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As Dragon's Disciple enters the battlefield, you may reveal a Dragon card from your hand. If you do or if you control a Dragon, Dragon's Disciple enters the battlefield with a +1/+1 counter on it.
Dragons you control have ward {1}. (Whenever a Dragon you control becomes the target of a spell or ability an opponent controls, counter it unless that player pays {1}.)
A Dragon card is a card with the creature type Dragon in its type line. Similarly, a creature on the battlefield is a Dragon if it has the Dragon creature type. A card that has “Dragon” in the name (such as Dragon's Disciple) isn't a Dragon card unless it also has the Dragon creature type.
If a player casts a spell that targets multiple permanents their opponent controls with ward, each of those ward abilities will trigger. If that player doesn't pay for all of them, the spell will be countered.
If you choose to reveal a Dragon card from your hand and also control a Dragon, Dragon's Disciple still only gets a single +1/+1 counter.
Players can respond to Dragon's Disciple while it is on the stack, but they cannot respond to the choice of whether or not to reveal a Dragon as it enters the battlefield. Notably, that means they can't remove your Dragon from play to prevent Dragon's Disciple from getting the counter once you've decided not to reveal a Dragon card.
Revealing a Dragon card happens as Dragon's Disciple resolves. It is not an additional cost for casting the spell.
