Board games, random boards and long boards

For any odd integer n≥3 a board (of size n) is square array of n×n positions with simple rule how to move between positions. The goal the game we introduce find path from upper left corner center square. If there exists such say that solvable, and length this shortest path. There are 8n2 different boards. We discuss various properties these boards present some questions conjectures. In particular, show for n≫1 roughly 38 expected random solvable tends 20996, i.e., very big tend have extremely short solutions.