Unlur

2006-03-31T18:44:33Z

SAS: comment out "as in the figure", as there is no figure yet

Unlur is a [[connection game]] invented by [[Jorge Gómez Arrausi]] in [http://en.wikipedia.org/wiki/2001 2001]. It won the 2002 Unequal Forces Game Design Competition which was sponsored by the [[Abstract Games Magazine]], [[About Board Games]] and the [[Strategy Gaming Society]].

It is played by two [[player (general)|players]], black and white, on a [[hexagonal grid of hexagons]]. The two players have different objectives, and must therefore use different strategies to achieve their goals.



A [[Y (chain)|Y]] is a [[chain (Y)|chain]] [[connection|connecting]] three non-adjacent sides. A [[line (Y)|line]] is a chain connecting two opposite sides.

Black wins if he creates a black Y, while White wins if he creates a white line. However, a player loses if he achieves his opponent's objective. That is, if Black creates a line without at the same time creating a Y, White wins. Similarly, if White creates a Y without at the same time creating a line, Black wins. If a player creates a line and a Y in the same move, he wins.

== The contract ==

White clearly has an easier objective than Black, since a line requires fewer pieces than a Y. Therefore a generalizations of the [[Swap rule|pie rule]] is used to balance the game.

In the first phase of the game both players play with the black pieces. A move consists of placing a black piece anywhere on the board, except at the border. Instead of making a move a player may [[Pass (Y)|pass]]. In that case, the player passing becomes Black for the rest of the game, while the other player becomes White, and the players then play with their respective pieces. White makes the first move.

The first phase is called the [[contract phase]].

Draw

2006-03-31T14:21:14Z

SAS: some corrections and link for Brouwer's Fixed Point Theorem

One of the beautiful properties of Hex is that the game can never end in a '''draw''', i.e., there is always a winner.

There are various ways of proving this, for example:

* A [http://www.cs.ualberta.ca/~javhar/hex/hex-galeproof.html proof by David Gale] that used the fact that exactly three hexes meet at every vertex.
* A [http://www.cs.ualberta.ca/~javhar/hex/hex-yproof.html elegant proof] using the [[Y|game of Y]].

In fact, the no-draw property is equivalent to the 2-dimensional case of [http://en.wikipedia.org/wiki/Brouwer_fixed_point_theorem Brouwer's fixed point theorem] (a non-trivial theorem from topology saying that any continuous map from the unit square into itself must have a fixed point).

HexWiki - User contributions [en]

Unlur

Draw