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Prove that the starting chess position isn't zugzwang for white

Chess is similar to reversi, in that both are entirely information-based zero-sum games with limited choices. But it is impossible for most / any chess player[s] to master all possible positions in chess, so blunders would likely occur in all games. In that sense, similar to reversi where the second player has an advantage when both players are of optimal play, black has an advantage.
You: "There is an advantage for the player who has the initiative."

Me: "Here's a bunch of games where the second person can force a win no matter what the first player does."

You: "Here's a bunch of games where the first person can force a win no matter what the second player does."

Me: "That doesn't matter, you're first statement is still false."
You're looking at it from too abstract a point of view. Chess is a game of concrete positions. There are concrete positions where the right to move becomes a disadvantage - but in the overwhelming majority of positions it is demonstrably favorable.

A vague similarity to a solved game where the second player has an advantage does nothing to establish why that should be the same for chess.

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