Rock Paper Scissors is the only game on this shelf where the rules have no best move. Every throw beats one throw and loses to another. So a single round is a coin toss, and anyone who tells you they have a system is really telling you about their opponent.
That is the interesting part. Over a match, the game stops being about the throws and starts being about the thrower. The four computer opponents here each have a different brain, from one that ignores you completely to one that keeps notes on everything you do.
How to play
- Both players choose rock, paper or scissors in secret and reveal at the same moment.
- Rock beats scissors, scissors beats paper, paper beats rock.
- If both throw the same, the round is a draw and nobody scores.
- Otherwise the winner scores a point. The first player to reach 5 points wins the match; draws do not count, so a match can run longer than nine rounds.
Here you throw by pressing a button (or R, P, S), and the computer commits to its throw at the same instant, based only on your earlier rounds. It never sees the throw you are making.
A worked example
Suppose you play Pattern hunter and, trying to be “varied”, you cycle rock, paper, scissors, rock, paper…
| Round | You | It | Why it threw that |
|---|---|---|---|
| 1 | Rock | random | Nothing to go on yet |
| 2 | Paper | Paper | Your favourite so far is rock, so it throws paper: draw |
| 3 | Scissors | Scissors or Paper | Rock and paper are tied, so it guesses between them |
| 4 | Rock | random | No move has followed scissors yet |
| 5 | Paper | Scissors | After rock, you once played paper; scissors cuts it |
| 6 | Scissors | Rock | After rock then paper, you once played scissors |
From round 5 on, every one of your throws has happened before in the same context, so it wins every round. A strict cycle is the most predictable thing a human can do, and it loses the match 5–0 or close to it.
Now flip it. Against Copycat, which repeats your last throw, the same cycle wins every round: after rock it throws rock, and your paper covers it.
Strategy
Beginner: play the equilibrium
If you pick each throw with probability one in three, independent of everything, no opponent can do better than break even against you in the long run. You will win, lose and draw about a third of the time each. That is safe, not strong.
Intermediate: spot a simple rule
Watch what the opponent does after your throws. If it copies you, beat your own last throw. If it keeps throwing the move that beats your favourite, find your favourite on the frequency bars and throw what beats its answer. For example, if you have thrown rock most, Counter expects rock and throws paper, so you throw scissors.
Advanced: exploit, but don’t become exploitable
Every time you deviate from one-in-three to exploit someone, you create a pattern they could exploit back. Pattern hunter does exactly this to you. Good players exploit in short bursts and return to unpredictable play when the opponent starts adapting. Against Pattern hunter, a useful trick is to repeat a context on purpose once, then do something different the next time it appears: its table now predicts the old follow-up, and you throw what beats its counter.
Human tendencies, used cautiously
Studies of people playing many rounds have reported that winners tend to repeat a winning throw a bit more often than chance, and losers tend to switch. People asked to act randomly also tend to avoid repeating the same choice several times in a row, which real randomness does quite often. These are small population averages, not laws; treat them as a first guess and let the history strip overrule them.
The idea underneath
A mixed strategy is a probability for each move rather than a fixed choice. In Rock Paper Scissors the only Nash equilibrium, the pair of strategies where neither player gains by changing alone, is both players choosing uniformly at random.
Why uniform? Suppose you throw rock with probability r, paper p and scissors s. If rock is more likely than the others, paper wins more than it loses against you, so your opponent would throw paper more. The only mix that gives your opponent no better answer is r = p = s = 1/3. Against that mix, every opponent strategy has an expected score of exactly zero.
The catch is that the equilibrium never wins. It only guarantees you cannot be beaten on average. To win, you must deviate from it and bet that your opponent is predictable, which is what the pattern hunter does with a frequency table: it counts what you threw after each pair of throws and plays the counter to the most common follow-up. The same idea, predicting the next symbol from the last few, powers text prediction and compression.
Common mistakes
- Cycling to “be random”. A cycle is a perfectly predictable pattern.
- Reading meaning into a short streak. Three losses in a row happens by chance about once every 27 tries.
- Chasing the last result. Always switching after a loss is itself a pattern.
