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.
Speaking of games without pieces, it's hard to develop one for only 2 players, but I've tried: https://news.ycombinator.com/item?id=43110448 (yes that is my alt account, sorry but I forgot my password)
Sounds like a dating game. "Delay texting her back or expressing your feelings as long as possible, until just the moment before she will give up on you"
Which reminds me that I just lost the game.
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.
I've lost it a lot lately, for some reason, after what I suppose was my third multi-year victory streak.
Like, five or so losses this year.
Damnit, I am pretty sure I had a few-year-streak going until just now. Welp, off to the grind again, I suppose.
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Wait, how is the "put off checkmate" objective scored? Turns before checkmate? Or what?
Is it just a joke?
I have never played it, but I could imagine a scoring mechanism that would make it interesting, and perhaps is implied by the rules:
The score value starts at 1. Every additional "check" multiplies the score value by 2 (so 2, 4, 8, 16...). The first player to say "checkmate" receives the score. Track your summed score between games; the player with the highest overall score at any given time is "winning."
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.
Exactly. Feels like R K N would be a more suitable initial position in which castling would swap the king into safety, provided it has not moved and is not in check...
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)
1D Go is also interesting and doesn't require any change in rules or starting position. TIL that it is known as Alak [1].
One of the open problems in our Combinatorics of Go paper [2] is whether you can play a game that goes through all possible legal 1xn positions for any n>2, which we were only able to verify up to n=7.
If
1. Rx6,it is stalemate. So it must be
1. N4 N5.
Then we could proceed with,
2. Nx6+ K7.
Now, if you capture the knight (Rxe), it is stalemate again. So sacrifice the knight,
3. R4 Kx6
so that you force black to zugzwang with
4. K2 K7,
and finally,
5. Rx5#
This is really nice.
Incidentally, there is an actual 1D game that is one of the most popular games on the planet: Backgammon.
Good observation. Considering stacking of pieces maybe 1.5D though.
Chess has different pieces, which has higher entropy than a true 1d backgammon or 1d checkers with only one piece a field.
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.
The "dimensions" in these board games isn't a mathematical/topology thing, is it? Normally one dimension = one real number space. Every board game ever would fit in 1D then, "2D" chess included.
I'm fine calling Backgammon 1.5-D. Physically you focus on a single dimension, and the second one matters too but not so much.
Backgammon, the game everyone's seen and at the same time nobody knows how to play :P
Solitaire and Hearts too. Well I actually know and love Hearts, but most people seem to know it as "that game in Windows where you play random cards"
My brother and I once took a train trip from L.A. to Omaha and back for a friend’s wedding and played backgammon for most of the trip. For weeks afterwards, I saw backgammon everywhere (most notably when reading dialogue-heavy books with lots of 1-line paragraphs).
I learned to play backgammon because it was one of the three games on my Nokia phone circa 2001 :P
I love this! Such a simple game with a fun level of skill. High score 3097 feels pretty good.
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 :)
N4 N5 Nx6+ K7 R4 Kx6 R2 K7 Rx5#
That finally confirmed that I am too regarded for chess if even 1D is too hard yay
is that str.replace(g,t) ?
No. I am actually too highly regarded for measly single dimensional game
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.
you could also just move your king on that move
same result
knight cant move, only king can, so it has to back away
I honestly thought this post was going to be about the Iran war.
I was confused why 3.R2 is drawing, but not 3.R4 since black can check with the knight either way, but it's fairly obvious in hindsight - if black checks instead of capturing, you don't take, you go K2 and force black into zugzwang. Clever.
It took me an embarrassing number of attempts to win.
It was a lot more fun than I first thought!
I don’t know why this is stalemate: N4 N5, N6 K7, R5. Wouldn’t rook have the king in checkmate?
The rook doesnt attack the king because N6 is in the way.
So black is not in check and has no legal moves, so stalemate.
Black has no legal moves because of the knight but they aren't in check
Don't know when was the last time I had so much fun with chess. Quite intuitive, clicked on the first click.
Would enjoy so much if there were more of these, feels like an obligation-free chess puzzle.
I was only able to beat this after a couple retries. The hint was hard to read.
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I won after four attempts. Pretty sure it was perfect play so yes white has forced win
Yeah. I think 1. N4 leads to a white win. It's fairly easy to verify that a black rook move will lead to a white win (1...R5 2. R2 and 1...Rx4 2. Rx4 N5 3. Rx5#). So the critical line is 1. N4 N5, but then 2. Nx6+ K7 3. R4 also leads to a win: 3...Kx6 4. K2 K7 5. Rx5# and 3...N3+ 4. K2 N5 5. N8 Kx8 6. Rx5#.
There are probably other ways to win too.
Zugzwang!
Nice, fun and interesting! :)
Finally, a version of Chess I can understand. Thank you.
Oh very interesting. Even with these restrictions, there are quite a few variations, and it seems only one ends up with white winning.
I was expecting a blog post regarding Iran strategy...
That's actually a fun little puzzle.
Hello
It's very interesting and fun!)
Cool idea. This is smart and lean. I like it
Silly nice brain teaser
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Nice! :)
Fun stuff, love it!
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love 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 first move after the comma is yours (open with kNight to 4), and the second move is apparently predetermined or always chosen.
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>
There's a coordinate-based solution in the source code issues. I couldn't elucidate that notation either.
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.
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.
I'm not very good at chess, but I dont get why most things are considered a stalemate? I strategically remove all pieces of the enemy, leaving only the king against my rook/tower whatever its called, the king has nowhere to run. In my eyes it's a checkmate. The game just calls it a stalemate. Would be a stalemate if I couldn't do anything, but I can kill the enemy king.
There is an explanation further down. A stalemate is if the enemy has no valid loves and is not in check
It's a stalemate because while the king can't move, he isn't under active attack. There is nowhere he can legally move, but he's safe where he's at.
That rule caught me up too. In regular chess if it is your opponents turn and their only pieces are a king in the 1,8 square and a pawn that is pressed up against one of your pawns and you have rooks in the 2,1 and 8,7 squares that counts as a victory does it not?
No. That is a draw assuming it is the player with only a king’s turn to 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.
But why? That feels like a victory.
Because that’s the rule. There doesn’t have to be a rational reason.
... and if it weren't the rule, it'd make a lot of mid- and late-game play much safer for the player with the advantage. As it is, it's something they have to watch out for, which constrains them somewhat. You have to win, but not the wrong way, and your opponent can attempt to force you to "win" the "wrong way" (resulting in a stalemate).
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.
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.
[1] http://www.eblong.com/zarf/essays/mindgame.html
Speaking of games without pieces, it's hard to develop one for only 2 players, but I've tried: https://news.ycombinator.com/item?id=43110448 (yes that is my alt account, sorry but I forgot my password)
Sounds like a dating game. "Delay texting her back or expressing your feelings as long as possible, until just the moment before she will give up on you"
Which reminds me that I just lost the game.
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.
I've lost it a lot lately, for some reason, after what I suppose was my third multi-year victory streak.
Like, five or so losses this year.
Damnit, I am pretty sure I had a few-year-streak going until just now. Welp, off to the grind again, I suppose.
Wait, how is the "put off checkmate" objective scored? Turns before checkmate? Or what?
Is it just a joke?
I have never played it, but I could imagine a scoring mechanism that would make it interesting, and perhaps is implied by the rules:
The score value starts at 1. Every additional "check" multiplies the score value by 2 (so 2, 4, 8, 16...). The first player to say "checkmate" receives the score. Track your summed score between games; the player with the highest overall score at any given time is "winning."
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.
Exactly. Feels like R K N would be a more suitable initial position in which castling would swap the king into safety, provided it has not moved and is not in check...
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)
1D Go is also interesting and doesn't require any change in rules or starting position. TIL that it is known as Alak [1]. One of the open problems in our Combinatorics of Go paper [2] is whether you can play a game that goes through all possible legal 1xn positions for any n>2, which we were only able to verify up to n=7.
[1] https://senseis.xmp.net/?Alak
[2] https://tromp.github.io/go/gostate.pdf
Those who play go may enjoy the variants: https://www.govariants.com/variants/rules-list Tetris is a fun one to try!
I love chess! This version was fun too.
If 1. Rx6,it is stalemate. So it must be 1. N4 N5. Then we could proceed with, 2. Nx6+ K7. Now, if you capture the knight (Rxe), it is stalemate again. So sacrifice the knight, 3. R4 Kx6 so that you force black to zugzwang with 4. K2 K7, and finally, 5. Rx5#
This is really nice.
Incidentally, there is an actual 1D game that is one of the most popular games on the planet: Backgammon.
Good observation. Considering stacking of pieces maybe 1.5D though.
Chess has different pieces, which has higher entropy than a true 1d backgammon or 1d checkers with only one piece a field.
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.
The "dimensions" in these board games isn't a mathematical/topology thing, is it? Normally one dimension = one real number space. Every board game ever would fit in 1D then, "2D" chess included.
I'm fine calling Backgammon 1.5-D. Physically you focus on a single dimension, and the second one matters too but not so much.
Backgammon, the game everyone's seen and at the same time nobody knows how to play :P
Solitaire and Hearts too. Well I actually know and love Hearts, but most people seem to know it as "that game in Windows where you play random cards"
My brother and I once took a train trip from L.A. to Omaha and back for a friend’s wedding and played backgammon for most of the trip. For weeks afterwards, I saw backgammon everywhere (most notably when reading dialogue-heavy books with lots of 1-line paragraphs).
I learned to play backgammon because it was one of the three games on my Nokia phone circa 2001 :P
Mancala is roughly 1D too!
Very cool. Reminds me of 1D Pacman: https://abagames.itch.io/paku-paku
I love this! Such a simple game with a fun level of skill. High score 3097 feels pretty good.
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 :)
N4 N5 Nx6+ K7 R4 Kx6 R2 K7 Rx5#
That finally confirmed that I am too regarded for chess if even 1D is too hard yay
is that str.replace(g,t) ?
No. I am actually too highly regarded for measly single dimensional game
If you like 1D chess, you'll probably like other chess-themed puzzles as well: https://chedoku.com/blog/chessPuzzles
I went in other direction ;-) https://topce.github.io/chess960x32/
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.
you could also just move your king on that move same result knight cant move, only king can, so it has to back away
I honestly thought this post was going to be about the Iran war.
I was confused why 3.R2 is drawing, but not 3.R4 since black can check with the knight either way, but it's fairly obvious in hindsight - if black checks instead of capturing, you don't take, you go K2 and force black into zugzwang. Clever.
It took me an embarrassing number of attempts to win.
It was a lot more fun than I first thought!
I don’t know why this is stalemate: N4 N5, N6 K7, R5. Wouldn’t rook have the king in checkmate?
The rook doesnt attack the king because N6 is in the way.
So black is not in check and has no legal moves, so stalemate.
Black has no legal moves because of the knight but they aren't in check
Don't know when was the last time I had so much fun with chess. Quite intuitive, clicked on the first click.
Would enjoy so much if there were more of these, feels like an obligation-free chess puzzle.
I was only able to beat this after a couple retries. The hint was hard to read.
I won after four attempts. Pretty sure it was perfect play so yes white has forced win
Yeah. I think 1. N4 leads to a white win. It's fairly easy to verify that a black rook move will lead to a white win (1...R5 2. R2 and 1...Rx4 2. Rx4 N5 3. Rx5#). So the critical line is 1. N4 N5, but then 2. Nx6+ K7 3. R4 also leads to a win: 3...Kx6 4. K2 K7 5. Rx5# and 3...N3+ 4. K2 N5 5. N8 Kx8 6. Rx5#.
There are probably other ways to win too.
Zugzwang!
Nice, fun and interesting! :)
Finally, a version of Chess I can understand. Thank you.
Oh very interesting. Even with these restrictions, there are quite a few variations, and it seems only one ends up with white winning.
I was expecting a blog post regarding Iran strategy...
That's actually a fun little puzzle.
Hello
It's very interesting and fun!)
Cool idea. This is smart and lean. I like it
Silly nice brain teaser
Nice! :)
Fun stuff, love it!
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love 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 first move after the comma is yours (open with kNight to 4), and the second move is apparently predetermined or always chosen.
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>
There's a coordinate-based solution in the source code issues. I couldn't elucidate that notation either.
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.
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.
I'm not very good at chess, but I dont get why most things are considered a stalemate? I strategically remove all pieces of the enemy, leaving only the king against my rook/tower whatever its called, the king has nowhere to run. In my eyes it's a checkmate. The game just calls it a stalemate. Would be a stalemate if I couldn't do anything, but I can kill the enemy king.
There is an explanation further down. A stalemate is if the enemy has no valid loves and is not in check
It's a stalemate because while the king can't move, he isn't under active attack. There is nowhere he can legally move, but he's safe where he's at.
That rule caught me up too. In regular chess if it is your opponents turn and their only pieces are a king in the 1,8 square and a pawn that is pressed up against one of your pawns and you have rooks in the 2,1 and 8,7 squares that counts as a victory does it not?
No. That is a draw assuming it is the player with only a king’s turn to 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.
But why? That feels like a victory.
Because that’s the rule. There doesn’t have to be a rational reason.
... and if it weren't the rule, it'd make a lot of mid- and late-game play much safer for the player with the advantage. As it is, it's something they have to watch out for, which constrains them somewhat. You have to win, but not the wrong way, and your opponent can attempt to force you to "win" the "wrong way" (resulting in a stalemate).
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.