Rock Paper Scissors

Plays the classical hand game against the browser. The computer's choice is uniformly random; the win/loss/tie is determined by the standard rules (rock crushes scissors, scissors cut paper, paper covers rock).

No strategy is built into the AI by default. Adaptive variants would attempt to detect patterns in the user's choices, but this version uses pure random selection.

Rock paper scissors is the canonical zero-sum symmetric game with no Nash equilibrium other than the mixed strategy of choosing each option with equal probability. Game theory states that against an opponent playing the optimal mixed strategy, no deterministic counter-strategy can win more than 33% of games on average; the same holds for the opponent. Real human play deviates measurably from optimal: empirical studies (notably the 2014 paper by Wang, Xu, and Zhou using 360 students at Zhejiang University) found that winners tend to repeat their winning choice, while losers switch to the choice that would have beaten the previous winner, producing an exploitable cyclic pattern in repeated play.

A worked example: 100 rounds against the uniformly random computer should produce roughly 33 wins, 33 losses, 33 ties, with statistical fluctuation of ±5-6 per category. Streaks of 5-10 consecutive wins or losses are entirely consistent with random play; intuition tends to overinterpret these as evidence the computer is rigged. Any strategy that doesn't adapt to opponent behavior, including 'always rock' or 'rock-paper-scissors-rock-paper-scissors', wins exactly 33% against a random opponent because the computer's choice is independent of the user's choice.

Limitations of pure random play matter only when the opponent is exploitable. Against humans, simple pattern-detection strategies can achieve 35-40% win rates by tracking opponent move frequencies and biasing the counter-move accordingly. The competitive RPS scene (yes, it exists; the World RPS Society held world championships through 2009) developed elaborate gambit strategies and meta-strategies that work against humans but are useless against true random play. The implementation here makes no attempt to detect or exploit user patterns; the choice is generated independently each round using Math.random.

Variants extend the game to more options. Rock Paper Scissors Lizard Spock, popularized by The Big Bang Theory but invented earlier by Sam Kass, adds two options with a 5-way relationship that maintains the cyclic structure. Higher-order generalizations (RPS-7, RPS-25, RPS-101) are possible and have been formalized; they preserve the no-pure-strategy-equilibrium property as long as the relationship graph is structured correctly. The classic three-option version remains dominant because it's the smallest non-trivial instance and the easiest to play with hand gestures.