"That is who he'd really love to get together with," Bill says, watching Otto from across the table, "but she doesn't want to be partners with him. Unfortunately, she just wants to be friends."

"I love her more," Otto says. He means that he loves Hannah more than Matthew does; Matthew is her boyfriend.

"But they're not together anymore?" Bill wonders aloud.

"Yesssss!" Otto shouts. His fists go skyward. "Matthew can fuck off."

Otto's wearing a T-shirt that he bought on one of his journeys with Bill; on it are the Tibetan symbols for the most beloved of Buddhist mantras, om mani padme hum. Otto picks up a Heinz ketchup bottle and holds it as though it were a puppet.

"Hello, Mr. Ketchup!" he says.

"Hello!" the ketchup squeaks back.

Bill gently steers the conversation back to the topic at hand.

"Who are the girlfriends that you've had?" he asks.

"Sarah," Otto says. "We had a great romance together. I'd take her out to the theater." I ask Otto whether Sarah has Down syndrome.

"I don't know," he says.

"You should know," Bill says. A delicate nudge.

"Yes, she does," Otto says. There were also a few evenings out with a woman named Vicky, whom Otto met through Mates & Dates, a matchmaking agency for people with learning disabilities, but that led nowhere.

"What happened with both of those two?" Bill asks.

"They had carers," Otto says.

"And what did the carers say?" asks Bill.

"'No, you can't have a boyfriend,'" Otto remembers. "Disappointing." He hangs his head. He puts the ketchup aside.

"Yeah, it's a very difficult subject, that," Bill says. "We've had some very emotional conversations about it." The parents and caretakers of women with Down syndrome often cut off a relationship because they're afraid of where it might lead.

"It's hard," Otto says. "It hurts right in my heart." He presses his fist against his chest.

"It's one of the big things you have to deal with, Otto, isn't it?" Bill continues. "A part of his life that is very difficult to accept."

There is a long pause. Otto silently bobs his head back and forth for a while. Then he looks around, his eyes taking in the restaurant and the casino and the four women at the next table.

"This is good," he says.

"It is good, isn't it?" says Bill. "We'd better go absolutely mental tonight to make the most of it."

Otto grabs the ketchup bottle again and drapes an open napkin over it. "It's a magic show!" he says. With his free hand he reaches up, snatches away the bottle, and hides it under the table.

"Quick as a flash," Bill tells him. "I didn't even see it."

7.

Otto and Bill make the most of their last night in Las Vegas, even though, no, after all of the dancing and flirting and drinking and erotic speechifying, Otto never gets anywhere close to losing his virginity. The highlight for him is attending a show at the Mirage by the singing ventriloquist Terry Fator, who ushers out a series of puppets that do note-perfect musical impersonations of acts like Roy Orbison, James Blunt, and Brooks & Dunn. The Terry Fator show leaves a tremendous imprint on Otto, and later that night, when he and Bill find themselves in the foyer of a weirdly empty karaoke joint, Otto gets an idea. Decked out in his cowboy hat and a tuxedo, he shuffles to an open space in the center of the room and, while pretending to hold a microphone, announces that he would like to call a dummy up to the stage.

"He's quite shy!" Otto says. "He likes his girlfriend's body! Will you welcome, please, my very own dummy . . . my friend Bill!"

People who know Otto Baxter will tell you that the kid is bound to surprise you—that there are moments when Otto will say or do something that seems unexpectedly moving, even profound. This is one of those moments. Bill gamely walks up to the front of the room. Otto places his hand on Bill's back and Bill simply stands there, as unblinking and motionless as a ventriloquist's wooden sidekick. "So take it away, Mr. Bill," Otto says, and then Otto begins to sing. Or rather they begin to sing, both of them, deftly in sync, with Bill moving his mouth up and down while Otto croons the lyrics in a stilted but passionate monotone.

I see trees of green, red roses, too.
I see them bloom for me and you.
And I think to myself,
What a wonderful world.

Otto finishes the song and the two of them stand side by side.

"A very good reproduction, Otto," Bill says.

"You like that?"

"Yes," Bill says. "Now that's entertainment."

But Otto, as we've come to expect, has very little patience for empty karaoke joints and moments of sentimental rumination. There are still a few hours left before he and Bill have to catch a flight back to England. There's still time to score, or at least time for Otto to drop to his kneecaps on the dance floor. He dashes outside, hoping to hail a taxi back to wherever the action is. Bill tags along. As he and Otto stand on the curb together, shivering in the cold desert air, Otto glances back at the karaoke joint and then looks right at Bill. "That place," Otto says, smiling broadly, "was a shithole."