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Azul by the Numbers

by Trace Studio

#board-game#azul

Azul looks like a craft project — draft some pretty tiles, line them up, decorate a wall. But there’s a cold little optimisation puzzle hiding under the ceramic, and the questions it picks at the table (“did I just take tiles I can’t place?”, “is the big colour-set bonus worth chasing?”) all have answers.

So we went and found them. We built a roster of computer players — from ones that move at random, to hand-tuned strategists, to AIs that think several moves ahead — and had them play thousands of games against each other. We always rotate who goes first, so nobody gets a seat freebie in the standings. Every number below comes out of those games, not out of a rulebook.

Here’s the gist before we dig in:

0%
of games the bag steals
when there's a real skill gap
69%
the second mover's win rate
going first is a tax (2 players)
+7
the bonus actually worth chasing
the flashy +10 is a decoy
85%
look-ahead beats the best hand bot
here, thinking ahead truly wins

Is Azul mostly luck or skill?

Skill — overwhelmingly. Of our three studied games, Azul is the one where the better player wins the most reliably.

The only randomness in Azul is the bag: which tiles tumble out into the factories each round. So we ran the clean test — deal the exact same bags to a strong bot and a weak one, then swap their seats and deal them again. If the bag were calling the shots, a lucky draw would rescue the weaker player sometimes. It never did.

Deal the same bags to a clearly stronger player and a weaker one. How many of those bags did the stronger player still win?

Every bag, both seats, the better player won. When there’s a real skill gap, the bag decides nothing. The shuffle only starts to matter when two players are near-mirror images of each other — and even then, here’s the surprise: between equals, which seat you got swings more games than which bag you drew. The luck in Azul isn’t really the tiles. It’s the turn order.

Bottom line — Azul is a skill game wearing a craft-project costume. You can’t blame the bag — if you lost to a clearly better player, the tiles were never going to save you. Play more, get better, win more. It’s that direct.

So does going first matter — and which seat is best?

It matters, and here’s the twist that catches everyone: in Azul you want to go second.

Take one strong bot, clone it, and sit the two identical copies down with the same bags. Skill is now perfectly equal, so any gap is pure seat advantage. The player who moves second wins about 69% of the time.

Two identical players, same bags. The only difference is who moves first — and second is the seat you want.

Why? Going first means deciding with less information about how the round will shake out — and whoever grabs the first-player marker has to eat a tile on the floor line for the privilege, a guaranteed little point penalty. The reward for moving first next round just doesn’t cover the bill.

And it gets sharper with a crowd. At a four-player table a fair share of wins is 25% — but the seats are wildly uneven, and the second seat is the place to be while the seat holding the start marker is the worst in the house:

Win rate by seat at a four-player table. A fair share is 25% — the second seat towers, the first sinks.

Bottom line — if you can pick, take the second seat, not the first. The first-player marker looks like power (“I get to lead next round!”) but it’s really a small tax you pay in floor-line points. Grab it late, when you actually need to steer the next round — not out of habit.

How badly does the floor line punish greed?

Enough to lose you the game on its own. The floor line — where every tile you can’t place goes to rot — is the single biggest skill in Azul, and it’s almost pure discipline.

We proved it by sabotage. We took a top bot and switched off only its floor-avoidance — everything else about how it plays stayed identical. Against a random opponent it still won basically every game; raw scoring is easy. But sit it across from equally-skilled bots that do respect the floor, and its win rate collapsed:

The same bot with floor-discipline switched off. It still crushes a random player — but against floor-aware equals, it falls apart.

From a coin flip down to losing nearly two games in three — and the only thing we changed was whether it cared about the floor. The mechanism is exactly what you’d fear: the trouble starts when you leave a long row (the four- and five-tile rows) half-open. Long rows are slow to fill, so the tiles you keep drafting for them have nowhere to sit yet and spill onto the floor. Bots carrying a half-open long row end up with measurably more clutter on the floor than bots that keep their rows clean:

How cluttered the floor line gets (average), depending on whether a long row is left hanging open.

Bottom line — never draft tiles you don’t have a home for. Don’t open a four- or five-tile row until you can realistically finish it, and when in doubt, take fewer tiles. “Floor discipline” sounds boring, but it’s the difference between a winner and a loser among players who are otherwise dead even.

Rows, columns, or colour sets — what should I chase?

Chase columns. The end-game bonuses are a beautiful little bit of misdirection, and the biggest number on the board is the worst bet.

The rulebook dangles three completion bonuses: finish a row for +2, a column for +7, or collect all five of one colour for +10. The +10 is the showstopper — so naturally everyone reaches for it. But watch what a winning bot actually banks:

Points a winner actually collects from each end-game bonus (top-level play). The flashy +10 barely shows up.

The +10 colour-set is a decoy. It’s nominally the biggest prize, but it’s so slow and so easy for the bag (or an opponent) to deny that winners almost never finish one — it pays barely half a point a game on average. The unglamorous +7 column is the real engine: winners bank nearly ten times as much from columns as from colour sets. (The rows that show up here are mostly just the rows you finish naturally on your way to triggering the end — not something to build your plan around.)

Bottom line — build vertically. Columns are worth seven points and they’re achievable; the +10 colour set is a trap that mostly never closes. Only go for the colour set if it’s nearly free and you can clearly finish it — otherwise it’s a slow way to lose.

Should I bother blocking my opponent?

Mostly, no — and this one surprised us too. Denying your opponent the tiles they need feels like sharp play, but spend a turn on it and you’re not spending it on your own wall.

We pitted a bot that actively blocks against an identical bot that never bothers, and changed nothing else:

A bot that actively blocks versus an identical bot that never does. 50% is break-even.

Dead even. And here’s the kicker: when we let the blocking bot think ahead, it got better at actually landing its blocks — it denied opponents more often — and its win rate still didn’t budge off 50%. The blocks worked; they just didn’t translate into wins. The tempo you burn setting them up cancels out the damage you do.

Bottom line — play your own game. Tend your wall, mind your floor, chase your columns — that beats hovering over your opponent’s board. (Blocking might pay off for a player who can calculate very deep into the future; for the rest of us, it’s a distraction.)

So how good can an Azul AI get?

Here’s where Azul flips the script on its quieter cousins. We lined our players up on a single skill ladder (a chess-style rating — higher is stronger), and the story is a clean staircase:

Skill rating across the roster. The moment a player starts thinking ahead, it clears the entire hand-tuned crowd.

Look at the gap. The hand-tuned strategists — the careful, floor-disciplined, column-building rule-followers — all cluster in a tight band. Then an AI that genuinely thinks ahead shows up and even our lightest look-ahead bot clears the entire crowd. The deepest one beats the best hand strategy about 85% of the time. In Azul, foresight doesn’t just keep pace — it wins outright.

That’s the satisfying part, because it isn’t always true. In some games, calculation only catches up to the best simple rules and stalls there. Azul is different: its rewards are long-horizon (that +7 column you’ve been quietly assembling, the floor disaster three turns away), and seeing the future is exactly how you cash them in. Thinking ahead is the skill that breaks the ceiling.

Is that the top? Probably not. We’re also training a player that learns Azul from scratch, with no human strategy handed to it — and right now it’s still in its early lessons, sitting below even the hand-tuned bots while it figures the game out. Whether a fully-trained self-taught player can climb past our deepest thinker is the open question — it’s mostly a matter of training time, and that race is still on. We’ll update this report when our self-taught player has something to say.


Every figure here is measured from AI-versus-AI games on Trace Studio’s Azul engine, with seats rotated and bags paired so neither turn order nor a lucky shuffle skews the standings. We’ve kept the machinery in the background on purpose; if you want the gritty details — how the players are built, how strength is rated, how the games are sampled — those live in the project’s technical notes.