Arrange the steps a player should take in a game theory scenario using backward induction to maximize their strategy: A) Analyze potential outcomes and payoffs, B) Decide on the current move based on the analysis, C) Observe the opponent's previous moves, D) Make an informed strategy choice based on the observed responses.

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To use backward induction, a player should first observe the opponent's previous moves (C) to understand their strategy. Next, the player analyzes the potential outcomes and payoffs (A) that could result from each possible action. With that analysis, the player makes an informed strategy choice based on the observed responses (D). Finally, the player decides on the current move that maximizes their payoff given that informed choice (B). For example, if a chess opponent consistently uses a particular opening, a player will first note that opening, evaluate all possible endgame positions, choose the best defensive line, and then play the move that leads to the most favorable outcome.

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