>> Nobody can assess the entire game tree, so the fact that it is theoretically knowable isn't actually relevant in a game.
That's not the point though. The point is that you only need to consider current state when considering your next move in Go or Chess. This is not the case in an incomplete information game, since the sequence of moves that led to the current state contains a lot of information. That's not the case in Chess or Go. Basically, Chess and Go satisfy the Markov Property, while Poker does not.
The current state in Go is the state of the board, the current state of poker includes some historical data. This difference is only significant to humans because we have quite poor memories.
An AI has perfect recall, and the fact that a variable is temporal really doesn't make a difference to the theory.
(Coincidental aside, this is an issue in Go as well due to the ko rule; but it isn't a major part of the game such as in poker.)
Which AI architecture has perfect recall, in a way that actually makes use of this information?
Pretty sure AlphaGo etc does not make use of memory at all.
That's not the point though. The point is that you only need to consider current state when considering your next move in Go or Chess. This is not the case in an incomplete information game, since the sequence of moves that led to the current state contains a lot of information. That's not the case in Chess or Go. Basically, Chess and Go satisfy the Markov Property, while Poker does not.