Azul looks like a peaceful drafting game and plays like a denial puzzle. The single biggest skill jump in the game is realising that what you take is less important than what you leave behind.
The denial draft is the master move. When you take the last colour-A tile from a factory, the remaining tiles on that factory go to the centre — where your opponents will take them. If you can leave the centre stocked only with colours your opponents already have rows full of (forcing them onto the negative track), you've gained more than any direct play.
Row completion timing matters more than people realise. Filling a row at the top of your wall scores fewer adjacency bonuses than filling a row at the centre, because middle tiles touch more potential neighbours. Plan your fills inward, not outward. The 2-point and 7-point completion bonuses also stack with adjacency, so a single late-game tile can be worth 9-10 points if placed correctly.
The negative-track gambit is the advanced move. Taking one or two penalties on purpose to deny your opponents a critical colour is often worth a +5 swing even after the -2 to -4 cost. It only works if you can count the tiles remaining of that colour and confirm you're starving the opponent who needs them. Track colour counts from round one — most beginners ignore this entirely.
End-game bonuses (complete column +7, complete colour +10, complete row +2) decide tight games. If you're going to lose the round-by-round count, switch into long-game mode by round three and chase the +10 colour bonus quietly while opponents fight over the visible plays.