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Drafting depends a lot on context. And most importantly, there is no "right" way to draft. But here are general tips that can help you make better decisions.
Some cards work really well in draft, pick them if possible.
These cards require specific counters that your opponent may not have drafted. Without them, they're difficult to deal with.
Keep in mind what you're giving to your opponent.
Drafting is not only about choosing your cards, but also about giving cards to your opponent. It is important to draft a good deck for yourself, but it is even more important NOT to draft a good deck for your opponent. Don't give him counters to your cards. Give him cards to which you have counters.
Some cards are more universal.
More often than not, these cards will bring you value, so it is generally safe to pick them.
Pick a win condition.
It is good to have at least one win condition. A card that can actually win you the game. Without it, you can find yourself in a situation where your pushes just don't reach the opponent's tower. Try picking one of these cards if available:
When facing a choice between a card and its counter, go for the counter.
In most cases, the counter allows you to make a positive elixir trade. Think Arrows vs. Minion horde. When faced with such choice, you should nearly always pick Arrows.
Pick a removal spell.
Sometimes the draft is so weird that no player has a clear win condition. Then the game is about small damage, mainly with spells. So it is good to have a spell to be able to spell-cycle your opponent.
Aim for a balanced deck.
You can only choose 4 cards out of 8 so it is not entirely possible, but you should aim for it. Balanced deck means having: tank / win condition, support, spell, cheap cycle / defense cards. For example:
Don't pick duplicate cards for a specific role. It is possible your opponent gives you one more similar card and then you're in trouble. For example if you choose Zap, then Log and you're given Arrows, there's a high probability, you won't have enough good units to push with.
Don't automatically pick cards that you like, don't go for a specific deck.
It is tempting to go for cards that you like. Or for those that the Challenge is about (Bandit, Heal). But it is more important to have a balanced deck than trying to draft your favorite zap bait deck. Meta decks are well-thought and each card plays its role. There's a very little chance you'll be able to make exactly that deck.
Play defensively, play safe.
In draft, there are no meta decks, that you're trained to play against. You don't know what to expect from your opponent. It is better to play safe, wait for him to make a first move, don't overcommit on your pushes until you know their deck. Don't let them catch you off guard with eBarbs on the bridge.
Know when to spam units.
Sometimes, your opponent doesn't have any big or small spells. If you know it, you can get away with playing way more aggressively than you ever could with normal decks. Learn to recognize it and use this to your advantage. A lot of drafts can be won by spamming units if you know your opponent doesn't have any good way to counter it.
If you feel you can't win, try to surprise your opponent.
When you're caught in a bad cycle (you attack, the opponent defends and counterpushes and does damage to you, and this is repeated several times) or you drafted a bad deck, try doing something crazy. For example a surprise push on the other side. It is risky, but it can pay off, where as repeating the same attack over and over will be a guaranteed damage to your towers.
Accept your losses and move on.
Sometimes, you have a really bad luck and you draft a deck without a win condition. When matched against a decent player, you stand no chance of winning. This happens even to the BEST players, don't be angry about it. Take the loss and try again.
Good luck with your drafting!