Quoridor

Quoridor
	white and black pawn near walls
Genres	Board game; Abstract strategy game
Players	2 or 4
Setup time	< 1 minute
Playing time	15 - 25 minutes
Chance	None
Skills	Deduction

Quoridor is a 2 or 4-player intuitive strategy game designed by Mirko Marchesi and published by Gigamic Games. Quoridor received the Mensa Mind Game award in 1997 and the Game Of The Year in the USA, France, Canada and Belgium.^[1]

Rules of the game

The starting position for a 4-player game. In a 2 player game, green and orange are omitted.

Quoridor is played on a game board of 81 square spaces (9x9). Each player is represented by a pawn which begins at the center space of one edge of the board (in a two-player game, the pawns begin opposite each other). The objective is to be the first player to move their pawn to any space on the opposite side of the game board from which it begins.

The distinguishing characteristic of Quoridor is its twenty walls. Walls are flat two-space-wide pieces which can be placed in the groove that runs between the spaces. Walls block the path of all pawns, which must go around them. The walls are divided equally among the players at the start of the game, and once placed, cannot be moved or removed. On a turn, a player may either move their pawn, or, if possible, place a wall.

Pawns can be moved to any space at a right angle (but not diagonally). If adjacent to another pawn, the pawn may jump over that pawn. If an adjacent pawn has a third pawn or a wall on the other side of it, the player may move to either space that is immediately adjacent (left or right) to the first pawn. Multiple pawns may not be jumped. Walls may not be jumped, including when moving laterally due to a pawn or wall being behind a jumped pawn.

Walls can be placed directly between two spaces, in any groove not already occupied by a wall. However, a wall may not be placed which cuts off the only remaining path of any pawn to the side of the board it must reach.

History

Quoridor is also based on an earlier game invented by Philip Slater, Blockade, in 1975. Marchesi also created another version of this game, called Pinko Pallino, which was published in 1995 by Epta. Pinko Pallino was only for two players and was played on an 11×11 game board with a total of 42 walls and slightly different rules.^[2]

History of the Notation(s): There isn't a notation provided by Gigamic. In 2005, Lisa Glendenning's thesis^[3] proposed a reasonable notation, though it lacks consistency. The notation changes depends of where one looks. In 2014, Kevin Lamenzo^[4] fixed this ambiguity by providing a notation similar to algebraic chess notation.

Notation

Each square gets a unique letter-number designation. Columns are labeled a through i from player 1's left and rows are numbered 1 through 9 from player 2's side to player 1's side. From player 1's perspective the far left square is labeled as a1. A move is recorded as the column followed by the row as in e2. For example: player 1's pawn starts on e1 and player 2's pawn starts on e9. See the image here.

Each pawn move is defined by the new square occupied by the pawn. For example, if player 1 moves from square e1 to e2, player 1’s move is denoted as e2.

Each wall move is defined by the square directly to the northwest of the wall center from player 1's perspective, as well as an orientation designation. For example: a vertical wall between columns e and f and spanning rows 3 and 4 would be given the designation e3v.

Every wall touches four squares. A wall move is denoted by the closest square to a1, and the direction (horizontal or vertical).

Games are notated as they are in chess: by the move number, player 1's move, and player 2's move. For example, a game might start with each player moving their pawn towards the center:

1. e2 e8

2. e3 e7

Then the players might add walls to lengthen the other player's path:

3. e6h e3h

and the game continues.

4. __ __

Forsyth–Edwards Notation (FEN) can be adapted for describing a particular board position of Quoridor. Optimally, it follows the pattern below.

H:[horizontal walls] / V:[vertical walls] / [position of player pawns (from 1 to 2 (or 4))] / [number of walls in the players hands (from 1 to 2 or 4)] / [whose turn it is]

There is an example from a 2 player game:

H:d4f4e7 / V:a2a8 / e4 e6 / 7 8 / 2

Game Phases

A game can be divided into 3 phases, namely opening, middle game, and endgame. The first 5-7 moves can be considered as the opening phase. A typical mid-game consist ~10 moves. The endgame starts when one of the players have less than 3 pieces.

Opening

In this phase both players make relatively long-term plans.

Middle Game

In the mid-game both players tries to maximize the possible opponents paths (most commonly 2) and close their back. Closing the back prevents the possibility of making a roundabout. Not closing the back mostly results in a loss.

Endgame

When both of the players uses all walls in the hand, the game can be ended (upon agreement) by simply counting the shortest path length for both players.

Strategies

Between games common patterns can be seen. The openings can be divided into two categories, orthodox and unorthodox openings. In orthodox openings the goal is to advance ones pawn to the center. Unorthodox openings are not common and uses 2 or more wall moves before ones pawn reaches e4 or e6.

Openings

Reed opening: This opening consists in placing, during the first two moves of the game, two walls on the third row in front of the opponent with a single gap in the middle (c3h and f3h). A counter-strategy to the Reed opening is to place two horizontal walls on the third row, one at the extreme left and one at the extreme right, which effectively reduces both players' path counts to one. The game would start as follows: 1.c3h a3h 2.f3h h3h . This opening is attributed to Dr. Scott Reed (Edinburgh, UK), a known military strategist and frequent player.

Shiller opening: Both players advance their pawns three times (1.e2 e8 2.e3 e7 3.e4 e6). Then the first player places one wall vertically in the column closest to him (4.c3v, 4.d3v, 4.e3v, or 4.f3v), providing two paths for the other player while maintaining just one path for herself. The Shiller opening implements the strategy of maximizing the opponent's path count and of minimizing one's own path count. This opening is attributed to Larry Shiller, who is also known as the Voice of Backgammon.

The Stonewall: After both players advance their pawns two times (1.e2 e8 2.e3 e7), one of the players starts building a stonewall with 3.d2h __ or 3. __ g7h. If the first player starts the stonewall the idea is 3.d2h __ 4.f2h __ 5.b2h __ 6.h2v __ (or mirrored version). The goal is to push back the opponents if they advances their pawn further. A common idea is to close the back rank with a vertical wall. (i.e. e1v) So, the opponent cannot make the Stonewall player to go back all the way behind the wall.

Ala opening: Both players advance their pawns three times (1.e2 e8 2.e3 e7 3.e4 e6). then the first player places one wall horizontally behind their pawn (d5h). Next turn the first player places their second fence next to their first fence (f5h) and creates a wall behind them. In their third and fourth turns they places their fences perpendicular to their previous fences (c4v and g4v). By this opening the first player provides two paths at the corners of the board for the other player while maintaining one easy path for themselves.

Standard Opening: Both players advance their pawns three times (1.e2 e8 2.e3 e7 3.e4 e6) and the first player plays 4.e3v. There are 2 options for the second player: 4.__ e6v (mirrored variation) or 4.__ d6v (symmetrical variation).

Rush Variation: 4.d5v e6h
- the goal is to create a big reverse box like shape: 5.e4h f6 6.g4h f5 7. h5v g5
- counter play = ?

Gap opening: After both players advance their pawns three times (1.e2 e8 2.e3 e7 3.e4 e6)

mainline: 5.__ g6h
Anti-gap: 5.__ b3h
double-gap:

The Sidewall: Both players advance their pawns (1.e2 e8). 1st player places a wall next to 2nd players pawn 2.d7v

possible continuation: 2.__ f8 (this reaction from black is considered as bad because: 3.e6h g8 4.g6h h8 5.h7v 5. __ h9 6.h4h i9 7.f4h i8 8.b5h i7 9.a6v c6h).

proper counter play: 2.__ c7h (beginning to close the side of the board)
Quick Box variation: 2.__d1h

Shatranj Opening: Named after an online player, Shatranj. The game starts with the move 1. d1v, which is considered as an unorthodox opening. The goal is to canalize ones path to the last rank. The move 1. e1v has the same idea in mind but flipped.

Lee Variation: The first player advances once before placing a vertical wall immediately to one side, connecting to the back wall 1.e1v. Usually, the opponent will then "help" to build a winding path for the player (ie. 1.__ c2h 2.d2 b2h 3.c2 a2v note that at this position 4.c1 is necessary to prevent b1h which lengthens the path 1 to 3 moves). At a critical moment the first player can slam the door by playing the moves f2h and h2h (the Lee Switcharoo), sending the opponent up and around the path he helped create. If the opponent elects not to participate in building the maze, trivially the player can execute a Samson Bowl^[?].

Mirroring

Mirroring can be a powerful strategy if the opponent doesn't know how to respond.

Walls

The walls are the used to direct the game. Their value increases as the games progresses.

The walls become more important in the endgame. If there is a major difference in the number of the walls in hand, generally the player with more walls wins the game. Nonetheless, if the movable area lacks space, this may result in a loss because if none of the moves increases the path length of the opponents' they become useless.

Leaving the position complex(er)

Shiller opening and Gap opening are the perfect example for this strategy.

Spacial advantage

Sidestepping: Within the first 3 moves the first player moves their pawn horizontally left or right, giving the opponent the opportunity to move forward or place the first wall. The goal is to make a corridor to make the opponent go backwards. However, by doing so, the first player loses their spacial advantage and the second player can force the first player go backwards. Therefore, this is considered as a bad move.

Misc

Time control

In competition, Quoridor games are played with a time control. If a player's time runs out before the game is completed, the game is automatically lost.

Time can be controlled controlled using a chess clock that has two displays, one for each player's remaining time. Analog chess clocks have been largely replaced by digital clocks, which allow for time controls with increments.

References

^ "Mensa Mind Games Winners Available Now at Barnes & Noble" (Press release). American Mensa Ltd. December 15, 2000. Archived from the original on 2008-05-03.
^ Pinko Pallino at BoardGameGeek
^ Glendenning, Lisa (May 2005). Mastering Quoridor (PDF). Computer Science (B.Sc. thesis). University of New Mexico. S2CID 18564930.
^ "User lameK". Mathematics Stack Exchange. Retrieved 2021-02-01.