Lhexus is played on a hexagonal board with a honeycomb grid. Different sizes are possible. The diagram shows a base-10 board.

There are two players, Black and White. Both have a sufficient number of stones in their color. The game starts on an empty board, with a swap option for the second player: the first player puts a white man on the board after which the second player decides whether he accepts that move as his first, and thus plays white, or rejects it, in which case it is his turn and he plays black.

Rules

a word on notation

Definition: a group consists of one stone or two or more like colored connected stones. On his move a player has two options, and can use both, either or neither (the latter without losing the right to move next turn). He may: Grow any or every of his existing groups by one stone. A stone connecting two or three different groups is considered to have grown all off them. No group, considered at the beginning of the player's turn, may grow more than one stone in that particular turn. ... and/or put a stone on a vacant cell, not adjacent to a like colored group, thereby creating a new group. The first option, if used, precedes the second. For example, bottom-left black has two existing groups. He can connect them by growing each towards the other. On the right, if he grows at the cell in between, both groups have grown and he cannot complete a line of six at either side, because one of the original groups would have two new stones adjacent to it.

Valid configurations
There are three valid configurations, each consisting of six stones:

• A straight line
• A compact triangle
• A small hexagon

Object
The game ends on two successive passes.
The winner is now the player with the highest score. A player's score is counted as the number of valid configurations he has created on the board. Any stone on the board may only be counted in ONE configuration.
In case both have an equal number of valid configurations, the player with the least number of stones on the board wins. If that too is equal, the game ends in a draw.

Observations
Since each stone may only count in one valid configuration, a group would have to consist of twelve stones minimum to contain two valid configurations, eighteen stones minimum to contain three. The moment a valid configuration is completed, further growth at that group may aim at a second or third one, but if the prospects on that are bleak, it may also have a defensive objective: preventing the opponent from growing onto the cells concerned.
If no local offensive or defensive goal can be served, one should refrain from growing a group, because the object implies that anything done, should be done with the least possible means, in case the valid configuration count is a tie.


Lhexus © MindSports
Java applet © Ed van Zon