Every throw is a coin with three sides: win, tie and lose are each exactly 33.33%

Asked:

Chances to win in rock scissors paper

Standard two-player rock-paper-scissors, both players throwing rock, paper or scissors independently and uniformly at random. Nine equally likely matchups decide one round; probabilities are exact fractions, shown as percentages.

If ties are replayed until someone wins, symmetry gives each player an eventual 50% chance — conditional on a decisive result, the round is a fair coin flip.

A specified player wins 3 of the 9 equally likely matchups — a 1/3 chance per round. quantamagazine.org

Ties come from the 3 matching throws, so a draw is exactly as likely as a win. quantamagazine.org

No single throw is better than another against a random opponent — each wins one matchup, ties one and loses one. quantamagazine.org

Outcome	Probability	Counting basis	Source

Data: 3 outcome rows for standard two-player rock-paper-scissors under uniform random play; probability is the exact chance of the outcome in one round, rounded to two decimals for display. Nothing was cut.

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