Quoridor — the Rule That Holds It Up
Play Quoridor, and see why the no-blocking rule is the whole game: without it three walls would win outright, yet it refuses barely 1% of placements.
You are blue at the bottom, heading for the top row. Move one square, or spend a wall to lengthen your opponent’s route — you may never seal them in completely.
Without the no-blocking rule, three walls would win the game
The rule reads like a technicality: a wall may not be placed if it would leave either player with no path at all to their goal row. It is the only thing standing between Quoridor and a three-move win. Searching exhaustively for the fewest walls that would seal a pawn off, if the rule allowed it:
| A pawn in… | Walls needed to seal it |
|---|---|
| a corner | 2 |
| the middle of its back row — where the game starts | 3 |
| the centre | 4 |
Each player holds 10 walls. Three of them, played immediately, would end the game before anyone had moved a pawn. The rule is not a technicality — it is the entire reason there is a game to play.
The two walls that trap a corner pawn are not the two across its exits, incidentally — those would cross each other and be illegal anyway. The real seal pens it into a two-square pocket: one wall across the top of both squares, one closing the far end.
And yet it almost never fires
What share of otherwise-legal placements does the rule actually refuse, as walls pile up? Measured over four hundred random boards at each stage:
| Walls already down | Placements the rule refuses | |
|---|---|---|
| 0 | 0.00% | |
| 4 | 0.02% | |
| 8 | 0.14% | |
| 12 | 0.63% | |
| 16 | 1.44% |
On an empty board the rule cannot fire at all. Even late in a crowded game, roughly one placement in seventy is refused. Play a hundred games and you might never see it happen.
So the rule the whole game rests on is one most players have never watched take effect — load-bearing and nearly invisible at the same time, which is an unusual and rather satisfying thing for a rule to be.
How to use
- Move your pawn one square towards the far side, or place a wall.
- Walls are two squares long and may not cross or overlap.
- A wall that would seal either player in is refused.
- You have ten walls; the shortest route counter shows who is ahead.
Frequently asked questions
What is the no-blocking rule in Quoridor?
A wall may not be placed if it would leave either player with no path at all to their goal row. You may lengthen someone journey as much as you like, but never close it off entirely.
Why does Quoridor need that rule?
Because without it the game would be over in three moves. Searching exhaustively, two walls are enough to seal a pawn in a corner, three for a pawn on the middle of its back row where the game actually starts, and four for one in the centre. Each player holds ten walls.
How often does the blocking rule actually stop a placement?
Almost never. On an empty board it cannot fire at all, and even with sixteen walls down it refuses only about 1.4% of otherwise-legal placements. Play a hundred games and you might never watch it take effect, which is a strange property for the rule the whole game rests on.
How do you seal a pawn in a corner with two walls?
Not with the two walls across its exits — those would cross each other and be illegal anyway. The real seal pens the pawn into a two-square pocket: one wall across the top of both squares, and a second closing the far end.
Can pawns jump over each other in Quoridor?
Yes. If your opponent stands on an adjacent square you may jump straight over them to the square behind. If that square is walled off or off the board, you step diagonally past instead.
How long are Quoridor walls?
Two squares. They sit in the grooves between squares, may not overlap another wall along their length, and may not cross one lying the other way at the same intersection.
What is the aim of Quoridor?
To get your pawn to any square on the far side of the board. You start facing each other on opposite back rows, and every wall you spend is one you cannot spend later, so the race and the blocking trade off against each other.
Does this send anything anywhere?
No. The game and the opponent both run entirely in your browser.
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