Blackjack barricaded himself, hiding from Alexandra. He doesn't want to have to kill her, but he doesn't want to get shot either (he's unaware that Alexandra needs him alive). If the player gets Alexandra off Blackjack's back, he'll head over to Hoover Dam to find some card games, and Alexandra, if still alive, will head over to Fort Abandon to hang out. If the PC helps Alexandra capture Blackjack, she'll take him to Denver and give him to the Caesar's Legion slavers before returning to Fort Abandon.
Science Boy - After speaking to Alexandra, just tell Blackjack that he's worthless to her dead, and he'll make a break for it.
Stealth Boy- After speaking to Alexandra, just tell Blackjack that he's worthless to her dead, and he'll make a break for it.
Combat Boy - Attack Blackjack and take him down using non-lethal methods. If you kill Blackjack, however, you get no reward from Alexandra. You can also knock out or kill Alexandra and help Blackjack escape. He'll be regretful if she's dead, but he won't hold it against you.
Charisma Boy - Offer to compensate Alexandra if she'll let Blackjack go (Barter) or persuade her to tag along with you by promising bigger rewards in the future (Persuasion/Average). You can't persuade Blackjack to give up, but you can trick him into coming out (Deception/Average) if you're helping Alexandra.
There were two proposed Journal Entries. One would be the regular entry, and the other would be a "Dumb Journal Entry" presumably the one you'd see if you had low Intelligence. The entry also shows the different ways of finishing the quest.