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If you would draw a card while you have no cards in hand, instead you draw two cards and you lose 1 life.
Each additional Blood Scrivener you control will effectively add one card and 1 life lost. Say you control two Blood Scriveners and would draw a card while you have no cards in hand. The effect of one Blood Scrivener will replace the event “draw a card” with “draw two cards and lose 1 life.” The effect of the other Blood Scrivener will replace the drawing of the first of those two cards with “draw two cards and lose 1 life.” You’ll draw two cards and lose 1 life, then draw another card and lose another 1 life.