Understanding how Beatty behaves is of little consequence if we don't first analyze his motives concerning Montag. Captain Beatty is clearly a well-read man. Sure, he might claim that as a fire captain he has to be full of bits and pieces, but his continual quoting of literature to make points suggests Beatty has analyzed and absorbed the content of the books he's read. Why, then, is he so all-in with his job of enforcing this shallow, unthinking way of life? Perhaps Beatty feels he is superior to everyone else because he can handle the knowledge gained from books but no one else can. He also may have realized the value of the books and the terrible mistake their society has made, but believes it would be impossible to undo the damage now. Perhaps Beatty does not worry about public access to books because, as a fire chief, he can legally read books. This selfish view would be consistent with Beatty's willingness to let the woman choose to be burned alive with her books.
Either way, deep down Beatty knows society's way of life is wrong, yet he is defensively stubborn about upholding the rules. As a result, Beatty is insulted one of his own firemen suddenly develops a conscience about the many problems with their way of life, since he is unwilling to risk his life and take a stand. When Montag returns back to work after a day of soul-searching (and book reading), Beatty is ready for him.
When Montag enters, the captain is standing there, pretending not to be waiting. He openly tells the other firefighters that Montag is a fool. Not looking Montag in the eye, he nonchalantly holds out his hand for the stolen book, then throws it in the garbage without even looking at the title. This must feel horribly ironic to Montag, who agonized over whether to hand over the actual book he smuggled out that day, the Bible, or a less historically important title. Ultimately, Montag worried giving a lesser book would make Beatty suspicious. It turns out Montag could have saved that Bible. Why doesn't Beatty look at it? We soon learn Beatty already knows Montag has more books; the firemen will burn his house shortly. Beatty's real goal here is to make an example of Montag in front of the other firefighters, which will allow the captain to save face and keep control of the other men.
That's why Beatty invites Montag to play cards. He can lecture him in front of the men, show them what an intellectual snob sounds like. He quotes Alexander Pope: "A little learning is a dangerous thing... shallow draughts intoxicate the brain, and drinking largely sobers us again." Beatty explains his belief that gaining a little knowledge makes a person ready to go out and conquer the system, change it all. He says, "I know, I've been through it all." So Beatty did try to balk the system, and apparently failed. He couldn't beat them, so he joined them. All the men know what has happened with Montag and they have listened to Beatty's lecture. So when the alarm goes off and the Salamander stops in front of Montag's house, no one protests, not even Montag. For the moment, it seems, Beatty's plan has worked.