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You just can't play with mirrors in Game of Thrones...
But you can! The format just needs to be slightly different. For example, if you've come up with a mirrored map template, you flip a coin to decide whose castle we're playing with. The player whose castle it is plays with their starting hero, and the second player chooses any starting hero from those not in the opponent's team – like a bastard. In short, anything is possible if you want it to be.