There's a formula, and it's not actually that sneaky. It's based on a behavioral pattern that shows up consistently enough across large samples that it got published in an academic paper and won a major research award. The formula: watch what your opponent just did, and play accordingly.
Winners tend to throw the same thing again. This is called win-stay. It's a reinforcement response — the brain treats the winning throw as the right answer and defaults to repeating it. If your opponent just won with Rock, throw Paper.
Losers tend to shift in a predictable cycle: Rock to Paper, Paper to Scissors, Scissors to Rock. Not to the counter that beats you — to the next throw in the sequence. This is called lose-shift, and it's the more surprising of the two tendencies. It means if you just beat your opponent with Rock while they threw Scissors, they're most likely to throw Paper next. You should throw Scissors.
Combined, the pattern is called win-stay/lose-shift (WSLS), and it was confirmed by Zhijian Wang's 2014 study at Zhejiang University — 72 players across controlled conditions, consistent enough to statistically outperform pure chance. The paper won a Best of 2014 award from MIT Technology Review, which is a remarkable thing to win with a study about Rock Paper Scissors.
The practical application: after each throw, process what happened and adjust. After their win: expect a repeat, counter it. After their loss: expect the next throw in the cycle, counter that. It breaks down when your opponent knows about it. Experienced players actively fight win-stay and lose-shift because they've been told about it, which makes them more genuinely random than they'd otherwise be. Against those players, the formula doesn't help much. Against everyone else — casual games, office tournaments, family gatherings — it's a real edge.
A few additional notes from competitive experience: the opening throw is worth paying attention to. Rock is the most common opener, especially from casual players who haven't thought about strategy. It's a closed fist, which is what your hand starts as before the count. Paper is your optimal first move if you don't know anything about your opponent. Throw Paper first, then let the WSLS read take over from throw two onward.
In a best-of-three match, you're working with limited data. The formula is most useful across longer sessions or multiple matches against the same opponent. In a single match, the read is more impressionistic — you're picking up on tendencies from minimal evidence and making a judgment call. That's fine. One correctly predicted throw in a best-of-three is the difference between winning and losing. The formula gives you a marginally better shot at getting that one throw right.