1b. Board Wargames 
Hex map with cardboard counters
"[I] invented a war game where different empires move across the map capturing, and I played that a lot by myself until Finland captured all of Europe. At that point I figured it was time to retire that game."

Sid Sackson, An Exclusive Interview (Sackson is the well-known creator of Uncle Wiggly and other games).

Board games are a broad and popular field of games that may have very little to do with war.  Some board games have nothing to do with war.  Some "wargames" (for instance Battleship) are so abstracted from war as to be only nominally wargames.Generally, people who play board games may sometimes play board games with military themes (Risk, Axis and Allies) and sometimes play non-military games (like Monopoly or Othello) based on the entertainment value of the game. 

Nevertheless, from the 1950ís to the 1980ís, hobby wargames were typically understood to be board games.The market probably drove this tendency.Avalon Hill, the first and most famous wargame company, could print and box paper maps, cardboard counters, and rule sheets inexpensively for the market.[1]First-time players could draw upon the rules of chess and other board games and learn new rules quickly. 

The BoardHex map of Kiev and surrounding terrain
In wargame board games, the board generally represents a scaled map of some region (i.e. North Africa, Europe, the Rhineland).In games representing particular battles, the board often represents a much smaller area.Whatever the scale, the map is normally divided into spatial units in order to facilitate movement.In early games (like War Chess) these units were squares in a grid configuration, which led to the diagonal movement problem.Moving one square diagonally should theoretically take 1.4 times longer than moving one square horizontally or vertically since a diagonal move covers 1.4 times the distance.However, fracturing time this way does not make for clean, turn-based (my turn / your turn) movement.To solve this problem, game designers turned to a hexagonal grid, which allowed even distances of movement constrained in six directions rather than uneven movement in eight directions.[2]The hex grid became the standard board division pattern for military board games involving terrain and troop movements.(However, some variants exist, such as area movement games.)

Different colored hexes represent various terrains: light blue for shallow water, darker blue for deep water, green for plains, dark green for forests, etc.Some hexes often represent cities, towns, or structures.The character of a hex often influences the rules of combat and movement for units that are present in that hex.Forests, for example, will often help to conceal units within them, but may impede their movement.

The UnitsThe newly revised Diplomacy gameboard
Pieces of cardboard, plastic, metal, or a combination of these typically represent military units in board games.In world or hemisphere scale games, these units might represent fleets, infantries, or other large-scale aggregations of military forces.In smaller scale games, these units sometime represent individual soldiers or pieces of equipment.Cardboard pieces which represent units often contain numbers giving information about the movement rate, defensive and offensive capabilities, and special abilities of the unit.

Many a board game has been designed using merely a board with spatial units, a set of units to place in spaces, and a set of rules to govern play. (i.e., chess, latrunculi).  However, many games also use additional materials, such as cards, dice, and non-unit counters or chits to facilitate play.  Since thousands of board wargames exist, and since novelty is not an uncommon aspiration of game designers, there can be few categorical statements made about the precise way that these additional materials contribute to game play.

Are Board Wargames Disappearing?
Game designers (Jim Dunnigan and Mike Joslyn, among others) have noted the recent decline in sales and popularity of war board games.  Though the popularity of board wargaming discussion boards such as ConsimWorld and board wargaming companies such as Avalon Hill would seem to belie this argument, it is clear that role-playing games, computer wargames, and fantasy/science fiction board and card games have dramatically expanded their audiences during the past twenty years.  Presumably a portion of this number were former board wargamers who broke ranks in favor of the new genres. 

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1(back).  See Peter P. Perla, The Art of Wargaming 115 (1990).

2(back). Id. at 116.

Please note image owners retain copyrights. Image of hex board courtesy GMT Games.