Chessboard Thinking, usually described with the phrase "Spinning the Chessboard Around" (チェス盤をひっくり返す Chesu-ban o Hikkurikaesu) is a reasoning tool often employed by Battler to change his or another person's approach to a particular mystery by considering the perspective of one's opponent. It was originally devised by Kyrie, who took inspiration from game theory.
Chess is a highly strategic board game where opponents face each other and move pieces on the board according to a specific set of rules. The perspective one takes on the board partially influences the strategies and threats one notices. As such, spinning the chessboard around (180 degrees) allows one to see the board from the point of view of one's opponents, allowing one to both have a better idea of their opponent's strategy as well as come up with a new plan of attack.
The concept may be extended to reasoning in general. For example, in Legend of the Golden Witch Battler initially assumes that a 19th person does exist, as each the 18 people denied giving Maria the umbrella and letter, and because there are many possible hiding spots on the island. By spinning the chessboard around, Kyrie is able to observe that there is a contradiction between the fact that a 19th person would have hidden themselves and the fact that they chose to personally appear to Maria in order to give her the letter. If remaining hidden were Beatrice's goal, she should have mailed the letter to the family. Conversely, if making her presence known were her goal, she should have simply presented herself in front of everyone. Her conclusion using this reasoning is thus that this situation would be most beneficial if one of the 18 people were trying to create the illusion of a 19th person on the island.
Kyrie herself acknowledges that chessboard thinking is not perfect, as real life is filled with noise—additional information that makes it difficult to identify the relevant details. The weaknesses of chessboard thinking are discussed at several points in the story by the characters.
One major weakness of chessboard thinking is the possibility of imperfect information. This is due to the fact that real life is not constrained by the fixed rules and fixed gameboard found in chess, but contains an infinitely large number of possible actions and information. The knowledge that one gains about one's opponent and their actions may be limited and skewed, resulting in a faulty prediction. In addition, Maria suggests that an opponent like Beatrice may have the ability to move her pieces in ways that humans cannot.
Chessboard thinking often makes the rationality assumption, treating the opponent's moves as if they are the best ones possible for them. Kyrie observes that human emotions contribute noise, reducing the predictability of a person's response in a given situation. A human player may choose a weak move on a whim, toy with their opponent, or simply make an honest mistake. Thus, treating one's opponent's moves as perfectly rational runs the risk of resulting in an incorrect reading of their situation and goals.
Misreading the Opponent
Chessboard thinking is about reading your opponent and their motives, and thus the foundation of its reasoning collapses if one makes the wrong assumption about their opponent's goals. Because chessboard thinking involves projecting oneself onto one's opponents, a greedy person may simply imagine money to be their opponent's goal. If one's opponent has a goal other than victory, chessboard theory will fail without information on their true motives.