Expert — Quoridor AI Opponent

Oracle is the expert tier: the fourth rung of six, one step above advanced and one below master. It is the right opponent once you are beating the tier below more often than not and your losses have stopped being blunders — you lose because a wall you did not see coming cost you four squares, or because a wall you did place bought you nothing.

This page is about the part of the game those losses rest on, and it is the part strategy writing usually skips. The strategy framework prices a wall once you are holding one up against the position, and it says outright that pricing a move is not the same as finding one. Finding one is a search problem, and the expert tier is where the engine's answer to that problem becomes worth stealing.

What the extra budget actually buys

Oracle's playout ceiling is three times the tier below's (how the engine scores a move), and that gap is a real one rather than a label: in the last full measurement of the ladder, the expert tier beat the advanced tier in every game of the match. Not every rung of a difficulty ladder converts extra thinking into extra strength. This one does.

Where those playouts go matters more than how many there are. They split across every legal pawn step and every candidate wall the search is willing to consider, which leaves each individual candidate sampled in the hundreds (how a budget divides). A sample that size is not depth in the chess sense. What it buys is coverage — a wide list of candidate walls, each looked at often enough that the differences between them survive the noise.

Which makes the list itself the interesting quantity, and it is the thing the rest of this page is about. What is on it?

Where good walls live

Not everything. The engine never sweeps the board. It builds its wall candidates from four components, unions them, and keeps the placements that are legal.

The ring around your pawn. Up to sixteen slots surrounding a pawn's square — eight horizontal, eight vertical. Your pawn's ring is scanned from the third ply of the game onward.

The ring around its own pawn. The same sixteen slots on the other side of the board, switched on from the moment any wall is on the board at all, or by the sixth ply if none is.

The slots around a wall already down. Every wall on the board seeds its own neighbourhood: the in-line extensions running out from both ends, and the perpendicular slots that brace it or turn the corner.

The outermost columns. From the sixth ply on, horizontal walls in the far-left and far-right columns are candidates unconditionally, wherever the pawns happen to be. Vertical slots out there get in only if some other component reaches them.

That candidate generator is shared: the same stencil feeds the search at every difficulty, and it takes no account of which tier is using it. What moves as you climb the ladder is only how much sampling each entry gets. So this is the tier where the list starts to matter more than the budget — below it, the interesting limit is how thinly the playouts are spread; here, the playouts are spread well enough that the omissions in the list are what is left to exploit.

It is also a stencil worth borrowing, because those four checks take about ten seconds and cover nearly every wall worth playing. The pawn rings come first for a reason that is pure Quoridor: a wall only buys anything if it lies across ground somebody is actually going to walk, and the one square you know for certain a route runs through is the square the pawn is standing on. The ring pays best in the turns right after your opponent commits to one side of the board. Why the other two regions are rich — walls that extend a line or share a corner, walls that lean on an edge — is worked through in How to Play; what the stencil adds is the instruction to scan them at all, every turn, including the slots beside walls you placed, which are the ones players forget to reuse. Four checks, ten seconds, and you have looked almost everywhere worth looking — which is more than the player staring at the whole grid hoping something jumps out will manage.

The second scan: walk their path backwards

There is a sharper scan, and the engine switches to it in one specific situation — when its opponent has no walls left to answer with. Two things narrow at once there. Its own pawn moves stop being every legal step and become only steps along a shortest path, and its walls stop including anything that merely supports its own route: what is left is walls that interfere with the opponent's.

The way it builds that interference list is the part worth learning. It maps every shortest path the opponent has, walks backwards from every goal-row square sitting at the minimum distance, and for each step along the way marks the one or two wall slots that would sever that step. To that it adds the ring around the opponent's pawn — the same sixteen slots as before, included whether or not they touch a route — and then keeps what is legal. So the list is the race, plus the pawn's immediate surroundings, and nothing else on the board.

You can run the backward walk by hand, and it fixes the most common wasted wall in Quoridor. Trace your opponent's shortest route back from their goal row. Each step of it can be cut by only a couple of placements, so instead of hunting the whole board for something that "looks blocking", you have a short, exact list of the walls that lengthen their path at all. Everything off that list adds zero this turn, however threatening it looks sitting on the board.

The critical detail is the plural: every shortest path, not the one you happened to trace. Cut a step that only one of several equal-length routes uses and the route re-forms elsewhere at the same cost — the diverting- versus-lengthening distinction that Traps and Cages is built on. The scan is only worth running if you finish it, which means checking whether the step you are about to cut is shared by all the minimum-length routes or belongs to just one of them. Tempo and the Race is where the counting itself lives.

What it finds, and what it never looks at

Everything that survives the scan is filtered by one more condition: the placement has to leave both pawns a route to their goal. That is the no-sealing rule from the rules, applied as a filter on what the bot will even consider rather than as an afterthought at the end.

So the moves this tier finds reliably are the ones its stencil is shaped around — walls that punish a pawn the moment it commits to a lane, second and third walls that extend a structure either of you started, edge-anchored walls that cost it one wall and you several squares. Leave a loose pawn move next to your own half-built wall and it will find the slot that turns your work against you.

What it never looks at is a wall standing alone in open ground: one that touches no existing wall, sits in neither pawn's ring, and is not a horizontal wall in an outer column. A placement like that is not scored badly by the search, it is not scored at all, because it was never made a candidate. And the same stencil governs the walls it imagines opponents playing inside its playouts, so a wall of that shape is missing from its picture of the future as well as from its own list of moves.

Its characteristic weakness follows from the shape of that list rather than from any measurement. Every wall placed seeds a fresh neighbourhood, so the middlegame list is drawn from more sources than the opening's — while the playout allowance is not a fixed number at this tier but one resolved per position (how a position's complexity sets the budget), and the quantities that push it high are exactly the ones that fall as walls come off the board. The two curves run opposite ways. On a clean board the list is short and the sampling is deep; by the crowded middlegame the list is drawn from every structure on the board and the allowance is heading the other direction, which is where two candidates of genuinely similar value get separated on the thinnest evidence they will ever be separated on.

How to beat Oracle

Do not try to out-race it on a clean board. A sparse position is the shape its budget covers best, and once its own walls are gone it stops deliberating and simply runs — advanced covers that shortcut, which applies from that tier upward. Open races are where it is strongest relative to you.

Keep one wall in hand for as long as it is worth keeping. The moment you place your last one, the search changes shape: from that point on it stops generating walls that merely support its own route and generates only walls that cut yours, and its pawn branches narrow to steps along a shortest path. While you still hold a wall, part of every expansion goes on defensive placements — the part of its list you are not being hurt by. That is the one lever here that acts on the mechanism rather than on the position, and a marginal wall is worth more in your hand against this tier than it would be against a human.

Re-run the ring scan after every one of its pawn moves. The region it watches most closely travels with the pawns. The corollary matters more: the moment your pawn steps out of a ring it was sheltering in, the slot that punishes you has just entered its list — so check what your own step exposes before you take it, not after it has been punished.

Do the backward walk before you spend anything. Against this tier a wall that misses the race is not a small loss. It is a wall gone, a turn gone, and a fresh neighbourhood of candidates handed to an opponent that will scan it next move. Whether the wall you found clears the bar for spending at all is the framework's question; this page only gets you to the short list.

Who this tier is for

Play Oracle if your walls are already sound when you find them and the problem is finding them at all. It punishes a miss quickly enough to teach, and it does not hand out the free walls the tier below hands out. If you are winning here comfortably, master is the next rung; if the losses are one-sided, drop back to advanced for a while. The current roster and its ratings live on the Bots page, and the Glossary defines any term here that was new.

Playing bots is part of the free game; the optional paid plans add coaching and analysis tools on top of it, listed on Pricing.