Identification of implicit structures in dynamic systems is a fundamental problem in Artificial Intelligence. In this paper, we focus on General Game Playing where games are modeled as finite state machines. We define a new property of game states called invariant projections which strongly corresponds to humans' intuition of game boards and may be applied in General Game Playing to support powerful heuristics, and to automate the design of game visualizations. We prove that the computation of invariant projections is Pi_{2}^{P}-complete in the size of the game description. We also show that invariant projections form a lattice, and the lattice ordering may be used to reduce the time to compute invariant projections potentially by a factor that is exponential in the schema size of game states. To enable competitive general game players to efficiently identify boards, we propose a sound (but incomplete) heuristic for computing invariant projections and evaluate its performance.