Nate Hand Gesture is a psychological horror game that draws inspiration from the game you played as a child. You sit across the table from Nate, a cannibal setting the terms of your survival.
You're not trying to beat her; you're trying to entertain her. You'll need to be a student of psychology, not statistics...unless you want her to kill you in a sorry manner.
Rock-paper-scissors in this visual novel is a joke. Rather, the outcome of a round is totally dependent on Nate's mood at the moment. If she's amused, she may let you win, but if she's irritated, she might even cheat to defeat your selections. As for luck, she doesn't care halfway as much about that as remaining intrigued by you, listening to her, and looking out for subtle expressions on her cheek to catch up to her servitude.

The game is rather brief, but it branches off early, so you only want to save before notable dialog options, not the rock-paper-scissors rounds. Remember that it saves to your local storage in the browser version. If you wish to save your progress, do not play in private/incognito mode or remove your page data.
Play your first time by your gut and let one branch play out organically. Then on another playthrough, completely switch your mentality: be submissive if you were fighting back. You'll contrast these two paths and really get a sense of Nate and her triggering of lethal instincts. In the end, the challenge in Nate Hand Gesture isn't this game, but your own psychology.