Six Chess Games—Compare Features

Hexes Chess games	number of players	number of hexes	pieces per player	game density	degrees of freedom	opening moves	full size or compressed
3-Pawn	2	30	12	80%	330	13	compressed
4-Pawn	2	34	13	76%	430	15	compressed
6-Pawn	2	54	15	55%	838	31	full size
9-Pawn	2	72	18	50%	1162	55	full size
3P3	3	46	12	78%	552	16	compressed
4P3	3	55	13	71%	780	19	compressed
square chess shown below for comparison
square chess	2	64 squares	16	50%	756	20	full size

Number of Players

Hexes Chess provides four chess games for two players and two chess games for three players.

Number of Hexes

This number indicates how many hexagons (or squares) comprise the chess board.

Pieces per Player

This number indicates how many pieces each player starts with. All Hexes Chess games accommodate 1 king, 1 queen, 2 rooks, 2 knights, 3 bishops, and either 3, 4, 6 or 9 pawns per player, depending on which chess board you use. There are three bishops because hexagonal chess boards are in three colors, and each bishop is constrained to traveling on a single color.

Game Density

This number is the percentage of hexes (or squares) occupied by chess pieces at the beginning of the game. For example, in square chess, and in Hexes Chess 9-pawn, half of the "spaces" are occupied by chess pieces, so their game density is 50%.

Degrees of Freedom*

This metric was created by the designer to calculate an overall score for any chess board that uses standard chess pieces. The number is calculated by counting every direction a king can move, plus every destination a knight can reach from every hex (or square) on the chess board. For example, in square chess, a square near the center of the board has eight directions that a king can move plus eight destinations a knight can reach. These added together give sixteen degrees of freedom for that square. A square at the edge of the chess board has fewer degrees of freedom, and a corner square has the fewest. The degrees of freedom of all the squares added together give a total of 756 degrees of freedom for square chess. On the Hexes Chess 9-Pawn board, a hex near the center of the chess board would have twenty four degrees of freedom—twelve directions a king can move, plus twelve destinations a knight can reach. The Hexes Chess 9-Pawn board has 1162 degrees of freedom. The higher the degrees of freedom, the more options per move a player will generally have.

Opening Moves

This is the number of choices available to a player on the first move of the game.

Full Size or Compressed

Full size Hexes Chess games accommodate two-hex opening moves for pawns, and include the en passant rule. The compressed chess games are simpler and tighter. The pawns do not get two-hex opening moves and consequently have no en passant rule. Hexes Chess has two full-size games—the 6-Pawn and the 9-Pawn, and four compressed games—the 3-Pawn, the 4-Pawn, the 3P3 (3-Pawn for three players) and the 4P3 (4-Pawn for three players).

*The term "degrees of freedom" as it pertains to chess has elsewhere been defined as the number of optional chess moves a player has when it is their turn to play. It is here calculated and defined as a measure of the whole chess game.