1. What you win with matters more than winning

Winning with scissors scores 1, with rock 2, with paper 3. So an equal win rate does not mean an equal score. Lay your hand against theirs and write down the score difference:

Look at the paper row. Catching rock earns 3, and losing to scissors costs only 1. If the opponent plays all three hands evenly, paper is worth +0.67 per turn while scissors and rock are both −0.33. That single line beats a random opponent.

function onTurnStart() {
	return 3;              // always paper
}

function onTurnEnd(result) {}

RANDOM wins every game LEVEL 1·2·3 loses every game

2. Habits get read. Including yours

Always playing paper is a habit. Once an opponent counts your frequencies, they switch to scissors. So try the other direction and read their habit instead: next turn, throw whatever beats what they just threw.

var next = 2;

function onTurnStart() {
	return next;
}

function onTurnEnd(result) {
	next = result.opponentchoice % 3 + 1;
}

LEVEL 1 wins every game LEVEL 2·3 loses every game

LEVEL 1 never looks at your previous move, so it walks straight into this rule. LEVEL 2 does something else: it counts the distribution of your last 50 turns, works out the score-weighted value against it, and answers probabilistically. A fixed rule leaves a distribution behind, and distributions get read.

3. A distribution with nothing to read

Then give them nothing to read. There is one set of frequencies where no answer earns your opponent anything. Solve the table above for the mix that drives all three hands to an expected value of zero and you get one half scissors, one sixth rock, one third paper.

function onTurnStart() {
	var r = Math.random();

	if (r < 1 / 2) { return 1; }       // scissors 50%
	if (r < 1 / 2 + 1 / 6) { return 2; }  // rock 16.7%
	return 3;                          // paper 33.3%
}

function onTurnEnd(result) {}

RANDOM · LEVEL 1·2·3 roughly even

Scissors, the lowest-scoring hand, takes half your throws. Paper is attractive precisely because it scores 3, so the scissors that catch it are needed just as often. Hold this mix and your expected value is zero no matter what the opponent does. Where every other strategy loses every game to LEVEL 2 and 3, this one holds even. The price is that it cannot beat weak opponents either.