Imperfect-information games present significant challenges for General Game Playing (GGP) agents. Traditional models have limitations that hinder their applicability in this domain. These models require agents to construct and maintain estimates about the game state, a process that is often game-specific and can unintentionally introduce domain-specific knowledge. Furthermore, this specificity undermines the core goal of GGP to generate domain-independent strategies. To overcome these challenges, we propose the Belief Stochastic Game model. This novel framework shifts the responsibility of state estimation from the agent to the game model itself, allowing agents to focus solely on strategy development. This externalisation of the state estimation process is enabled by the exploitation of the common structures found in many imperfect-information games. The new model facilitates the development of more general agents that can adapt to a wide range of games.