Huh! I don't follow chess closely enough to have known the tables go that deep. Do high-level players memorize (enough of) those that their strategy in a losing position shifts to creating a drawing piece combination? Or do the tables only formalize something was that always done intuitively?
I don't think human players memorize tables in the same way that they memorize opening lines. The number of possible endgame position values is astronomical; "Syzygy" for 7 pieces is a few TB of data, for example.
Heuristics get them very close, but I vaguely remember hearing that sometimes the tables will find an obscure move sequence to turn around a draw to a win 15 or 20 moves in that a human has no chance of spotting.
These tablebases do have something eerie to them, as they represent the phase transition from heuristics to the "solved" part of chess. Lichess will automatically swap to them once it's feasible, and instead of a position evaluation, you'll just instantly see whether it's winning, losing, or drawing. Ken Thompson called it "playing chess with God": https://en.wikipedia.org/wiki/Endgame_tablebase#%22Play_ches...
That said, this can happen with chess engines as well; if a position can be exhaustively analyzed, it'll show you "winning/losing/drawing in n moves" just like the tablebases. The tablebases just guarantee that they'll find that solution in constant time.
