Lambchop

Lambchop is a 2001 game by Dan Troyka, published online.

The game is played on a square board, say 5x5, initially empty.

Each player has just one piece (the lamb).

Rules:

• Initially, the players drop their lamb on an empty square
• On his turn, the player moves his lamb to an empty square
• if the square is unmarked, the player marks it for himself (thematically, the lamb just eaten the grass of that square)
• Wins the player with more marked squares

In the following position, White's turn to move, having each player marked nine squares. 

If White goes north to capture d5 and e5, he loses the game, since he would leave to Black three of the remaining seven grass (unmarked) squares. Then, White either captures b2 or a5, Black will capture the other.

There's a ZRF to play Lambchop. It includes several variants with different board sizes, and the use of more than one lamb per player.

Conflict

Conflict is a 2000 game by Alexander Stevens, published online.

The game is played on a 10x10 board, initially empty.

Each player has eight soldiers (myrmidons), twelve shields (bucklers) and four jumpers (assassins).

Rules:

• Initially players take turns to drop their pieces in their first four rows
• On his turn, the player moves a friendly piece:
• soldiers and shields move like Chess queens
• soldiers can only capture if they are in moving range from another friendly soldier
• captures are by replacement
  
• shields cannot capture or be captured 
• assassins can move one or two steps in straight line, or jump over a piece landing in the immediate next square that must be empty or occupied by an enemy piece (that is captured)
• Wins who capture all enemy soldiers.
  

The game originality is in the restricted capturing ability of soldiers. On the downside, the initial phase of dropping 48 pieces on board is not a good way to start a game.  It's too long. The game needs a fixed setup, just like Chess or Checkers (the old ones knew a thing or two). This is important to improve the game's interaction.

after grueling 48 turns,
all pieces are finally on board

Also, having twelve shields seems a bit too much. It might give an opportunity for very defensive tactics.

There is a ZRF to play Conflict.

Quadraphage on Winning Ways

Winning Ways for Your Mathematical Plays, from 1982, is a book that marks the beginning of an entire mathematical area, Combinatorial Game Theory, and a new set of numbers, the Surreal Numbers. It was written by Elwyn R. Berlekamp, John H. Conway, and Richard K. Guy. The book contains an impressive number of mathematical techniques and insight and has very hard sections in it (there are more recent books with the goal of introducing the main concepts with a more pedagogical approach). Below, let's call the book just WW (for Winning Ways).

Among the many games explored in the book, some are closer to the idea of abstract games that motivate this blog. This post mentions one of them: Quadraphage.

The rules of Quadraphage (meaning, the square eater) by Richard Epstein in 1973: 

• In a NxN empty board, a King is placed on a square
• One player moves the King (the Mover), the other player drops a stone (e.g., a Go stone) on any empty square (the Placer)
• Turns alternate, as usual. 
• Goal: if the King reaches any square at the edge, the Mover wins; if the Go stones surround the King, the Placer wins

Since moving first is never a disadvantage, there are three possible outcomes: (a) the Eater always wins, (b) the Mover always wins, (c) the first player to move wins. The book calls a fair position every square for the King to begin, where option (c) occurs.

The book includes the use of other pieces besides the King. It calls Chessgo to this family, and it considers Kinggo (the previous rules) and Dukego (using a Duke, ie, a one-step Rook). Other reasonable options include Knightgo and Ferzgo (using a Ferz, ie, a one-step Queen).

One interesting result from WW is that there are only two possible board sizes where fair positions occur, and that are 33x33 and 34x34 boards (!). On a smaller board the Mover always wins, and for bigger boards the Mover always wins (cf. chapter 19).

Also, the author mentions the game in his 2009's book The Theory of Gambling and Statistical Logic:

 

This game is an offspring of the medieval Tafl games, and a member of the Fox Games' family.

Quintus

Quintus, or Quintun, is a 2003 game by Martin Windischer.

The game is played on a 10*10 hexagonal board. 

There are enough white and black pieces, and enough neutral stones of five different colors.

Definitions:

• the 54 hexes on the edges are the ring
• the remaining hexes are the playing area

Rules:

• On her turn, the player either:
• drops a friendly piece on an empty hex inside the playing area
• drops, on the ring, one neutral piece of a new color
  
• this piece must be at least five empty hexes from other neutral stones in both directions of the ring
• drops, on the ring, two neutral pieces of a color already played
• these pieces must be adjacent to pieces of the same color
• Wins the player that either:
• connects a friendly group with four different neutral colors
• connects two friendly groups, each with three different neutral colors

In the next diagram (from a real match), White resigns: there's no possibility for his large group to connect to a third neutral color

  

This is imho a very good game, a connection game that does not have a fixed connection goal. The only point where this could be improved is in the condition of dropping the first neutral stone of a new color (so to remove the arbitrary distance of five empty hexes). The suggested new rule: 

• drops, on the ring, one neutral piece of a new color in a side with no neutral pieces already in it (including corners) if this is possible, otherwise any ring hex

There are six edges for five colors. If a small number of neutral colors get to have large groups, a new tactical avenue would open by dropping the new neutral color anywhere in the ring.

Diagonal

Diagonal is a 2004 game by Luca Cerrato, published at Fogliaccio degli Astratti #23.

The game is played on an 8x8 board, initially empty.

Rules:

• On her turn, the player drops a friendly piece on an empty square
• After her move, the player scores as many points as the number of their pieces in the completed diagonals where the current piece belongs
• a single piece color in a diagonal does not score
• When the board is full, wins the player with highest score 

in this position, if Black plays [1] the score is 3 points
while if it was White playing at [1], the score is 3+3=6 points

Cerrato also proposes a variant, Diagonal Plus:

• Initially, players drop a number of neutral pieces on board
• These pieces are labeled with positive (bonus points) or negative (malus points) numbers
• Bonus and malus points cannot be placed on the same diagonal.
  
• For the 8x8 board, it is suggested to use: two pieces +2, one piece +3, one piece -2
• It is forbidden to complete a diagonal using only neutral pieces (besides the dropped piece)
• The scores should include the bonus/malus points besides the standard diagonal points

Fox Games: part 2

Fox games are not only from Europe. There are board games with asymmetrical forces in other places.

A well-known traditional game is  Baghchal from Nepal,

As BGG reviews:

At the start of the game, there are four tigers on the board while there are no goats. The goat player places his/her pieces on the board one by one wherever they choose, with the tiger player getting a move between each placing. Once all the goats are on the board, the two players take turns moving one of their pieces one space. A tiger can alternatively capture a single goat by jumping over it in a line to an empty space. The tigers win if they can capture five goats. The goal for the goats (who cannot make captures) is to hem the tigers in, giving them no opportunity to move or jump.

Other traditional examples are

• Diviyan Keliya (Leopards and Cows) played in India and Sri Lanka
  
• The medieval Cercar la Liebre (Catch the Hare) played in Spain, which derived to Coyote played in Mexico c.19th century

• Len Choa (Len Cua Kin Ngoa) from Thailand [1]
• Komikan (El Leoncito) from Chile with a first known reference from 1787 [2]
  

This ludeme is just too simple and attractive and continues to be used in modern games.

One example is 1975's Buffalo Chess (aka Bison) from Alex Randolph.

Ludii description:

Buffalos move one step forward to a free space. Dogs move like a chess queen but cannot capture. The villager moves like a chess king, and can capture buffalos. Dogs and the villager cannot enter the top or bottom rows of the board. Buffalos start, and win by reaching the top row. They lose if they cannot move anymore.

Another (less well-known) example is 1970 Carapace (aka Revanche):

The board is, in essence, hexagonal. The asymmetry here is more pronounced, where one player will win for sure. The adversary goal is resistance. A game consists of two matches, where players switch sides. Some spaces have extra value (check the number of dots in the previous board) that are used for scoring. Wins the player with the better score.

Steve Sisk wrote the next rules:

A modern variant -- in fact, more a puzzle than a game -- is the 2001's Wild Goose Chase by Dan Troyka:

 

The tame geese move one step orthogonally, while the wild goose is unable to capture, but moves like a Queen and is also able to fly to the adversary's first row. The geese have 15 turns to capture it. There's a ZRF to play it.

[1] Captain James Low, On Siamese Literature, Asiatic Researches vol.20[2] (1839)
[2] Thierry Depaulis, Inca Dice and Board Games, Board Games Studies 1 (1998)

Rosette

Rosette is a 1975 game by Mark Berger, published at Games & Puzzles #34:

Mindsports has more information about this early Go variant. Also check this BGG forum discussion.

Turning Point

Turning Point is a 1969 game by Phyllis Frederick and Peter H. Justin, published by Mattel.

Each player starts with 27 regular pieces, two double pieces and one 'stop' piece. Each stop piece is given initially to the adversary. There are also two scoring pegs that are placed at the zeros of the scoring columns.

The game uses custodian capture, i.e., when a player 'sandwiches' a line of enemy pieces by two of his own pieces, he captures (here, flips) those sandwiched pieces. Captures can occur orthogonally and/or diagonally.

• First, the players take turns placing two pieces each at the 4x4 center area.
• Then, each player, on his turn, drops a friendly piece on an empty space.
• If he captures/flips one or more enemy pieces, the player gets one point for each piece in the line(s) he just formed (that includes not only the flipped pieces, but his own pieces).
  
• For each scoring line that includes N double pieces (or either army) the score of that line is multiplied by 2N (eg, a line with three doubles, gets a multiplier of six). 
• A double piece just dropped cannot be used as a multiplier (it only counts at subsequent turns).
• A player can play the adversary stop piece, but side down, whenever he wants.
• When the stop piece is turned back, the line it belongs to is not scored.
  
• When the board is full, the game ends. 
• Each player adds an extra point for each friendly piece on the board.
  
• Wins the player with the highest score.

The game is a variant of Othello. The interesting feature is the introduction of special pieces that change the dynamics of the game and might produce sudden differences at the final score. Of course, why stop at just the 'double' and 'stop' pieces? Imagination, as usual in design space, is boundless. Some possibilities:

• The switch: when flipped, it forces all eight neighbors to turn to the other color
• The pass: when flipped, the player must pass his next turn
• The negative: when flipped, the total current score turns negative
  

Also, the final 'one point per piece' rule seems an unnecessary vestige of Othello's ruleset and could probably be removed to make Turning Point a bit more different than its predecessor.

Ko-an

Ko-an is a 1994 game by David Welch and Paul Whitehorn, published at Image Games.

Each player has two types of pieces: five squared pieces and six octagonal pieces. The board is composed of a grid of yellow squares and green octagons.

This is the initial setup:

• Pieces only move forwards, not backwards nor sideways, to an empty space. There's a further move restriction: a piece cannot move between squares [in a better designed board, like the one below, it's easy to see why: squares do not touch on a 4.8.8 grid].
• Pieces can also move forwards to a space occupied by an enemy piece, which is then captured (captures are by replacement).
  
• However, captures also depend on piece type: octagonal pieces can only capture pieces on octagons, and squared pieces can only capture pieces on squares.
  
• Capturing is not mandatory.
  
• Wins the player that moves a friendly piece to the last row or stalemates the adversary (which includes capturing all the enemy army).

Here's a board (by r0cka) to play the game:

From a 1994 review by Richard Breese:

[...] Considering its simplicity, the game can develop in a surprising variety of ways. For example, pieces of both players may bunch up on one side of the board, several 'skirmishes' may occur all over the board, or a large stand off may arise across the center of the board. This variety adds to the attractiveness of the play.

Of the two types of playing pieces the octagonal piece is stronger and this factor probably explains why in most games it is a octagonal shaped piece which makes the winning break through. This strength arises from the situation where an octagonal shaped piece confronts a squared shaped piece. As the square spaces do not join each other it is necessary for all pieces to move onto the octagonal shaped spaces - the spaces on which the octagonal shaped pieces can capture. Consequently an octagonal shaped piece is much more likely to be able to capture a square shaped piece than vice versa.

Some pics from the original game package:

Fox Games: part 1

Fox Games is a term to refer to classic games based on the idea of asymmetric forces. One side needs to encircle/block the adversary, while the other needs to escape or capture all enemy pieces.

Perhaps the oldest game in this family is Hnefatafl played in medieval Scandinavia, where one player with the central player tries to escape to the edge of the board.

The Ballinderry Halatafl-Board

Alea evangelii (Game of the Gospels) in a 11th century manuscript

A more well-known modern game is Fox and Geese where, instead of escaping the board, the Fox needs to capture all the Geese (by jumping over one piece at a time, checkers-like), while these can only try to block the Fox. The next board uses one fox against 13 geese (or hens, in this case),

Nouveau Jeu du Renard (The New Game of the Fox)
board from Collection de Jeux Anciens

Another variant is The Game of Assault (Le Jeu de Assaut), with more pieces, making the board more crowded: there are two defenders against 24 besiegers:

Collection de Jeux Anciens

This previous board, c.1860, is from the game The Siege of Sebastopol (Jeu de l'Assaut de Sébastopol). The theme is based in the War of the Crimea

 

Assault games had several war motives over the 19th century; check the excellent blog Collection de Jeux Anciens for more examples. 

 

The next board is older, c.1814, again with a (rather abstract) military theme,

Two other games with foxes (renards in French),

 

 

patricia m, Flickr

This one has a sports-based theme:

 

A simpler version of this family was mathematically analyzed at Winning Ways, the bible of Combinatorial Game Theory (chapter 20 is dedicated to Fox Games),

This more abstract setup is older than Winning Ways, since it appears in 1938, published by Spear Spiele, and named 4 Gegen 1 (1 against 4).

 

Concours International de Créateurs de Jeux de Société

The Concours International de Créateurs de Jeux de Société (International Contest of Designers of Society Games) is an annual event organized by the Centre Ludique de Boulogne-Billancourt. The event started in 1977 and still occurs nowadays.

There are many awarded games (check their archive), and some became quite well known, namely Abalone, Quarto, Gygès, and Quits. Unfortunately, there is almost no information available about most of the board and rules of the submitted games over the years, including the awarded games!

Of the few there are board and rules available (in French), these seem to be within the blog's interests:

• Alpha, rules, GaalN (2001)
  
• Gadis, rules, Gérald Saiveau (1987)
  
• Court-circuit, rules, Max Gerchambeau (1983)
  
• Palanquée, rules, Ludovic Robillard (1988)
  
• Tchag, rules, Jean Georges (2003)
  
• Tor, rules, Alain Couchot, Bernard Klein (1996)
  

Of the ones where the board is known but not the rules:

• Dooble, Jean-Luc Hipeau (2000)
  
• Joséphine, Philippe Battesti (1999)
  
• Le Labyrinthe, Claude Fagret (1986)
  
• Pionmor, Bernard Tavitian (2000)
  

There are lots of other games in their archive without online information.

Ra

Ra is a 1981 game by Marco Donadoni, published by International Team.

It is played on the following hex board,

Each player has nine stackable pieces, that are initially set on stacks of size three around each player's Ra area (the black hex in the picture).

• Stacks move in straight lines. The player might decide to move just part of stack.
• A stack of size 3 moves one hex, a stack of size 2 moves two hexes, and a stack of size 1 moves three hexes.
• Captures are by replacement, but a stack cannot capture an enemy stack with higher size. Captures are not mandatory.
• The moving pieces may land on a friendly stack, increasing its size (up to the maximum size of 3)
  
• Stacks cannot move over other stacks.
• Unimpeded moves must be completed (eg, a stack of size 1 must move exactly three hexes, not less). 
• Obstructed moves occur if a stack reaches the board edge, captures an enemy stack, reaches a friendly stack, or lands over the adversary Ra area.
• Wins the player reaching the adversary Ra area or captures all enemy stacks.

The rules also include scoring: the player wins 1 point if a stack of size 1 arrives at the Ra area; 3 points for a stack of size 2, and 6 points for a stack of size 3. If a player wins by capturing the adversary army, it wins 3 points.

Players may decide the number of points needed to win a match (the ruleset suggests more than 6 points, with an advantage of at least 2 points). 

Some advice from the ruleset:

Ra is a game based on attack; playing only defensively often means losing the game.

It is important to carefully calculate the timing of moves: the winner is the one who enters first, not the one with the highest number of pieces. Losing a game by one point, with the advantage of starting first in the next round, can often provide the opportunity to attack and gain more points.

In case of a risk of heavy losses, try to minimize the defeat by threatening your opponent, if possible. One of two things will happen: they will enter immediately, or you will.

Some spaces play an important role: conquering them means gaining an advantage.

The Italian magazine Per Gioco, in May 1985, mentioned the game and published some matches: