1D Chess

Mentioned in TFA: This version of chess is given by Martin Gardner in his "Mathematical Games" column of July 1980 (pages 27 and 31) — https://www.jstor.org/stable/24966361 — and the analysis of White's mate is given in the column of August 1980 (page 18) — https://www.jstor.org/stable/24966383.

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.

It's very interesting and fun!)

Reminds me of Edwin A. Abbott's Flatland, where he describes Lineland. A one-dimensional world whose King can only move forward and backward, cannot conceive of sideways, and considers his tiny segment of existence complete and sufficient. The Linelanders are portrayed as pitiable, intellectually imprisoned by their single dimension. Much like us in our three :)

I vibed 3d chess the other day, its sort of ok https://sphere-chess.replit.app/

This is really nice.

Incidentally, there is an actual 1D game that is one of the most popular games on the planet: Backgammon.

Haha, i was taking N4 and N6, but didn’t figure the steps after that.

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.

I was only able to beat this after a couple retries. The hint was hard to read.

It was a lot more fun than I first thought!

Oh very interesting. Even with these restrictions, there are quite a few variations, and it seems only one ends up with white winning.

It took me an embarrassing number of attempts to win.

Finally, a version of Chess I can understand. Thank you.

i could not beat it, and i can't read that chess notation

Cool idea. This is smart and lean. I like it

The first move is always: white rook takes black rook, then the only remaining move for black is to move the knight away, which results in checkmate.

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

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.

It's very interesting and fun!)

I vibed 3d chess the other day, its sort of ok https://sphere-chess.replit.app/

This is really nice.

Incidentally, there is an actual 1D game that is one of the most popular games on the planet: Backgammon.

Haha, i was taking N4 and N6, but didn’t figure the steps after that.

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.

I was only able to beat this after a couple retries. The hint was hard to read.

It was a lot more fun than I first thought!

Oh very interesting. Even with these restrictions, there are quite a few variations, and it seems only one ends up with white winning.

It took me an embarrassing number of attempts to win.

Finally, a version of Chess I can understand. Thank you.

Cool idea. This is smart and lean. I like it

i could not beat it, and i can't read that chess notation

The letter is the piece to move, and the number is the index to move to, starting from 1 on the left. The first alphanumeric pair is your move, then the computer's move. Comma. Your move, computer's move...

the notation is just an array of move tuples, each tuple contains 1 move for white and 1 move for black, where each move is written as <1st letter of piece><destination square>

The first move is always: white rook takes black rook, then the only remaining move for black is to move the knight away, which results in checkmate.

If you play the game, you realise this ends up in stalemate.

the notation is just an array of move tuples, each tuple contains 1 move for white and 1 move for black, where each move is written as <1st letter of piece><destination square>

If you play the game, you realise this ends up in stalemate.

1d-chess is a new variant where you can play the beautiful game without all those unneccessary and complicated extra dimensions. Play as white against the AI. You might initally find it more difficult than expected, but assming optimal play, is there a forced win for white?

Mouse over to reveal answer: Try this line: N4 N5, N6 K7, R4 K6, R2 K7, R5++

Rules

There are three pieces in 1d-chess:

King:

Can move one square in any direction.

Knight:

Can move 2 squares forward or backward. (jumping over any pieces in the way)

Rook:

Can move in a straight line in any direction.

Win by checkmating the enemy king. This occurs when the enemy king is in check (under attack by one of your pieces) and there are no legal moves for the opponent to get their king out of check.

Careful! A draw can occur if:

A player is not in check and there are no legal moves for them to play (Stalemate)
The same board position is repeated 3 times in a game. (3 Fold Repetition)
There are only kings left on the board, thus it is impossible to checkmate the opponent (Insufficient Material)

Credits

This chess variant was first described by Martin Gardner in the Mathematical Games column of the July 1980 issue of Scientific American
See The column on JSTOR

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