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I understand the core of the issue.
It's about the color change. If you alternate colors, blue gains an advantage in choosing the castle, while red has the advantage of the first turn. If you play, alternating colors from game to game – one player plays blue twice and red once, the other – vice versa. This creates some inequality. That's why a full random selection and color change after a subjective restart are used.
Full random selection is suitable for restoring equality, but it's unlikely to be useful for determining the stronger player.
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