Quoridor
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. Rules of the game. 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 that square is not accessible (e.g., off the edge or the board or blocked by a third pawn or a wall), 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. Though it can be played with 3 players, it's advised against. Since the 3rd player doesn't have player on the opposite side, they have an advantage. History. Quoridor is based on an earlier game, namely Blockade (also known as "Cul-de-sac"), invented by Philip Slater in 1975. Mirko Marchesi, a well-known famous board game designer, created another version of this game, called "Pinko Pallino", which was published  in 1995 by Epta games. "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. After initial release, the game aroused interest. By 1997, the five biggest game companies in the world (including Gigamic) American bought the copyright of this game and released it to the world. As a result, Quoridor quickly became popular all over the world. Many European educational institutions (e.g. MindLab) have also selected Quoridor as teaching aids and brought them into the classroom. History of the Notations Since there isn't  a notation provided by Gigamic, there are a lot of types of notations used in the history of quoridor. They are listed below in chronological order. Criticism Because there are lots of notations some people like some over the others. NESW notation relatively hard to follow because if one doesn't know the pawns location, it must be traced again from the starting position. Glendenning's notation is acceptable but some don't like the fact that the board is always upside down. Notation. Board. Each square is denoted using algebraic notation. Pawns. Starting positions. Two players: Four players: Moves . Each pawn move is defined by the new square occupied by the pawn. Walls. Every wall touches four squares. A wall move is denoted by the closest square to a1, with a horizontal h or vertical v orientation. Formatting. A game or series of moves is generally written in one of two ways. Moves may be interspersed with commentary (annotations). When the game score resumes with "player 2", "player 3" or "player 4"’s move, an ellipsis (...) fills the position of "player 1"’s move, for example: Defined game positions. A Forsyth–Edwards Notation-like record can define a particular  game position: codice_5 <nowiki>*</nowiki>Four player only. Two player example. codice_6 Four player example. codice_7 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 has less than 3 pieces. Opening. In this phase both players make relatively long-term plans. 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 uncommon and uses 2 or more wall moves before ones pawn reaches e4 or e6. 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 (codice_8 and codice_9). 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: codice_10 . This  opening is attributed to Dr. Scott Reed (Edinburgh, UK). Students of the University of Edinburgh have studied the opening in an AI 2021 course and discovered that it is not a particularly strong opening. The analysis was done using an implementation of the Minimax algorithm and different heuristics. Shiller opening: Both players advance their pawns three times (codice_11). Then the first player places one wall vertically in the column closest to him (codice_12, codice_13, codice_14, or codice_15), 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 (codice_16), one of the players starts building a stonewall with codice_17 or codice_18. If the first player starts the stonewall the idea is codice_19 (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. codice_20) 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 (codice_11). then the first player places one wall horizontally behind their pawn (codice_22). Next turn the first player places their second fence next to their first fence (codice_23) and creates a wall behind them. In their third and fourth turns they places their fences perpendicular to their previous fences (codice_24 and codice_25). 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 (codice_11) and the first player plays codice_14. There are 2 options for the second player: codice_28 (mirrored variation) or codice_29 (symmetrical variation). Gap opening: After both players advance their pawns three times (codice_11) The Sidewall: Both players advance their pawns (codice_36). 1st player places a wall next to 2nd players pawn codice_37. The purpose of this strategy is to create two paths, one that continues to move straight ahead, and the second path is to retreat and detour to the other side. Obviously route 1 would be closer to the destination, so  second player blocks the shorter path with codice_38. This reaction from second player is considered bad because first player can continue to put walls in the way. (i.e. codice_39) The aim of the strategy is to create redundant moves for the second player in a direction that will inevitably be blocked in the future. Proper counter-play: Second players' move is codice_40. With this move a horizontal wall on the left side is placed, exactly 2 spaces from the edge of the board. The goal is to create up to 3 different wall layouts to block the detour to your  left. Quick Box variation: codice_41 Shatranj Opening: Named after an online player, Shatranj. The game starts with the move codice_42, which is considered as an unorthodox opening. The goal is to canalize ones path to the last rank. The move codice_43 has the same idea in mind but flipped. 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. 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 (more) complex Shiller opening and Gap opening are the perfect example for this strategy. Spatial advantage The space each player has can give them advantages. 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 spatial  advantage and the second player can force the first player go backwards. Therefore, this is considered as a bad move. Derivations of the game. There are different board sizes of the game: Pocket < Mini < Standard < Deluxe < Giant Quoridor Kid: In 2004 Gigamic released the Children's version. The number of squares on the board is 7x7 squares, which is one size smaller than the regular version, and the number of walls is 16 (for 2 players, each player gets 8 walls; for 4 players, 4 each). Other rules are the same. The board is round and  yellow, where classic figures are replaced with a mice. The top is in the shape of a mouse, and a cheese top is placed in the back of the row on the other side, adding the theme of "a mouse is trying to reach the cheese." Awards. In 1997, the game was awarded the Mensa Select, a prize given to five board games by the American Mensa every year. It was also by Games Magazine named "Game of the Year 1998". The Children's version of the game "Quoridor Kid" won 4 awards. Competitions. Mindsports Olympiad: As part of the  Mindsports Olympiad 2020, Quoridor was played. Pentamind World Championship: In 2018, Quoridor was played among 5 games in the Pentamind tournament. MINDLAB: Kids between the ages 9-12 can participate in this yearly tournament. 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. Mathematical complexity of the game. Quoridor has a relatively large complexity, the number of valid positions in the game (state space) is formula_1. The number of nodes on the game tree respectively is formula_1 and formula_3. In each position, there are an average of formula_4 valid moves. For comparison these numbers are in chess formula_5, formula_6 and formula_7, respectively. In the starting state there are formula_8 positions of valid walls and formula_9 moves so the game has a total of formula_10 branches. There are a total of formula_11 possible positions of the game.