Despite the move history (usually) not mattering, looking close to to the last move is actually a very useful heuristic! If we take the average of distances between successive moves, this number will surely be lower for a good player than for a random bot.
(but of course, a weak human player may be playing too much locally, and will have an even lower average distance compared to strong play)
So for instance, when making an AI, it is counterintuitively helpful to supply it with the last few moves, even disregarding anything to do with ko.
I think it would be fun to make some sort of histogram over move distances throughout games at different levels, it’s a very easy thing to compute but could reveal some interesting patterns. I wonder if it’s better to use Manhattan or Euclidean distance for this purpose?