What is Quickdraw in Hearthstone?
Hearthstone has many card effects that are common enough that they get their own keyword - a word or two that immediately tells you how the card works. Let's take a look at the Quickdraw keyword.
Quickdraw is a mechanic that appears in Showdown in the Badlands (alongside Excavate). Cards with Quickdraw have a bonus effect that activate if you play the card on the same turn that it enters your hand. Whether that be through drawing it or generating it from outside your starting deck somehow, as long as it enters your hand and play it that turn, the Quickdraw will activate.
This type of condition has appeared on a few cards prior to Showdown in the Badlands (such as Oil Rig Ambusher or Keli'dan the Breaker), but these cards are not considered to be Quickdraw cards despite being mechanically identical.
Keywords that Work Great with Quickdraw
The Dredge mechanic from Voyage to the Sunken City compliments the top-decky nature of Quickdraw by allowing you to choose a Quickdraw card to place on top of your deck (or not place one there if you couldn't afford it next turn).
Playing Against Quickdraw in Hearthstone
Quickdraw cards are unfortunately quite difficult to predict since there's very few ways to know exactly what card your opponent will draw before they draw it. In most situations, playing against Quickdraw cards will simply just come down to hoping that they can't make great use of Quickdraw (and therefore, might not be incentivized to play the card) on the turn they draw it.
Cards like Algalon the Observer can function as a form of disruption for Quickdraw by either delaying them from drawing it at a time where the Quickdraw could be useful to also forcing them to draw a Quickdraw card early at a time where your opponent may either not afford to play it or wouldn't want to play it in the current board state. Disarming Elemental can accomplish a similar purpose and also making said card too expensive to play or a bad play in general.
Example Hearthstone Quickdraw Cards
Dehydrate is a simple Shaman spell akin to Tidal Surge or Demon Hunter's Eye Beam. Naturally, it costs 3 mana, but its Quickdraw effect changes its Cost to 1 mana on the turn you draw it, which in turn makes it easier to play it that turn.
Trolley Problem is a Quickdraw spell for Warlock with summons two 3/3 minions with Rush and discards the lowest-Cost spell in your hand. Here, the Quickdraw effect can actually impose a dilemma for Warlock where some Warlock decks might want the card to discard a spell for discard synergies and the Quickdraw can act as a net-positive or a net-negative overall.