesar's Legion are paying handsomely for live super mutants and as such he has become the favored target of Alexandra. By the time the Prisoner arrives at Mesa Verde, Blackjack has barricaded himself inside a cave in the canyon. He had been running from Alexandra, who'd been on his trail for days, and he didn't realize the canyon didn't go any further. He claims to have a minigun (actually just a bundle of sticks and pipes painted black with charcoal), and hopes Alexandra will eventually give up and go away. He has a large pack of supplies, which combined with his super mutant endurance, means Alexandra's hopes of starving him out seems unlikely.
Resolve the Alexandra-Blackjack situation: Blackjack and Alexandra appear to be at a stalemate, but the Prisoner can help resolve it. The Prisoner can tell Blackjack he is wanted alive so it's worth making a break for it, kill or knock out either Blackjack or Alexandra, or convince one of the two to give up.
If he is handed over to Alexandra he will be taken to Denver and made a slave at the Legion camp. If he escapes he will make his way to Hoover Dam where he will found at the casino.
While at Hoover Dam Blackjack will spend his time gambling; he will offer some of his winnings as thanks for helping him.
The Prisoner is aware Blackjack may need to be taken back to Tibbets, if he is at Hoover Dam he will say that he understands but wants to gamble some more first. It will soon become obvious that Blackjack isn't going to turn himself in as soon as the Prisoner would like and he will need to be torn away from his game.