Hexagonia

Hexagonia is one of the first two hexagonal Chess in the literature^(*), c.1860. It was published by Jaques & Son, and its author is possibly J. W. Smith [1].

A new game for two players, played on a board divided into hexagons. Each player had fourteen pieces, representing infantry, cavalry, and artillery, and one principal piece, the King. The various pieces have certain moves on the board analogous to those of a real army, and the game is won by the player who first succeeds in placing his King (without liability to capture) on the central hexagon.

In Cazaux and Knowlton's A World of Chess, [2], the game is described. Each army is composed of one King, two Cannons, four Knights and eight Pawns. However, it is not known how the pieces moved. The book also refers that this game appears to have been invented, some years earlier, in New Zealand.

The book also includes the following quote about the game (page 377):

The last game which we have to notice is undoubtedly the most scientific of the lot, and somewhat resembles chess. It is called" Hexagonia," and is published by Mr. Jaques, of Hatton Garden. The board is in the shape of a hexagon, and contains hexagonal figures, painted red, blue, or white. Two play at this game. To each combatant is given a king, four knights, and two pieces in the shape of cannon, called artillery, and eight pawns, or pieces of infantry. Each piece has a different mode of moving, and can capture an enemy; and the object is to place the king on a gold square in the centre of the board. This sovereign can never be taken, but can be checked as in chess. The reader will gather fom this that much head-work and tact can be brought into play in this game, and that a knowledge of chess is often highly advantageous. We have endeavoured somewhat briefly to state the chief points of the new in-door games. We feel sure that they are varied enough to please the tastes of everybody, and we sincerely hope that our youngfiends may enjoy many a pleasant hour in the enjoyment of the intricate manoeuvres that these games involve" (Edmund Routledge, "The New Winter In-door Games," Routledge's Every Boy's Annual, an Entertaining Miscellany of Original Literature, George Routledge and Sons, 1866, New York, p. 35)

Pritchard's book, [3], also refers to the game: 

Hexagonia (Proprietary game, John Jaques and Son). Published in 1860 according to van der Linde, and allegedly awarded two prize medals in 1862, the game was in fact published on 23 September 1864 and registered at Stationers’ Hall the following January. 127-cell hexagonal board, central cell distinguished. Each player has 1 x King, 2 x Cannon (artillery), 4 x Knight (cavalry), 8 x Pawn (infantry). The moves of the pieces are not recorded. The object was to get one’s K safely to the central cell.

About the piece's moves. The King, Knight and Pawn moves are directly translated to hexagonal boards. The Cannon however could have been like a Rook, sliding rows of hexes, or like Bishops sliding thru diagonals, which might explain the use of three colors in the Hexagonia board (since it makes it easier to follow these diagonals). Both hypotheses for the Cannon would be stronger than the Knight's, which is compatible with their smaller number (two) compared to the Knights' (four). However, this is just speculation.

Since the game's goal is not to capture or stalemate the enemy King, it's arguably not a chess variant, but most of Chess themes are here, nonetheless. The first known hexagonal Chess with checkmate was 1910's Mars by M. van Leeuwen and published by F. H. Ayres.
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(*) the other early Hexagonal Chess (also without checkmate) was designed by Thomas Hanmer Croughton, c.1853.

[1] Michael Thompson, Hexagonia, https://michaelthomson.org/game/hexagonia
[2] Jean-Louis Cazaux, Rick Knowlton - A World of Chess (2017)
[3] David Pritchard's The Classified Encyclopedia of Chess Variants (2007)

The commercial offsprings of Chess: Ploy

Ploy, aka Imperium, is a 1970 game by Frank Thibault, published by 3M among other companies. 

The initial setup:

The rules by Mats Winther from his Zillions implementation:

The goal is to capture the enemy Commander, or reduce the opponent army to a single Commander. Each piece has an indicator which determines at which directions the piece can move. This can be altered by rotating the piece 45 degrees, left or right (a direction move). Rotating the piece costs a move.

Each player has three Shields, five Probes, six Lances, and one Commander. The Shield moves one step and has only one movement freedom at any time. The Probe slides two steps and has two freedoms. The Lance slides three steps and has three freedoms. The Commander has four, but can only move one step.

A player must either make a direction move or a motion move. The three Shields are the only pieces that can perform a direction move immediately after a motion move. Capture occurs by displacement

Winther also includes some tactical advice:

This game seldom ends in a draw. It is sometimes worthwhile to sacrifice material if you can gain an attack on the Commander. When the pieces become scarce, the Commander is more vulnerable to attack. As it can only move four ways, it cannot easily escape. The Lance with the three forward directions is especially suited to attacking the Commander. Remember that you can also win by capturing all enemy pieces except the Commander.

The game can also be played with Ludii.

The official rules:

Here is a review of the game at Games & Puzzles #22:

The game was seriously promoted as shown by this full-page ad in The General magazine #13:

There is a similar game, but played on a hexagonal board, Michael Flynn's Omnigon (1998):

More information about this game at chessvariants.com.

The commercial offsprings of Chess: Smess

Smess, aka All The King's Men, is a 1970 game by Perry Grant and Reuben Klamer, published by Milton Bradley among others.

The game is played on this 7x8 board. Each army has twelve pieces: One King called Brain, four Numskulls, and seven Ninnys. Initially, the two Brains are placed at d1 and d8. Each Brain has two Numskulls at each side, and the seven Ninnys occupy the second row (just like Chess pawns).

The rules:

• On her turn, each player moves one friendly piece in a direction printed on its current standing square.
• Brains and Ninnys move only one square per turn,
• A Numskull can move in a straight line as many empty squares as possible
  
• Nb: only the initial standing square determines the possible moving directions
  
• Captures are by replacement (and not mandatory, just like in Chess).
• A Ninny that reaches an initial square of an enemy Numbskull is promoted to a previously captured Numbskull (if there's no Numbskull captured, the promotion does not happen).
  
• Wins the player that captures the enemy Brain. The game is a draw if only the two Brains remain on board.
  

The game was also known as Take the Brain. There's a review of it in Abstract Games Magazine #9.

The commercial offsprings of Chess: Wendo

FIDE Chess is the most played abstract game in the Western hemisphere. It is not unexpected that publishers try to use this fact to create and promote their own commercial Chess-inspired games. Modern games like Kamisado, Arimaa, and Onitama are examples of this trend.

This is the first post on a series that describes some older Chess-like games.

Wendo is a 1977 uncredited game, published by Brain Center. It is played on a 7x8 board (plus two home bases), and each player controls an army of ten pieces with exotic movements.

the initial setup

The pieces move as described in the tiles, and their move capabilities are described in next diagram:

The leftmost piece is the Hydra, which is the game's King. There's also a tile named Barrier. 

• On his turn, the player moves one friendly piece to an empty square, or rotates it, or even flips it over (the pieces are transparent).
• Pieces can move over friendly pieces, including the Barrier.
• Pieces can also move over the enemy Barrier if it is unprotected.
• A Barrier is protected if it is in the movement range of a friendly piece
  
• Captures are by replacement. The exception is the Barrier that cannot be captured.
• Barriers cannot move but can be pushed by friendly pieces. The push happens if the Barrier is on the way of the moving piece, and all the intervening squares are empty. The Barrier will stop at the next square, after the piece's final square.
• When a piece reaches the last row, the piece can optionally be promoted by being replaced with any piece previously captured. The promoted piece is placed with the direction the player prefers. This must be done at the turn the piece moves into the last row.
  
• A player wins by capturing the enemy Hydra, or by capturing all its army (except, of course, the Barrier).
  

Tic-Tac-Toe redux

In December 1985, the french magazine Science & Vie #819 listed several variants to be played on the standard 3x3 board of Tic-Tac-Toe. 

Here are some:

• Decentra: the first player cannot play at the central square. Does the second player wins by playing himself there?
• Misera or Toe-Tac-Tic: this is the misère variant, the one that makes a 3 in-a-row loses
• Doulima: each player must place one, two or three pieces or either color on a given row or column; the last player to move wins
• Nullita: game is played normally, but one player wins if any 3 in-a-row is made (of either color), while the other player wins otherwise
• Toucha: the first player forced to place a piece touching one of their own on a horizontal or vertical side loses the game.
• Connecta: this is the opposite of Toucha, the first player placing an isolated piece (ie, not connected to any friendly pieces) loses (except for the first turn).

The article has even more variants:

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Another, older, variant of Tic-Tac-Toe is 1943's Tic-Tac-Tics by Henry Lewis which uses a score approach. The game is played on a 5x5 board, where each 3, 4 and 5 in-a-row scores an increasing amount of points:

  

Even with the central placement restriction for the first player, there still might be an advantage to start. One possible approach, simpler than the 'inning' system the rules propose, is to play just two games, where each player starts in one, and sum the two scores to decide the winner.

Bantu

Bantu is a 1955 uncredited game, published by Parker Brothers.

Bantu is a race game where players must traverse the following circular board:

 

Each player has four pieces labelled from 1 to 4, which determines each piece's moving range.

Games & Puzzles #68 reviewed the game and its rules:

 

Here's also a review from Games International #4,

 

Check the official rules. 

The game made the cover of Abstract Games Magazine #15.  Check also this blog post about the game.

Atchin

"Atchin, new amusing conquest game" is a game from the Netherlands published in 1874. The name Atchin refers to Aceh, a province in northern Sumatra (in Indonesia). The goal of the game is to protect or conquer the Kraton, the Sultan's palace.

The next rules are my interpretation of the ruleset written in the board (nb: I don't speak Dutch):

• The ten black pieces, the Indonesians, are placed in the red circles with a black dot. The nine blue pieces, the Dutch, are placed in the outer semicircle also marked with black dots.
• Black moves first. Black pieces move to an empty adjacent space over the red lines, while Blue pieces do the same but only across the black lines.
• If any piece (black or blue) lands on a Fort (Benting) it may capture an adjacent enemy piece by jumping (Checkers-like) over it (black pieces over the red lines, blue pieces over the black lines). 
• Black pieces can capture pieces on a Village (Kampong) by jumping over them along the red lines. This rule also applies to the red circles with white dots.
• Black wins by occupying all nine spaces in the inner circle around the Kraton. Blue wins by moving one piece from the inner circle to the interior of the Kraton.

There was a war launched by the Dutch at Aceh in 1873, the First Aceh Expedition, which probably was the event that gave the theme to this wargame.

The rules in Dutch (sorry for any typo):

VERKLARING VAN HET NIEUW VERMAKELIJK VEROVERING-SPEL.

Men bepaalt den prijs voor den inzet en stelt de schijven als volgt: De zwarte of Aschineezen aan weêrszijde der pot of Kraton op de roode cirkels, welke met een zwarte stip zijn geteekend, de blauwe of Nederlanders op de onderste halve cirkel waar de cirkeltjes met een zwarte stip zijn aangeduid. De zwarte speelt het eerst en zorgt dat hij het halfrond om de pot of Kraton bezet krijgt, en mag daarom in alle richtingen zetten, terwijl de blauwe alleen de zwarte lijnen volgen moet. Wanneer de blauwe of zwarte op een Benting of Fort staat. moet hij de nevenstaande van zijn tegenpartij slaan: doch de zwarte alleen in de richting der roode lijnen en de blauwe in de richting der zwarte lijnen*. Terwijl allen de zwarte naast een Kampong of Dorp staande, daarover heen mag springen in de richting der roode lijnen, doch alleen wanneer zij onbezet zijn; dit geldt ook voor de vijf roode cirkels met witte stip in het bovenste halfrond. Wanneer er slechts één blauwe in den pot of Kraton komt, dan heeft hij het spel gewonnen. Terwijl dezen het verloren heeft, als de zwarten de negen punten om den Kraton voor de toegang der blaauwen hebben afgesloten.

* Het slaan geschiedt even als bij het damspel.

Gimel

Gimel is a 1980 game by Manuel A. Widmaier, published at Bütehorn Spiele, and later at Hexagames.

It is played on a 8x18 board -- I suppose a shape emulating Senet's -- and each player has 24 pieces between three types:

• Eight scarabs or beetles (represented as disks) that move like chess Kings
• Eight bastets, i.e, the cat gods (as pyramids) that move as chess Knights or as a single 2-step orthogonally
• Eight horus pieces (as cylinders) each moving to any place on the perimeter of a 3x3 square centered in the moving piece (see picture below)

Initially the board is empty. On his turn, each player might do one of the following actions:

• Drop a friendly piece (still in reserve) on an empty square
• Move a friendly piece (already on board) to an empty square
• Capture an enemy piece by replacement
  

The goal is to score points by capturing enemy pieces: scarabs value 1 point, bastets 3 points, and each Horus values 6 points. If players have the same score, win the one with more pieces captured.

The game mixes the typical two phases of dropping the army, then moving. This can make it hard to plan ahead, since any new piece can appear at any place, anytime. Shogi has this mechanism but is much more controlled, because usually there are few pieces in reserve to drop, and they are achieved afterwards, as captures in the middle of the game. Not with Gimel!

Here's a positive review on Jeux et Strategie #2:

The review on Games & Puzzles #78 is less enthusiastic:

Pencil and paper games: Blocking

Another theme is pencil and paper games is blocking, i.e., as the game advances, less and less squares are available, until the stalemated player loses the game.

A well-known example is 1970's Snort by Simon Norton, aka Cats & Dogs. 

The rules: on an 8x8 grid, players take turns marking an empty square, provided that the square is not orthogonally adjacent to an adversary mark. The first player unable to move, loses the game.

To prevent mirror strategies, in the beginning the first player should play in the central 2x2 area, and the second player must play outside that area.

There's also a faster variant, called Obstruction, that includes diagonal adjacencies as illegal moves.

Slimetrail, designed by Bill Taylor in 1993, is also a pencil and paper game with a blocking theme. To recap, in Slimetrail each player has a home, each one staying in opposite corners. The snail mark starts at the middle of the board. Each player, on his turn, shades the snail mark, and places/marks the snail on an adjacent empty square. Wins the player that moves the snail into his home or stalemates the adversary.

Domineering (aka Stop-Gate, Crosscram) is another example. Designed by John Conway in 1976, the game is also played on a square grid, where each player marks two adjacent empty squares with a domino. One player marks vertical dominoes, while the other player marks horizontal dominoes. The first player to be stalemated loses (i.e., the last player to move wins).

Cram is a variant where both players can mark dominoes horizontally or vertically. It is what's called an impartial game in Combinatorial Game Theory. This means that Cram is just the game of Nim with other clothes (I mean, rules).

Chomp, by Frederik Schuh in 1952, and later by David Gale, is another example. The game is played on a rectangular grid. Each player on his turn selects an empty square, and shades all squares that form a rectangle between itself and the grid's bottom-right corner. The player that moves last loses the game.

Blue lost the match after move 11

Another example comes from JeuMok Plus. There are 24 shared 1x2x4 blocks. The game comes with a rulebook containing five different games (one is a NIM game, another is a Jenga), where the main game rules that players drop blocks in empty squares on a board, and each tile must be adjacent to at least another already on board. The board center cannot be used. The player that moves last wins the game.

Pencil and paper games: Improving Tic Tac Toe

Among the most well-known pencil and paper abstract games are Tic-Tac-Toe, Gomoku, and Dots'n'Boxes. Another famous game that can be played with a pen is Connect4 (but many families have bought this game anyway). 

Many connection games can be also played with pencil and paper, like Hex, TwixT or Bridgit. Of course, there are other famous games in this genre like Hangman or Battleship but, as usual, we'll stick here with the abstract ones.

In this post let's check some examples that improve the playability of Tic Tac Toe, one of the simplest abstract games.

An interesting version is Ultimate Tic Tac Toe and is played on a 9x9 grid of nine 3x3 areas (like in a Sudoku board). Each player makes a move on one of the nine mini-boards. But the next player must play at the board relative to the previous opponent's move. For eg, when a player plays at the upper-left corner, the next player must play at the upper-left 3x3 board. When a player makes a 3 in-a-row that mini-board belongs to her. If a move goes to again to that finished 3x3 board, the player can choose whatever open board she prefers. Wins the player that makes a 3 in-a-row of mini-boards (play online here). A similar game is 1976's Tri-o Tri-x.

The next variant is SOS. In this game, played on a square grid of size 3x3 or larger, players can write an S or a O on an empty square. Every time a player makes a orthogonal or diagonal row with the S-O-S sequence, he crosses it with his color and scores one point. The player with highest score wins.

Another variant is 3D Tic Tac Toe, played on a stack of four 4x4 boards (a 3x3x3 version is a trivial win for the first player). So, a player wins by making a 4 in-a-row using orthogonal or diagonal lines in all three dimensions. This can be represented in a page by drawing a line of four 4x4 boards, where the leftmost board is the bottom, and the rightmost is the top. This game was published in 1947 as Qubic:

One variant designed by Trevor Truran in 1981 for Games and Puzzles #81 is Knights and Crosses:

Here's another pen and pencil game called Order and Chaos by Stephen Sniderman that appeared on GAMES #25:

[addendum] Another 3D Tic-Tac-Toe is 1969's Stop Dot, published by Mattel.

Here the game is played on five faces of a 3x3x2 cube, and the goal is to make a 5 in-a-row with five different colors (at least over two faces):

These are the rules: 

Pencil and paper games: Dots and Bugs

Pencil and paper games all share the property that each grid cell can only be used a very limited number of times (usually once or twice). Walter Joris is probably the game designer that most contributed to this genre with his 2002 book 100 Strategic Games for Pen and Paper. There's more recent Joris fun on his pinterest page.

Here are two pencil and paper games played in the Eastern bloc.

Dots. Played on a grid of any size - traditionally on a 39x32 grid typical of a squared copybook in Russia [wikipedia].

Each player draws a dot of his color on an empty intersection. If the player closes a chain of his own dots (including diagonal connections) and the interior includes at least one enemy dot, then the player connects his dots with lines. Those dots, including the inner area, are out of the game (let's say the player captures the area). The player scores one point per surrounded enemy dot. If the inner area does not have an enemy dot, then the player cannot capture that area. Also, if there are more than one option to close chains, the player must select just one of those to close.

When the board is full, the player with more points wins.

Usually, the game starts by playing a limited number of moves in a central area to prevent players moving initially in the borders (since those dots cannot be captured). A nice way to solve this problem would be to make a toroidal board, but at a probably high cost in clarity.

The wikipedia page mentions a variant that allows for knight-like connections, which encourages more offensive play. 

Another variant prevents a chain from scoring if it gets surrounded by a larger enemy chain.

An extra rule is the idea of Houses. A House is a chain that surrounds an area with only empty spaces. If the adversary moves there, and does not close a chain himself, then the House becomes a closed chain. This rule seems to open a cold phase at the endgame, when dots must be placed in the remaining intersections that penalize the players (getting the game closer to a no-pass Go).

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The second game is Клоподавка (Bug Supression) aka Virus War. Again, the game is played on a large grid. The players decide on a move budget (say N usually between 3 and 6) relative to the size of the grid.

Each player has a home base, each on opposite corners. On his turn, each player marks N squares on the grid. Markings can be on empty squares, or by shading a square marked by the adversary (let's call it a wall). A wall becomes unplayable. However, players can only mark or shade squares that have a connected path from their home bases. 

A player that cannot complete his move, loses the game.

In the following example (with N=6) Blue answered Red's early and over-extended attack by making four walls, cutting red walls from the rest of their army. Now, if Red wants to reconnect, he must spend four markings to get to his three walls.

play this game here

Virus is a very underrated game, I find it quite fun to play and surprisingly tactical. Perhaps the game is too decisive, being hard to counter an early advantage, but who knows what good players could make of it?