| Random Links is a connection game played on a randomly generated board. The rules are the same as for Hex. The players take turns claiming an empty space on the board, with Red going first. The object is to form a chain connecting the player's two sides of the board. Red seeks to connect the two red sides, and Blue seeks to connect the two blue sides. Blue is given the option of claiming Red's first space as an equalizing move. As in Hex, draws are impossible. One player will always form a winning connection. Click anywhere on the board to begin the game.
The board is created by randomly dropping walls into a 15x15 grid (25x25 in the variant). The only restriction on wall placement is that four walls can never touch at a common point. With this restriction, the board is guaranteed to be draw-proof. Four walls meeting at a common point are necessary for spaces to be diagonally adjacent (i.e., touch only at a point). Diagonally adjacent spaces can block an opponent connection without themselves being connected. This is the formula for stalemate. When diagonal connections are prohibited, the only way to block an opponent connection is to form a connection yourself. The only way for a player to completely block the opponent is to place a chain of pieces separating the opponent's two sides. Such a chain equals a winning connection, meaning that the only way to completely block an opponent is to win.
Walls are dropped into the grid until no further drops are possible. The resulting spaces can take a variety of shapes consisting of one or more unit squares. When a player clicks on a unit square within a space, all unit squares within that space are claimed.
Unlike Hex, neither player has a theoretical win. The strategy-stealing proof of a first player win in Hex depends upon the symmetry of the board when rotated from the perspective of one player to the other. This proof holds that if the second player has a forced win, the first player can steal this winning strategy by placing a random stone on the first turn and then adopting the second player's strategy. An extra stone on the board can never harm the first player. Because the first player can always steal a winning strategy from the second player, no such strategy exists for the second player.
With asymmetrical boards such as those generated in Random Links, the lack of symmetry generally prevents the first player from adopting any winning strategy that the second player might have. For example, on a 3x11 Hex board, one player has a simple winning strategy along the short axis -- play in the middle of a row, then connect to an edge on the next two turns -- that cannot be stolen by the opponent.
Nonetheless, the first player in Random Links will normally have an advantage. There are three basic forced win scenarios. Red can have a forced win regardless of who goes first, Blue can have a forced win regardless of who goes first, or either player can have a forced win if given the first move. The random generation of the board requires that the first two possibilities happen with equal frequency. The third option always favors the first mover and thus gives Red a statistical advantage.
In order to neutralize Red's first move advantage, Blue is given the option of claiming Red's first move. This is accomplished by clicking on the first space claimed by Red and converting it to Blue. This is similar to the swap option commonly used in Hex, with the difference being that the players do not actually change places.
Win detection is turned off in the "Freestyle" variants, allowing you to fill up the entire board. |
