In principle, every configuration of a Go board has a single “best next move”. The story of previous plays should not matter to determine future plays! And that’s probably how it would be if Go was played by planet-sized computers who could work out all possible games arising from that situation, and just play the best move every move.
Nitpicking—but actually in Go, multiple moves may have the same (maximal) value—and go is normally played with either a “ko” rule which says that the location of the last move played can make a difference—or a “superko” rule—in which case the entire history of the board can matter.
The superko rule can be reinterpreted so that each move is considered to be showing an entry in an immutable look-up table for “my move in this game given this (historyless) position” (something like the loop shortcut rules in Magic: the Gathering). If the look-up table is immutable, repeating a position would create a loop. If “best next move” is defined so that a loop is worse than a loss, and the other player’s look-up table is known, then it would not be possible for a perfect player to have a look-up table that caused a loop. In some other situations, breaking the superko rule with only “best next moves” would entail circular preferences, so that a perfect player would never want to break superko. In that case, the history of the board wouldn’t matter for defining the best next move for a given configuration. But maybe in some situations, perfect players who played by showing entire immutable look-up tables at the start of the game, in a go game without a superko rule, might use mixed strategies with a nonzero probability of a loop. Perfect players with source code access might get into games of timeless chicken.
The superko rule can be reinterpreted so that each move is considered to be showing an entry in an immutable look-up table for “my move in this game given this (historyless) position” (something like the loop shortcut rules in Magic: the Gathering). If the look-up table is immutable, repeating a position would create a loop. If “best next move” is defined so that a loop is worse than a loss, and the other player’s look-up table is known, then it would not be possible for a perfect player to have a look-up table that caused a loop. In some other situations, breaking the superko rule with only “best next moves” would entail circular preferences, so that a perfect player would never want to break superko. In that case, the history of the board wouldn’t matter for defining the best next move for a given configuration. But maybe in some situations, perfect players who played by showing entire immutable look-up tables at the start of the game, in a go game without a superko rule, might use mixed strategies with a nonzero probability of a loop. Perfect players with source code access might get into games of timeless chicken.