Consider Mind Chess. Two players face each other. One says "Check." The other says "Check." The first says "Check." This continues until one of them says, instead, "Checkmate." That player wins -- superficially. In fact, the challenge is to put off checkmate for as long as possible, while still winning. This may be better stated: you truly win Mind Chess if you call "Checkmate" just before your opponent was about to.
I also lost the game not too long ago, but before that, I think I didn't actually lose it for a decade of more? And losing it wasn't even because it was mentioned anywhere, I genuinely just thought of it by myself, after forgetting about it for so long.
So my sincerest apologies if my comment just made any readers lose the game.
Like, five or so losses this year.
I do wonder how things would change if the board were 9 cells long; 10 cells long; etc. Also, it seems "in the spirit" to permit castling if neither K nor R has moved yet: i.e., from the position
K _ R N r _ n k
White ought to be permitted to
_ R K N r _ n k
(Or maybe there's a stronger argument for R K _ N r _ n k, actually. The former was conceptually "rook moves halfway toward king, then king moves to the other side of rook"; but the latter is "rook moves two steps in king's direction while king moves to the other side of rook.")
I'm pretty sure this wouldn't change the analysis on the 8-cell board at all, though. I wonder if it would change the analysis on any size of board.
Though maybe in that case the best first move for both is to castle and we are non the wiser (back to the original starting position)
Incidentally, there is an actual 1D game that is one of the most popular games on the planet: Backgammon.
You could play with pieces that have a value of 1..N instead. Starting with 2,3, and 5 value pieces, and splitting them as needed. Making it one-dimensional again, while keeping 100% of the rules.
Final verdict, therefore: backgammon is 1D, not 1.5.
We could pretend that the second dimension was not playing a role in tactics back then, since it was very recently invented, like the brothers Wright invented the third dimension a hundred years ago. Or some hot air balloon at a world faire did it.
To win we need to let knight die because rook can move multiple steps to kill the king.
From a third person perspective R2 is a deceptive move that takes advantage algorithm to make the black king back off to kill its knight.
So black is not in check and has no legal moves, so stalemate.
Would enjoy so much if there were more of these, feels like an obligation-free chess puzzle.
There are probably other ways to win too.
https://github.com/Rowan441/1d-chess/issues/1
Edit: There's a second solution where instead of moving the rook back 2, move the king forward one and the take the black knight with the rook as the checkmate move.
Translating your notation to normal chess notation:
White king on h1, black rooks on a2 and g8, black king in some random other place, white to move.
That is a draw, because white is NOT in check, but has no legal moves. That scenario is called stalemate. If white were in check, it would be checkmate and a win for black. Set it up on any chess analysis board website and it will say the game is a draw.