There are tons of 1D games. Somebody else mentioned Mancala, and I'd also mention the venerable Game of Goose, which can become anything from Candyland to sophisticated things like Kramer and Kiesling's That's Life or Parlett's Hare & Tortoise. Hell, Monopoly is also 1D if we're willing to allow circuits like Mancala.
Black can’t move the knight: it’s illegal to make a move that puts yourself in check. Thus black has no legal moves, but isn’t in check, so the result is a draw.
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 name><destination square>
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...
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.
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.
Maybe I'm not good enough at chess to understand the strategy here, but how would castling be useful in this 1-D game? Castling in a normal game protects your King and activates the Rook. In this 1-D game, your King starts out protected behind the Rook. If you castle and end up in a _ R K N position, your king is exposed and your Rook is trapped behind the King, useless, with no way to ever get it back out. The Rook seems essential for mate, and its power has been eliminated.
> It looks like white wins for n=6 and n=8 with perfect play, otherwise it is a draw.
For n=6 it's "1. N4 mate," right?
For n=7, "1. R5" is a stalemate; "1. R4 N4 2. N4 r4#" is a loss; "1. N4 n4 2. R2 r6 3. R3 r5 ..." is a draw by repetition; so yeah, it's a draw with best play.
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 :)
If you enjoyed this, you might like Mind Chess, which can be played without a board and pieces [1]:
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.
There's a fantastic game like Mind Chess and Rock-Paper-Scissors called "Hand Cricket". It is like cricket, but played by showing a number with the fingers of your hand. (Showing just a thumb is 6, folding all fingers is 0, and 1-5 is 1-5 fingers as usual).
Both players play a number simultaneously. If the numbers are the same, the batting player gets out. Otherwise, whatever number the batter showed gets added to their score. The innings continues till the batter gets out. And then the roles reverse, the other person becomes batter.
After both innings, the person with higher score wins.
It's spooky because you have 7 different choices for each ball but people still get out rather quickly.
97 comments
[ 2.7 ms ] story [ 91.0 ms ] threadIncidentally, there is an actual 1D game that is one of the most popular games on the planet: Backgammon.
No. N4 leads to a forced win.
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.
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 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.
I checked n=6...20. It looks like white wins for n=6 and n=8 with perfect play, otherwise it is a draw.
With random play, black seems to have the edge regardless of board size. About 2/3 of the games end in a draw, but black wins 20% and white 13%.
For n=6 it's "1. N4 mate," right?
For n=7, "1. R5" is a stalemate; "1. R4 N4 2. N4 r4#" is a loss; "1. N4 n4 2. R2 r6 3. R3 r5 ..." is a draw by repetition; so yeah, it's a draw with best play.
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.
[1] http://www.eblong.com/zarf/essays/mindgame.html
Both players play a number simultaneously. If the numbers are the same, the batting player gets out. Otherwise, whatever number the batter showed gets added to their score. The innings continues till the batter gets out. And then the roles reverse, the other person becomes batter.
After both innings, the person with higher score wins.
It's spooky because you have 7 different choices for each ball but people still get out rather quickly.