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We've been playing that if you want to trigger the 2-card ability for Clan of the Fox you have to have 3 cards in your hand and your opponent has to also have at least 3 cards in hand for the exchange can happen.You're right about the 3-card power, but not about the 2-card one: you can exchange cards even if you (or your opponent) have less than 3 cards in hand. Just exchange as many cards as you have up to 3. If you have no card in hand, your opponent just gives you 3 cards.
Also we've been playing that if you trigger the 3-card ability for Clan of the Fox you can have no cards in hand and your opponent gives you their hand.
Are we playing both of these Clan of the Fox abilities correctly?