*** LINAGE ***

INTRODUCTION

Linage is a finite territory game for two players: Vertical and Horizontal. It's played on the intersections (points) of an initially empty square board. Both players must have access to a shared pool of identical stones.

DEFINITIONS

A region is a maximal set of orthogonally contiguous empty points.

A line is a set of three orthogonally contiguous empty points on the same row or column.

A vertical region is a region that only contains vertical lines; a horizontal region is a region that only contains horizontal lines.

PLAY

Vertical plays first, then turns alternate. On their turn, a player must either pass or place a stone on an empty point which is not part of an enemy region. At all times, every empty region on the board must include at least one line.

When both players pass in succession, the game ends. A player's score is the number of points in the regions that they own, plus a komi in the case of white. The player with the highest score wins.

KOMI

The komi is the number of points which is added to Horizontal's score at the end of the game as a compensation for playing second. Before the game starts, the first player chooses the value of komi, and then the second player chooses sides. To avoid ties,
komi must be of the form n + 0.5, where n is a whole number.

VARIANT

_Two-color Linage_

Vertical places black stones and Horizontal places white stones. A player's score is the number of stones in orthogonal groups of their color orthogonally adjacent to their own regions. Playing in enemy regions is allowed. Region sizes can be added to
their owners' scores score if desired.

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)

Related idea:

At all times, all empty regions must fulfil some condition (like being bigger than n points). Player 1 wins if there is an odd number of regions at the end, and player 2 wins otherwise.

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)

El lunes, 26 de diciembre de 2016, 13:13:44 (UTC+1), Luis Bolaños Mures escribió:

Related idea:

At all times, all empty regions must fulfil some condition (like being bigger than n points). Player 1 wins if there is an odd number of regions at the end, and player 2 wins otherwise.

Note that n=0 can be used as well by ruling that you can never decrease the number of regions, which is implicit for bigger n values.

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)