Lava

Cameron Browne (2009)

Lava is an abstract strategy game in which two or three players strive to make blobs... but not of their colour!

Rules

Players: The two-player game is played between Red and Green. The three-player game is played between Red, Green and Blue.

Pieces: There are three types of dice as shown in Figure 1. Each die is a red, green or blue cube with four opposing corners in enemy colours (two each). A standard set has 16 dice of each type for a total of 48 pieces.


Figure 1.  The three types of dice.

Start: Red starts by placing a dice face showing all three colours in the centre of the playing area.


Figure 2.  Opening move.

Play: Players then take turns adding a die adjacent to at least one existing die such that edge colours match all neighbouring edges and corners. Only the uppermost faces have to match.

For example, Figure 3 shows a move forbidden due to a corner colour clash.


Figure 3.  Corner colour clashes are forbidden.

Auto Moves: If a placement creates a concave corner that matches only on dice face in one rotation, then that dice face is also played as part of the move. For example, move m in Figure 4 creates a concave corner c at which only one dice face in one rotation m' will fit; that dice face is also played as part of the turn.


Figure 4.  Move m triggers auto move m'.

Rule of thumb: Any concave corner at which all three colours meet constitutes an auto move.

Each auto move may trigger subsequent auto moves that turn.

Aim: A players loses by completing a closed blob of their colour. A player loses if an open blob of their colour extends 8 or more tiles in any direction (counting necks). A player wins if they complete a closed blob of any other colour or if they are the last surviving player.

For example, Figure 5 shows a game with a closed Blue blob. The outcome of this game depends on who completed the blob; if Red or Green then they win the game, else if Blue (three-player game) then they lose.


Figure 5.  A closed Blue blob.

If the tiles run out before a player wins then the game is drawn.

Three-Player Game: Played as per the rules above. A player's tiles are not removed when they are eliminated from a game.

Notes

In the two-player game, Blue is a neutral colour that either player may use to win (as shown in Figure 5).

A winning or losing blob may be of any size or shape, as long as it is closed.

The gap shown in Figure 3 does not constitute an auto move as only two colours face into the gap; either of two dice face rotations may be played there.

Each die has three unique faces, for example the Red die has unique faces {gRg, bRb, gRb}. These may exist in eight unique rotations, hence there are 24 unique rotations over all three dice types, labelled {a..x} for convenience.


Figure 6.  The 24 unique rotations.

The game could be played with tiles rather than dice, however the dice design has a number of advantages as it:
•  Reduces the number of different piece types from nine tiles to three dice.
•  Makes it easier for players to find pieces of their colour hence the exact face they want.
•  Means that one particular tile (face) will not run out before the others.
•  Allows the possibility of rolling the dice each turn to introduce a gambling element (see Variants section).
•  Allows the possibility of 3D stacking games not yet devised.

The dice have an inherent 1:1:4 colour bias as each die has two unique two-coloured faces and four similar three-coloured faces. For example, each Red die has two different two-coloured faces {gRg} and {bRb}, but four identical three-coloured faces {gRb, gRb, gRb, gRb}, as shown in Figure 7.


Figure 7.  The six Red dice faces.

It is not yet certain whether this 1:1:4 distribution approximates the usage of face types in the average game or not. The three-coloured faces make good defensive plays and are always used to fill the auto moves, however players must use two-coloured faces for Lava that they wish to extend but keep closable (explained shortly).

Strategy and Tactics

Consider the Blue blob shown in Figure 5, which has a neck that passes through a two-coloured face {gBg}. It turns out that for a blob to remain closable, every neck within the blob must pass through two-coloured faces of the same two colours; necks passing through three-coloured faces are flanked by two different colours that can never join to enclose the blob. This does not apply to neckless Lava, i.e. simple circles.

It is therefore a good defensive move to spoil open Lava that you don't want closed (i.e. of your colour) by extending them with three-coloured faces.

Variants

Tumbling Dice: Rather than playing the face of their choice, players must roll their die each turn to determine which face to play.

This introduces a random probabilistic element that could add some extra spice to the game. For example, a player may have to weigh up the risks and benefits of a move that gives them a 2 in 9 chance of winning on their next turn but a 1 in 6 chance of losing if the opponent makes a lucky roll beforehand.

The 1:1:4 colour bias inherent in the dice becomes very important in this version of the game.

History

Lava piece design and rules by Cameron Browne and copyright (c) Cyberite Ltd 2009.

Each die face is a tritone Truchet-like tile.

Lava can be played on Richard's PBeM server, please check out the help file for more details and challenge me (camb) to a game any time.


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Site designed by Cameron Browne © 2009.