Rules FAQ
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You only compare initiative when revealing new plots in the plot phase. That step is skipped when a player reveals a new plot with "The Rains of Castamere" or Battle of the Trident, so The Seed is Strong cannot be played at that time.
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If the initiative values are tied, you must first break that tie to determine who wins and loses initiative. In a melee game, you still lose initiative even if some of the other "losing" players have a lower initiative value than you.
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The reaction is triggered immediately after you lose initiative, before choosing a new first player, and well before resolving any When Revealed abilities. For instance, if Valar Morghulis is revealed, you would need to discard a card for The Seed is Strong before you could discard it for cards like Ser Rolly Duckfield or Umber Loyalist. Discarding a card for The Skahazadhan would come even later in this sequence.
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Players are not allowed to rearrange the order of their cards in shadows. Once the cards stop being revealed, any player with a good memory should still be able to tell which card is which.