[LegionMammal978]

How I'd put it is that there are two sets of stopping points under FIDE rules:

- After threefold repetition or 50 moves, either player may claim a draw.

- After fivefold repetition or 75 moves, the game is automatically drawn.

Most modern counts of the longest possible chess game, or the total number of possible chess games, are based on fivefold repetition and the 75-move rule.

Meanwhile, threefold repetition and the 50-move rule are still relevant in endgame tablebases, since they rule out certain forced mate sequences.

[Sesse__]

Endgame tablebases don't take into account threefold repetition; if so, you would have to basically be able to exclude any arbitrary position from the tree, which would seem impossible. The 50-move rule is respected by the Syzygy tablebases, though with the concession that they do not generally give the fewest possible moves to mate (they would rather delay the mate than delaying a pawn push or a capture).

Here's an example (adapted from the URL below): https://syzygy-tables.info/?fen=3R4/5R2/8/8/8/1K6/8/4k3_w_-_... — if you asked pretty much any player, even a child, how to win this, they'd show the staircase mate starting with Re7+ (mate in 4). If you asked a computer or the older Nalimov tablebases, it would say Kc2! (mate in 2). However, if you ask the Syzygy tablebases, they would argue that this is not optimal if we are extremely close to the 50-move rule, so the safest and thus best move is Rf2!! which forces Black to capture the rook on the next turn (they have no other legal moves), resetting the counter and giving a mate in 18.

There were a set of experimental DTM50 tablebases made at some point (though not made public); they store the shortest mate for all 100 possible zeroing counters in any position. See https://galen.xyz/egtb50/ for some discussion.