Aug 28, 2025

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.

Aug 23, 2025

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.

Aug 15, 2025

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.

Aug 10, 2025

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.

Aug 5, 2025

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