This may be stupid. But I remember reading about different ways to play Chess.
Quote:
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Armageddon: a single game guaranteed to produce a result, because Black has draw odds (that is, for Black, a draw is equal to a victory). To compensate, White has more time on the clock.
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If it really is Lambda and Bern playing against each other, then it would make sense for Lambda to be on the black side since she wishes for an eternal draw. Though, the "single game" and "What has more time" parts are a little hard for me to explain.
Unless the rule translates to:
Bernkastel can affect the game board using outside sources.
Lambdadelta is limited to affecting the game board only inside of the game board.
This might explain how Bernkastel gets Ange into the game... but once again, I'm probably way off.