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You are correct in the question that in RL terms chess a game of chess where the agent is one player, and the other player has an unknown state is a partially observable environment. Chess played like this is not a fully observable environment. I did not use the term "fully observable game" or "fully observable system" above , because ...


First, note that the current state does not determine the next state. What determines the next state are the dynamics of the environment, which, in the context of reinforcement learning and, in particular, MDPs, are encoded in the probability distribution $p(s', r \mid s, a)$. So, if the agent is in a certain state $s$, it could end up in another state $s'$, ...

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