Let's play "Rock, Paper, Scissors" game. If you play "rock", then would you say?
- I've got a rock
- I've got rock (without a)?
The first option seems much more natural. On Youglish you can find only examples supporting the first option. For example I got a rock in my shoe.
https://youglish.com/getbyid/87298883/i%20got%20a%20rock/english/us
The doubt weather the first option is correct lays in the lack of "a" before rock in the descriptions of the game. Whenever "rock" is mentioned, it goes without "a". Here are examples:
https://en.wikipedia.org/wiki/Rock_paper_scissors
In Rock paper scissors, rock is scissors' "Kryptonite", scissors are "what" to rock?
In one fell swoop, I would like to ask the same for scissors and paper. Scissors seem to be plural so I guess "I've got scissors" is a proper form. I am not that sure with paper. Can a native speaker shed a light on this trifle please?
Update after comments. I would like to use this game to engage children in practicing phrases as "I've got ...", "What have you got?" Obviously, the children deserve to be equipped with correct phrases. The focus of the question is in grammar rules, not in the game rules.
Update 2. Changed "I got" to "I've got..." following Edwin Ashworth's comment. Thanks.