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In the PS2 and Xbox versions, by default, you play as Obi-Wan, but after beating the game, you can choose to play as Anakin, which gets you an alternate ending where Anakin kills both Obi-Wan and Palpatine to rule the galaxy himself.
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Come the last stage, the character not being used becomes the boss (although you can still switch control of the characters even during the duel).
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Even if it's not to the death, the outcome of who wins may cause the story to branch off in different paths.
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If the battle is fought to the death, it can become a powerful Player Punch, especially the player is forced to decide which character lives and who dies. If the two playable characters are rivals or Arch Enemies to one another this is all but guaranteed to happen at some point. And then there are some that pit one player character against another, controlled by the player and the AI, respectively. Some feature more of them, with the player controlling each one of them in turns. Most single-player video games have a single Player Character whom the player steers throughout the adventure.
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