In one way or another, board games are concerned with the occupation of space. Certain board games are a matter of occupying the more space possible (Risk), while in other games you need to occupy some crucial areas on the board to secure a tactical advantage (Chess).
The way you occupy space in a game is ruled by certain constraints placed at three levels: placement, movement / expansion, and resource extractions.
Those constraints correspond to the rules of the game, they determine the player’s progression, and specifically how to move from one board state to another, to advance towards the victory conditions.
Placement
At the beginning of a game, and sometimes throughout the all game, constraints determine how to position the pieces on the board. For instance, in Settlers of Catan, you can only place a settlement on a location where three hexagones intersect. In the game of chess, the constraints are maximal as the initial placement of the pieces is fixed.
Movement / Expansion
Additional constraints rule the way you can move your pieces on the board. Here I distinguish movement and expansion constraints. I talk about movement constraints when a piece moves from a board area to another without retaining the advantages granted by its former position. This is the case in chess for example, which is not about acquiring territory but creating a configuration of pieces to control the opponent’s movements. I talk about expansion constraints when, after a displacement, the tactical advantages are kept (such as in Risk, and generally any territory acquisition game). In this case, the moving piece leaves a ‘trail’, which may consist in other pieces (that secure the position on the board) or any type of marker of the player’s evolution on the board.
Movement / Expansion constraints generally determine the possible direction your move on the board, and the amplitude of this move.
Resources extraction
Constraints on resource extraction regulate how the placement of your pieces on the board translates into options for victory (either the accumulation of victory points, or the control of a critical position on the board). In certain games, you need to occupy certain places that possess a specific value. For instance in Settlers of Catan, adjoining the hexagons allow the player to obtain resource cards matching the hexagon’s type. In Risk, the number of armies a player may draft hinges upon continent bonuses. In Monopoly, owning a property brings money to the player whenever another player lands on it. In other games, earning victory points is conditional upon certain configurations you need to realize on the board (such as in Ticket to Ride in which players have to connect cities with rail routes).
Antagonist principle
The antagonist principle corresponds to any resistance the player may encounter in her progression, at any of the three levels previously mentioned.
This resistance may come from other players if they are allowed to oppose directly to each other (like in any wargames), or from a game mechanic that may intervene randomly (in Settlers of Catan, the robber moves when the resulting number from rolling two dices is 7).
The antagonist principle has a status of its own. I don’t see it as a set of constraints per se, but rather as a modulation of the constraints on placement, movement/expansion and resource extraction. What I mean is that at some points the constraints are dynamically adjusted to embody a new game configuration, for instance by making more difficult to extract resources, or by reducing the movement options on the board. This principle have the effect of introducing an element of surprise, it may reshuffle the cards when the players’ skills are uneven, and generally gives vitality to the game.
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A board game is a combination of the different sets of constraints I’ve just described. Their respective importance determines the game identity and depth. Some games are all about placement (Go), whereas some games are all about movement (Chess). Some games place heavy constraints on movement (Monopoly: you can only move in one direction), while some other games let you choose freely how you want to arrange your pieces on the board (Warhammer).
Clearly, the tactic and strategic elements of the game depend on the specific selection of constraints and how they are emphasized. A game in which you can move in only one direction has not the same strategic flavor as a game in which multiple combinations of movement are allowed. But having multiple options does not equal being complex or deep. Chess is interesting because of the specific constraints it implements: without the restrictions on initial placement, you would not get the standardized canevas upon which players can elaborate multiple strategies. Without the constraints on movement, you would not have the possibility to anticipate your opponent’s movements, or plan ahead your own movements.