Difference between revisions of "Conventions"

Revision as of 06:17, 16 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.

On the other hand, 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

To avoid talking about physical attributes of the game, let us use "color 1" to refer to the color of the first piece played in the game, and "color 2" to the other color.

Cells are numbered in a grid, which each cell described by a letter and a number. Letters can be uppercase or lowercase. The following convention seems to be universally accepted:

• [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 cells that share a common number as a "row", and to cells that share a common letter as a "column".

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. The following convention seems to be very common:

• [Normal edge coloring]: The edge that is adjacent to the cells A1, B1, C1, etc., belongs to color 1. The edge that is adjacent to the cells A1, A2, A3, etc., belongs to color 2. In other words, the color 1 edges are parallel to rows, and the color 2 edges are parallel to columns.

Swapping:

There are two different ways of implementing the swap rule. Which convention is chosen will affect the notation for games. The two options are "player swap colors" and "board swaps colors".

• [Players swap colors]: If the second player decides to swap, then the players change colors and the board stays the same. For example: Player 1 plays a black piece at g4. Player 2 swaps. The board remains unchanged, i.e., the black piece remains at g4, and the coloring of the edges also remains unchanged. Immediately after the swap, it is therefore player 1's turn to play a white piece.

The other choice is:

• [Board swaps colors]: If the second player decides to swap, the piece already on the board is replaced by a piece of the opposite color and moved to a different position. If the piece was originally in the nth row and mth column, it is moved to the mth row and nth column instead. For example: Player 1 plays a black piece at g4. Player 2 swaps. The black piece at g4 is replaced by a white piece at d7. Immediately after the swap, it is player 1's turn to play a black piece.

When using a notation for a sequence of moves, it is important to know which convention was followed. For example, with the "players swap colors" 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. The same game would be described as "g4 Swap g6 g5" with the "board swaps colors" convention. Here, player 1 plays color 1 at g4, player 2 replaced this 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

Disregarding rotations, there are two possible conventions for the orientation of the board: clockwise and counterclockwise.

• [Clockwise]: The cells A1, B1, A2 form a clockwise triangle in that order. In other words, if the board is rotated so that the acute corners are pointing east and west, then the northwest and southeast edges are the color 1 edges, and the northeast and southwest edges are the color 2 edges. This convention could also be described as "letters above numbers", because if the A1 cell is on the left, the letters A,B,C for the columns will appear above the numbers 1,2,3 for the rows.

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

Regarding the rotation of the board, there is probably no need for a preferred convention; 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 shapes are the "diamond" shape, where the acute corners are pointing left and right and the orientation is clockwise, and the "flat" shape, where the color 1 edge is horizontal, the cell A1 is in the upper left corner, and the orientation is clockwise. Also relatively common is the "flat II" shape, which is the flat shape upside down, i.e., with A1 in the lower right corner and counterclockwise orientation.

Colors:

The most common color schemes are:

• black and white
• red and blue
• V and H

It seems to be the more common convention that black, red, or V goes first, and white, blue, or H goes second. However, the opposite convention also exists.

List of conventions used

Notes:

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

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

• MoHex does not seem to implement swapping.