Quoridor Openings

Quoridor has no development phase. There are no pieces to bring out, no structures to build, nothing that is worth doing now because it will be worth more later. Every move in the opening is measured in exactly the same currency as every move in the endgame: distance to your goal, and walls in your hand. That makes the opening unusually easy to reason about and unusually easy to mishandle, because there is nothing to do except the one thing that works, and doing it feels like doing nothing.

The beginner's version of this advice — walk forward, do not spend walls yet — is on How to Play. What follows is the arithmetic underneath it, and the one place in the opening where the arithmetic turns against you.

Why straight ahead is the default

On an empty nine-by-nine board, every square in a row is exactly as far from your goal edge as every other square in that row. Your goal is a whole edge rather than a square, so distance is just the number of rows between you and the far side — eight at the start — and your column has nothing to do with it. A pawn on the edge file and a pawn in the centre are equally far from home. Tempo and the Race sets out that distance model and how to count it once walls start bending routes.

Take it as a premise and the opening settles itself. A column change on open ground costs exactly one tempo and buys nothing, because your distance is unchanged. A wall costs a tempo as well, and one of your ten walls on top of it. The straight step forward is the only move available that reduces your own count, so it is the mainline by elimination rather than by taste.

The pull to change columns arrives around move three or four, when a wall goes down and you want to angle around it early. It is worth paying then and not before. Once walls are on the board a lateral step can put you onto a genuinely shorter route, and at that point it is not a loss at all but the cheapest way onto a better path; in the first few moves there is no shorter route to move onto, so the payment buys nothing. Exactly one column change escapes the charge: the diagonal jump moves you a row forward and a column across in the same turn. It is a fallback you cannot choose rather than a move you can plan — The Complete Rules has the conditions. The separate question of why the centre file in particular is the one to hold is answered on How to Play.

The mirror, and why it does not stay symmetric

The most common opening in the game is both players marching straight down the middle at each other. It looks like a stalemate of ideas — perfect symmetry, no information, nobody committing — and it is easy to assume it resolves in favour of the player who moves first, since they are one step ahead the whole way down.

It does not. Walk it out. Both pawns advance three times and stand on the centre column with a single empty square between them, and the first player is on move. If they step into that square the pawns are adjacent, and the second player is entitled to jump straight over — landing on the far side, two rows closer, in a single move.

That jump gains a full tempo, and a full tempo is precisely the first player's entire advantage. Trade it away and the race inverts: the second player arrives home one move ahead of a first player who did nothing wrong except walk forward eight times. The pure mirror is not a draw waiting to be broken. It is a slow loss for the player who starts it.

The meeting square

This is the opening's one genuinely sharp moment, and it is the whole reason the first real wall of a well-played game appears here rather than on move one. Both pawns are five rows from home, the gap between them is one square, and you cannot pass in Quoridor, so the player on move has to do something.

Three of the things they can do cost exactly one tempo each. Stepping in concedes the jump. Stepping sideways keeps the distance and spends the turn. Placing a wall spends the turn as well. Because the tempo goes either way it is already sunk, and the wall is no longer competing against a free forward step — it is competing against two moves that are worth nothing. That drops the bar by exactly one. The usual requirement, that a wall add two squares more to their route than it adds to yours (Wall Economy), becomes a requirement to add one. Check it: a wall with k − j = 1 leaves you five from home and them six, with them to move, and that is still a won race. Stepping in leaves you four and them three with you to move, which is lost. Sidling leaves the distances level with them to move, which is also lost.

There is a fourth idea everyone reaches for here, and at this position the move it asks for does not exist. Since the trouble is the jump, why not place a wall behind your own pawn and deny it? A wall on the far side of your pawn does downgrade a straight jump to the diagonal, and the diagonal gains the jumper one row instead of two. Head-on, you cannot place that wall. The straight jump you want to block crosses the edge between the contact square and the square you stepped from, and that is the same edge your own step has to cross: any wall that stops the jump stops you first. The defensive wall behind your own pawn is a real resource in Quoridor, but only where contact will be made from the side; straight down a shared column it is unavailable to the player who has to close the gap. Worth noticing too is that it would be a thin deal even if it were legal — a wall placed purely to block a jump adds nothing to their route, so it costs the same tempo that stepping in costs and only buys back the one the jump would have taken.

So it has to be an ordinary blocking wall, and the useful surprise is where that wall goes. Not next to the pawns, where the two routes are on top of each other and anything you build gets charged to both of you, but two or three rows short of your opponent's goal edge — ground you crossed on the way up and will not use again. Your remaining route runs from row four to row nine; theirs runs from row six to row one. A wall placed low is billed almost entirely to them. The general form of the wall-or-walk decision is Wall or Advance; what is specific to this position is only that the threshold is lower and the good ground is behind you.

Early walls that pay, and early walls that donate

That is also the structural reason opening walls are expensive, and it is not the reason usually given. Before the two pawns pass each other their remaining routes overlap heavily — both are still crossing the middle of the board, and your goal is the row your opponent started on — so a wall aimed at them will very often stand in your own way too, and your own detour is subtracted at full weight. After they pass, most of that overlap is gone. Most, not all: a structure ahead of you can make your own shortest route run backwards into ground you have already crossed, and a wall sitting there is billed to you after all. The crossing point, not the move number, is what makes walls cheap.

An early wall therefore has to find its asymmetry somewhere else, and there are three places it can. The first is a board edge, which is the only help that lets a lone two-square wall reach a yield of two on open ground — Wall or Advance derives the shoulder count that shows why. The second is a wall that answers a wall: you have both spent a tempo and a wall, so the count between you is unchanged, and you have not fallen behind by declining to respond. The third is a wall that commits your opponent to a column you intend to attack later, which is an investment rather than a purchase, and it only pays if the follow-up wall actually arrives — the structures that cash it in are in Traps and Cages.

The donations have recognisable shapes. A wall placed far from both pawns to "build something" is routed around for nothing, because a route with eight other columns available always has somewhere to go. A wall dropped in front of an opponent who has not committed to anything is nearly as bad: they shift a file, and you have paid a turn and a permanent piece of your supply for a square or two. And the wall that lengthens your own route by as much as it lengthens theirs is commonest of all in the opening, for the overlap reason above. Wall Economy prices all three, and the Glossary has short definitions for any term here that was new.

What this site's engine plays out of book

This site's MCTS engine consults a small hand-coded opening book before it runs any search at all, and only inside a window of the first six plies — three moves for each side (engine-v3.ts:86,243-250; the default path uses the hand-coded book rather than the harvested one, opening.ts:48). Past that window the book is never consulted again. Inside it the book plays the centre march: straight forward, one square at a time, for both sides (book.ts:112-127). Entries carry weights and a lookup returns the highest-weight legal entry (book.ts:27-39); early wall alternatives are stored at those same positions at much lower weight, so what actually comes out is the march. A separate rule handles each pawn's very first move — it takes the shortest-path step and plays it directly, but only when that step leaves the column unchanged, and otherwise falls through to search (overrides.ts:63-73).

Two things about that are worth noting as a player. The scripted window closes exactly at the meeting square: the last position the book can serve is ply five, which leaves the pawns on the centre column with one square between them, so the sharp decision at ply six is the first one the engine has to think about (engine-v3.ts:86,245). That is a reasonable place to stop trusting a script. And the book's prepared answer to an early wall is not a defensive step but another wall, reflected through the board — the two horizontal answers keep the file and mirror the row, while the two vertical answers flip both coordinates (book.ts:148-171). A fifth prepared reply exists in the source but is keyed seven plies deep, outside the window, so it can never actually fire (book.ts:172-185).

For the framing that ties tempo and terrain together, start at Strategy. For what the position becomes once the walls are gone and the opening is a distant memory, see Endgames.