The link between GR theory and Flow theory. The force is normalized over various mass with momentum and potential energy. Such a measure was discovered from the game's underlying mechanisms playing progress of Go, Chess, and Shogi board. Also, acceleration provides a reasonable indicator of the flow state to measure the balance between challenge and ability. The cross point at m=1/2 is vital as a border between competitive and non-game context (education). In contrast, potential energy peak at m=1/3 is prominent in non-game settings (e.g., most engaged).