Rock Paper Scissors

Three things people get wrong about RPS

1. "Humans play randomly, so strategy doesn't help." They don't. A 2014 Zhejiang University study by Wang, Xu, and Zhou ran 360 players through 300 rounds each and found the "win-stay, lose-shift" conditional response: winners repeat their throw, losers cycle to what would have beaten the opponent's last throw (arXiv:1404.5199). Against a human, counter-play works. Against this tool, which samples each throw at 1/3, it doesn't — which is the mistake.

2. "Rock is the most-thrown option." Popularized as 35.4%, that stat comes from a single World RPS Society tournament sample and replicates inconsistently. More recent lab studies (Wang et al.) find the marginals much closer to 1/3 when conditioning is controlled for — the real exploit is the transition probabilities between throws, not the raw frequency. "Always throw paper" beats an overconfident novice about once and then stops working.

3. "Streaks prove the computer is cheating." In 100 rounds against a uniform RNG, the expected longest run of any one throw is around 6, and a 7-or-higher streak of identical computer throws appears in roughly 15% of 100-round sessions — that's a normal sample, not a bug. The computer here re-rolls each round independently; it isn't tracking you, so any "it keeps throwing rock" feeling is the gambler's fallacy working in reverse. Edge case: ties count as no-contest, so a 10-game run can legitimately end 3-3-4 with no decisive winner.