Difference between revisions of "Conventions"

Revision as of 03:59, 22 March 2020

This page lists possible conventions for Hex games. These conventions concern the color of the players, who goes first, the orientation of the board, and the numbering of the positions on the board. Unlike much older games such as Chess and Go, there are no universally agreed upon conventions for Hex, and different people, game sites, books, and computer programs sometimes use different conventions.

We distinguish logical from physical conventions. Logical conventions are concerned with the abstract rules of Hex, irrespectively of how the players visualize the game. Physical conventions relate to the specific appearance of the game board. When the game is played remotely, for example on an internet game server or over email, it is in principle possible for the two players to follow different physical conventions; for example, each player may choose their own preferred orientation of the board, or their own preferred colors for the pieces. However, both players should follow the same logical conventions.

Universal vs. local conventions

There are several aspects of a game of Hex that are arbitrary and do not affect game play in an essential way. This includes the orientation (rotation and reflection) of the board, the colors of the players, who goes first, which edge belongs to which player, and whether and how the cells on the board are numbered.

The same also applies to other games; for example, the game of Chess would not change in an essential way if the white square were in the bottom left instead of the bottom right, if black went first instead of white, if the white queen started on a black square instead of a white one, if the ranks were lettered and the files numbered instead of the other way around, and so on.

In the case of established games such as Chess and Go, there are universal conventions that all players have agreed on. This has certain advantages. For example, every chess player understands what it means to move a white pawn from d2 to d4, without requiring further explanation.

In Hex, there are no universal conventions yet. Therefore, each player, book, game site, tournament, or hex program must define its own conventions. It may be desirable for a set of universal conventions to eventually crystallize.

Logical conventions

Cell naming

Cells are arranged in a grid, which each cell named by a letter and a number. Letters can be uppercase or lowercase. The following convention seems to be nearly universally used:

Convention: coordinate origin

Possible values:

• Acute: The cell A1 is an an acute corner of the board.

In particular, this means that the three cells A1, B1, and A2 are all adjacent to each other.

For the purpose of the following exposition, it is useful to refer to the cells that share a common number as a "rank", and to the cells that share a common letter as a "file", as in Chess. For example, the 1-rank consists of the cells A1, B1, C1, etc., and the A-file consists of the cells A1, A2, A3, etc.

Edge coloring

To avoid referencing specific physical attributes of the game, we will refer to the color of the first piece played in the game as "color 1", and to the other color as "color 2". One pair of opposite edges "belongs to" color 1; these are the edges that the player who is playing color 1 is trying to connect. The other pair of opposite edges belongs to color 2.

Convention: edge coloring

Possible values:

• Normal: The edge that is adjacent to the 1-rank belongs to color 1, and the edge that is adjacent to the A-file belongs to color 2.

In other words, the normal edge coloring convention states that the color 1 edges are parallel to ranks, and the color 2 edges are parallel to files. In a typical rendering of the board, the letters (naming files) are written along the color 1 edge and the numbers (naming ranks) are written along the color 2 edge.

I am not aware of anybody who has used the opposite convention. However, there are some authors who use no edge coloring convention at all.

Swapping

There are two different ways of implementing the swap rule. Which convention is chosen will affect the notation for games.

Convention: swap method

Possible values:

• Player swap: Upon playing a swap move, the board position stays the same and the players change colors.

• Mirror swap: Upon playing a swap move, the players keep their colors and the board position is mirrored. The board position is updated by replacing the piece currently on the board by a piece of the opposite color, and placing it in the location with rank and file interchanged. For example, a black piece at A2 would be replaced by a white piece at B1.

Here is an example using the player swap convention: Player 1 plays a black piece at g4. Player 2 swaps. The board state remains unchanged, and immediately after the swap, it is player 1's turn to play a white piece.

Here is an example using the mirror swap convention: Player 1 plays a black piece at g4. Player 2 swaps, and replaces the black piece at g4 with a white piece at d7. Immediately after the swap, it is player 1's turn to play a black piece.

When using algebraic notation for a sequence of moves, it is important to know which swap method was used. For example, with the player swap convention, the notation "g4 Swap f7 e7" means player 1 plays color 1 at g4, player 2 swaps, player 1 plays color 2 at f7, and player 2 plays color 1 at e7. With the mirror swap convention, the same game would be described as "g4 Swap g6 g5". Here, player 1 plays color 1 at g4, player 2 replaces this by a piece by color 2 at d7, then player 1 plays color 1 at g6 and player 2 plays color 2 at g5.

Note that the above logical conventions are purely symbolic. They do not depend on any particular board layout.

Physical conventions

Colors

The most common color schemes are:

• Black and white.
• Red and blue.
• V and H.

With each color scheme, there are two possible conventions to which color is color 1. The more common conventions seem to be "black goes first", "red goes first", and "V goes first", but the opposite conventions also exist.

Board orientatation

The board can be oriented in a number of different ways. It can be oriented in the positive or negative senses, and rotated to various angles.

Convention: board sense

Possible values:

• Positive: The cells A1, B1, A2 form a clockwise triangle in that order.

• Negative: The cells A1, B1, A2 form a counterclockwise triangle in that order.

The positive sense can also be described by saying that if the board is rotated so that A1 points west, then the ranks run from southwest to northeast, and the files run from northwest to southeast. This convention can also be described as "letters above numbers", because if A1 points left, the letters A,B,C marking the files appear above the numbers 1,2,3 marking the ranks.

Convention: board rotation

There is probably no need for a preferred board rotation; indeed, players using a physical game board may freely move around the board and look at it from any angle they want.

In computer hex, the most common board rotations are:

• Diamond: the A1 corner points east

• Flat: the A1 corner points northeast

• Flat II: the A1 corner points southeast

The following table illustrates some common board layouts. Here, color 1 is shown as black and color 2 is shown as white.

Positive diamond	Positive flat	Positive flat II
Negative diamond	Negative flat	Negative flat II

List of conventions used

Notes:

• Browne states that there is no universal convention for which color goes first, but black goes first in all examples in the book.

• Berge states that any player can go first, but white goes first in his example games.

• TRMPH implements swapping incorrectly. It changes the color of the piece, but not its location.

• MoHex does not seem to implement swapping.

• Board Game Arena uses a non-standard cell numbering. Each cell is named by a pair (x,y), where x denotes the rank, y denotes the file, and the origin of the coordinate system is in the obtuse corner. However, the edge coloring is normal is a standard cell numbering is used.