Exploit a Rock-Paper-Scissors Opponent with a Forbidden Gesture

Two rational players play rock-paper-scissors. After observing the opponent's first gesture, you know the opponent cannot use that gesture on the next round. Can you obtain an advantage, and what mixed strategies should the players use? ### Constraints and Clarifications The source says the opponent will not repeat a previously used gesture but does not distinguish only the last round from all earlier rounds. Analyze the immediate round after the first observation, where both readings forbid the one observed gesture. You remain unrestricted. Use payoff+1 for a win,0 for a tie,and-1 for a loss as an explicit practice convention. Longer play requires a rule for what happens after all gestures have been used. ### What a Strong Answer Covers Form the restricted payoff matrix, find a maximin mixture against a rational opponent, and distinguish positive expected payoff from winning more than half the rounds. ### Follow-up Questions - What changes if both players are subject to the same restriction? - Why is a deterministic best response to one guessed gesture exploitable?