Hex-Nut, and the boardless effect

Hex Nut is a 2001 game by Luke Miratrix, published at Pair-of-Dice Games.

The game has no board. There are two sets of ten hexes, one per player.

The players, on their turn, can either:

a) Drop a new hex that must be connected to more enemy hexes than friendly ones. 

In the next diagram, the marked hexes are the legal moves for White to drop a new piece:

notice that the piece is the entire hex,
not just the black or white circle
(the empty hexes don't exist in the playing arena)

b) Move a friendly hex to the next edge of an adjacent hex (of either color). When the hex moves, if there's a group of hexes that would become separated from the rest of the pieces, then that group moves in tandem. 

In the next diagram, White moves to [1] taking the three sized group with it,

 

Moving a hex is only possible if it can be freely moved around the surface. If a hex is surrounded by enough pieces, and moving it would imply moving over other hexes, then that hex is locked in. 

In the next example, the middle white hex cannot move to either [1] or [2] since there's not enough space to move it freely.

Wins the player that makes a chain of eight or more friendly hexes. Notice that this is not a connected group, a chain is a sequence of pieces where each hex is crossed only once.

In the next diagram we see two groups of eight hexes, but the White is not a sequence of eight pieces, since there's a branch at the left, implying that one of those stones cannot be counted.

A tip from the official rules: 

The main thing I tell people, but which they rarely follow is: never split your pieces! If your pieces get divided, and your opponents do not, then you have lost. Consider if you have three pieces separate from your main clump. You cannot win unless they rejoin, and in the process of rejoining, they always cause a spot where your opponent can extend. In fact, once this happens to you, you should resign.

I find it interesting the boardless feature of Hex Nut. The shape of the game is built during the match; there's no restriction except for the pieces' shape.

Trax is perhaps the most classic boardless game, a tile-oriented game where players try to make a loop or a long enough line,

Trax has lots of resources, check traxgame.com for more information.

Hive, from 2001, is another boardless successful game. Other examples are Six, Ringo, Bermude, Pent-Up, Cubeo, Kaliko, Exxit, and John Conway's Sprouts.

             

 

GAMES magazine #39

I would like to mention Cameron Browne who designed some visually stunning boardless games, like Mambo, a territorial/capturing game:

check his website for more great examples.

Babylon

Babylon is a 2003 game by Bruno Faidutti, published at Interlude (among others).

The game does not have a board, only twelve stackable tiles (three tiles for each one of four colors).

Initially, all tiles are placed in the gaming area. Let's denote a single tile as a stack of size one.

Rules:

• On her turn, the player must place an entire stack on top of another.
• A move is valid if either:
• both stacks are of the same height
• both stacks have the top-most piece with the same color 
• Wins the player making the last move

This is a game that seems very amenable for analysis using Combinatorial Game Theory. But I'm not aware of any article studying it.

DIY Draughts

Do-it-yourself draughts, or Dames en Kit, is a c.1890 game by Walter Sanders,

diagrams from Jeux Stratègie's page

Rules. Each player has ten pieces and 20 tiles (one light and one dark set).

First phase: On each turn, each player places (a) a friendly piece on an empty same-color tile, (b) a friendly tile at the side of another already placed tile, (c) or both.

Second phase: When all pieces and tiles are placed, pieces are allowed to move to any adjacent empty tile of its color (including diagonals). 

However, in both phases pieces also have the option to capture. Pieces capture by jumping one or more consecutive enemy pieces, assuming there is an immediate empty tile of its color to end its move.

Captures are multiple, i.e., after a capture, the player may continue capturing with the same piece. And, like Checkers, captures are mandatory (if there are several options, the player can choose which). Captures are mandatory in both phases.

• Notice that it is possible to place a tile, opening a capture option, that must be executed in that same turn. However, even if it is possible to place a tile in these conditions, players might choose not to.
  

Wins the player that captures or blocks all enemy pieces. If the interactions between pieces are no longer possible, wins the player with more moving pieces (blocked pieces do not count). Otherwise, the game is a draw.

Example: in this diagram, players cannot interact with each other. So, Black wins since he has two moving pieces against just one moving white piece.

The game appeared at Roger Millington's Games and Puzzles for Addicts (1979),

The game also appeared in Jeux et Stratègie #42 in 1986: