The Strategy of Chess
Chess is a game of sequence. There is a finite number of moves you can make initially, there are responses to those moves from your opponent, and there are responses to those moves and so on. This applies to game theory because for every move there is a best response to your opponent’s. Chess is also a game of infinite possibilities in that there are sequences which cause the game to go on forever.
There are strategies, like in every game, in that you can play aggressively or defensively. Something more specific to chess is that it has a finite amount of openings or variations. There are over a thousand different ways to start the game and they are all based on the moves that the players make at the beginning. There are no strictly dominant strategies because the game is so complex. However, there are moves and sequences that are objectively better than others, defining some weakly dominant strategies. After every opponent’s move, the player is presented with multiple choices. The payoffs of those choices are tied to how strategic the positioning is: How many more moves can the piece make? How close are you to capturing other pieces, namely, the King? Importantly, how hard is it for the opponent to move? The payoff of the move depends on what the opponent ends up doing, which makes the best strategy difficult to measure. This is because the opponent’s move is the best response to your move. However, chess does not have Nash equilibria in the usual sense because the moves happen continuously and sequentially– one must happen in order for the other to happen, it can’t happen backwards. It’s also hard to tell which move is objectively the best because players play subjectively– with style, psychological risk analysis, and a lack of ability to analyze the entire board. Thus, per Professor Gass of UMD writing for the Scientific American explains that while pure strategies may exist, they are hard to describe. In a scenario where both players play perfectly, then the game would come to a draw.
Because the beginning moves are limited, there’s a name for each specific sequence at the beginning. These sequences are called openings or variations. For example one of them is called the Queen’s gambit. This happens when white’s first move consists of moving its d-file pawn to d4. Black responds with moving its pawn to d5, then white moves another pawn to c4 for the third move of the game. At that point, black can either accept or decline the gambit. Accepting it would be capturing the c4 pawn with the d5 pawn, declining it would be not taking the pawn and choosing to defend the d5 pawn to maintain control of the center. Maintaining control of the center of the board is critical. It determines how many options the different pieces have and thus determines how easy it is to defend and attack. There is no strictly dominant strategy because the advantages pertain to personal preference and style. Some would argue that the better strategy would be to maintain control of the center because accepting the gambit loses positioning.
https://www.scientificamerican.com/article/what-is-game-theory-and-w/