As much as I like the idea, I don't know how much it adds over standard Rock, Paper, Scissors. Rock, Paper, Scissors is an inherently random game with no real sense of strategy. As such, I do like the idea of adding strategy to it. It is interesting to be able to think through what the other person might do with their different point values. Will the person put their strong rock on three with the risk of me putting my paper there, or will they instead use their lower strength paper thinking I'll use my rock? But then there's the problem: just like Rock, Paper, Scissors, I have no idea what the other person will do and the other person has no idea what I will do. While there are more mechanics, there isn't really any more strategy.
Other than the base idea, I do think the controls should be more clear. Maybe it's just itch.io messing up controller inputs, but it still took me a while to understand what the buttons were, especially with the use of PlayStation icons over the more standard Xbox lettering and the low resolution.
I do like the music, but it says you didn't make that so I won't dwell on it. You made good choices on the audio.
The graphics are pleasant. Everything looks good and I can definitely see this looking good on a hypothetical physical Pico-8 system. I think that the UI could be clearer just like I said regarding the controls, but the game looks good nonetheless.
Overall, I enjoyed the game. I do like the idea and it is a fun twist on the initial prompt. Unfortunately, doubling the randomness doesn't make the game less random, and I just can't see myself preferring this over standard Rock, Paper, Scissors in most situations.