This typically refers to a variation of "Rock Paper Scissors" (Janken) featuring a monkey character. It is often found in older arcade games or simple flash-style games.
Janken is the Japanese name for Rock-Paper-Scissors. In the arcade and early home console era, Janken mechanics were frequently used in "Medal Games" (gambling-lite machines) and adult-oriented titles. The "Monkey" prefix often refers to specific mascots or themes used in these titles, where a player competes against a character in a best-of-three or best-of-five format. 2. The Legacy of Flash and Strip Games monkey+janken+strip+hacked
It sounds like you’re describing a combination of concepts: This typically refers to a variation of "Rock