There is a mechanism missing in chess from the current rule set. When a locked position is engaged, such as a King being repeatedly checked in and out of a few spaces by the opposition, a new rule is required. This will break through the ugly barrier chess has built for itself, where oil is required to stop smoke to build from a grinding halt. A deadlock can result in:
A creative move from an otherwise limited piece. Example, a pawn can momentarily move up the chain of power (so a Knight or Bishop power for a move) to 'break free'. This option will be created as a representation of the natural genetic answers to the consequences of evolution, thus an erratic move with a surge of power from a cornered animal is a creative solution performed by the natural world is mirrored by chess strategies. Or a King gets an ability to 'jump' a piece by extending two spaces and over a barrier of another piece, when cornered and pressured to stalemate? The board is triggered with a fault line otherwise.
The psychological issue I wanted to note expression of is the phenomenon where a player is embroiled in a rhythm with their opponent and despite often having high skill levels, after much interplay a plane of social power is established which can engender decision making in a manner articulating the balance of the plane more than the chase to victory. So for example, a pair of players develop a rhythm of chess intercourse from a lot of moves together and despite a high rating, some training and experience they may choose moves which are more logical to the pursuit of a symbiosis than a victory such that a player who would otherwise take notice to seize a Queen or other high ranking power piece when opportunity arises, they may find interest to select alternate routes with both or either understanding there had been a play missed. This ethic is perhaps MOST important to all chess interplay because it forces the player to bond socially in a cooperative from the association yet the illusion of warfare continues. It proves you really want to be friends but need to battle for an illusion that you can only see that after one dominates the other in a pugilist exchange.