Identical positions in the sense of castling.

The castling can be:

-illegal.

-castling rights lost permanently.

The first condition doesn't necessarily imply the second, because when the king is in check and can't castle, you can block the checking piece instead of moving the king to not lose castling rights permanently.

Then there are two cases:

- Castling is illegal but right not lost permanently.

- Castling is illegal and castling rights are permanently lost.

Does these 2 cases count as same or different positions in the sense of threefold repetition, if piece setup otherwise are the same? Reading FIDEs rules I can't figure this out.

Same possibilities to move.

If for example the knights swap places the position is equal.

en.m.wikipedia.org/wiki/Threefold_repetition

sv.lichess.org/analysis/4k2r/r7/8/8/8/8/4R3/1K6_b_k_-#1

In this position black preserve his right to castle if he plays Re7.

However if 1, - Kf8 2. Rf2+ Ke8 3. Re2+ an identical position with the same possibilities to move as the first one has occured, but with the important difference that after Re7 black no longer preserves his right to castle.

Is the position still counted as identical? I can't figure this out from the FIDE rules.

Summary: 2 positions, same pieces at same places, same moves possible, but in the 1st case Re7 preserves the castling rights, in the other case it does not. Are these 2 different positions?

No, after the king has moved it's no longer the same "position" because the castle rights have gone. Mnenomic: the FEN are equal in that relevant cases (regarding castling, ep)

See this example in wikipedia

Fun fact: you can repeat a "position" (only the setting of the pieces) about 15 times if you move one rook after the other without the possibility to claim successfully (probably once more if ep is inflicted)

PS: actually 22 times "optical" equal but not 3 times in terms of
-player to move
-castling
-ep

I recall the following philosophical position in a debate:
lichess.org/editor/4k3/8/8/8/8/8/4p3/2B1K2R_w_K_-

(wBc1 to avoid discussions about white's last move)
How many positions? It is a fact that white can never castle at a future point in the game, so practically speaking both statuses of castling rights amount to the same thing. But in principle?

Inrerestong. If white play Kf2 and Ke1.Is it then a different position?

The answer I feel that most agree to would be yes, the position will be different. The right to castle has nothing to do if castling is currently (or will eventually be) achievable. It is simply a question of whether the king and the rook involved have previously moved.

interesting

This has also come up in an old "The Arbiter's Notebook" column by Geurt Gijssen on the Chess Cafe site. Don't know if it's still possible, but I recall that he didn't have a good answer.

We also discussed this in the arbiter course I took, and didn't reach a good conclusion either.

It's an ambiguity in the current rules.

That said, where computers are involved, I think it's sensible to see them as different positions because that's easier to program.