[DSMan195276]

It depends what rules you're using, but there are the three-fold repetition and 50-move rules which allow a player to force the game to end in a draw. The catch is they both require one of the players to claim a draw under the rule, otherwise they can keep playing.

There is additionally the 75-move rule where the the game is forced to be over without either player claiming the rule (the arbiter just ends the game), that rule would give an upper bound regardless of the players knowledge of the rules.

[jonah-archive]

In this lovely paper: https://tom7.org/chess/longest.pdf

The author points out that:

"This rule only applied to games started after its introduction, so it is possible that some pre-1561 games are still in progress and may never end."

[drpixie]

As I understand it, the 50-move rule must be invoked by one of the players, lets assume our immortal players agree not to invoke that rule.

The 75-move rule is automatic, so that would be the limiting factor.

Note, that 75-move rule is only applicable after no pawn has moved or a piece has been captured. So our immortals can do a lot of shuffling things around.

I'm thinking that the number of moves of the longest game is going to be (16 pawns * 7 moves each + 16 pawns being captured + 14 other pieces each being captured, not the kings) * 75 moves for shuffling around = 10650 moves.

That's only 1 week at 1 move per minute! But given the permutations, it might take much longer to calculate the actual moves required to get to the end state :)

[Sesse__]

Here's an actual constructed game that is presumably as long as possible (with explanation): https://www.reddit.com/r/chess/comments/168qmk6/longest_poss...

[DSMan195276]

Pawns only get 6 moves :) But also they can't all make 6 moves because they can only move past each-other via capture, so half of them would get 5 moves instead (if you're counting all the captures), so that gives a maximum of ~8850.

[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.