Yes and no

You get off of your beanie and watch. A crowd gathers around the new blonde Aussie as he reads his text from the showrunners.

“Jamie. As a new arrival, you will date one of the women at a beachside picnic. We have decided to send you on date, and we decided that you should date… Elizabeth,” Jamie says, looking shocked and then elated.

“What?” Liz says, also surprised, “That’s like so random oh my gosh.”

“Liz, how about it? You wanna go for a date?” Jamie says smiling. You see Jamie look at Liz in a completely different way. His eyes shifted from Liz to a tone of "this girl is pretty" to "I need to marry this woman".

“Uhh sure,” Liz says.

Rick looked uneasy as he watched Liz go inside to get changed for the date. Tom seemed relieved, and Paige looked exceptionally disappointed.

Liz goes upstairs to change into her dating clothes, putting on make-up and a dress. Sometime later, Jamie and Liz leave the villa to go to the beach for a picnic date.

In the corner of your eye, you see Tom talking to Paige by the pool. Paige, who looked as giddy as a schoolgirl whenever she was around Tom previously, looked a bit cooled off and distant from him suddenly. The two, Tom and Paige, converse for a while while you go to the outdoor gym and do some lifting.

Later, you see Tom leaving Paige with a stone face from the pool and heading up the outdoor canopied lounge area to talk to Jenna, who was sitting by herself.

Jenna lights up, and Tom’s stony expression leaves him. He changes expression and puts on a game face of a guy at a club hunting for women. Your intention of setting up Jamie and Liz was to keep Jenna isolated and Paige with Tom, but it looks like its all for nothing.

If things go ahead like this, it means you would still be the one left out. If Liz picks Jamie and Jenna picks Tom, that would leave Paige single and Rick single, and you single.

Either way, it would be between you and Rick for Paige’s vote and recoupling. Paige would definitely keep Rick around over you if she were playing the game. Rick would mean something that she can use to drive a wedge between Liz and Jamie. You were screwed. But is Paige that conniving or manipulative to play the game in that way? Maybe not. You couldn't risk it.

Your road to salvation was clear. You had to become friends with Paige.