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.
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 their long streak in the game.
I think once you lost the game once, it's much easier to lose it again relatively shortly after. It takes some long term distraction (and nobody mentioning it) to forget about it again.
Absolutely! Visualising a long string of opponents saying 'Check' to each other until one calls the checkmate reminded me of when you and your opponent both take the classic dub-Victoria understrategy and repeatedly 'Parsons Green' each other. Such memories!
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"
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)
The sibling comment proposed a possible scoring mechanism which might result in enjoyable gameplay, but I think the bigger point (for me, at least) is the Mind Chess represents a reducto ad absurdum of the strategy game genre. It eschews as many rules as possible, leaving you only with the goal of knowing your opponent's mind. So Mind Chess is more of a thought exercise.
It's similar to the 2-minute version of Diplomacy - get everyone together and the second sneakiest bastard wins; because nobody will let the sneakiest bastard win.
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."
I think to have any chance of making this work, you’d need to have a community of players in a tournament. Everybody gets to issue some number of challenges, and the winner is the person who accumulates the most points over the course of the tournament. I think you should only get points based on the length of games you win.
Then the game at least has a chance to develop some mechanics. Players who delayed longer have a chance at winning more points. They also might be challenged more…
Not in an iterated game. If my team agrees we'll never checkmate before turn 5, the game is the same except we start the actual game on turn 5 with a big score advantage compared to everyone else.
You can leave at any time by breaking the rule, but then you will be playing with other people who say checkmate immediately, and that would be much worse.
Being prosocial is in fact a stable equilibrium. As prophecized by gestures broadly at everything.
Both players choose a card. Players then in turns reveal their card, and if Check, make another choice. The player first revealing Checkmate wins if their opponent's currently-chosen card is also a Checkmate.
But then this just gives the win to the first person to open their card, since in that round they had both selected Checkmate. Or, you have an incentive to rush to open your card when you know you've selected Checkmate, as you want to be the first one to open.
Maybe I should've worded differently for clarity, the game doesn't go forever:
The player first revealing Checkmate ends the game. They win if their opponent's currently-chosen card is also a Checkmate, otherwise the opponent wins.
In the proposed game above, there is no rounds, just alternating plays, in which you have to select you play before the other player announces their play, then swap and repeat
So both players select their cards, then player 1 announces, then player 2, then select, then player 2 announces, then player 1? This seems a bit limiting, as you can't really select Checkmate on the play where you don't reveal first, because you only stand to lose.
Yeah, but what stops P1 from DDos'ing and picking checkmate each time?
If P2 picks check the first time, then they're done. At any point after if they pick checkmate, since P1 has checkmate selected they will reveal it and P2 will lose.
You're assume if someone picks 'checkmate' and the next player picks 'check' the games is over and the checkmate selector loses. I assumed that it means you treat it like 'check' 'check' and continue playing. But neither is actually specified in OPs post.
But let's assume it's your rules. Then winning is easy, just never pick checkmate. Literally never. As soon as your opponent picks it, they lose.
So is war (the card game), but people still play it
I think the proposed game has that both of you lose, like tic tac toe. The only way to win is to checkmate as described. Although it is a memoryless game as proposed, so all options (restart, continue, end) are indistinguishable. Maybe if you win, you go again?
Anyways, the game seems to be described to be the equivalent to the political doctrine of mutually assured destruction. Also a terribly designed game.
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.
I love this! Such a simple game with a fun level of skill. High score 17485 feels pretty good (edit: Oh! Low power mode on the computer makes the game run slow, thus much easier to get crazy high scores).
Reminds me of SFCave and Nanana Crash for the simplicity and surprising replay ability.
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 it's not the same.
That's a good point, you could surely model full chess in a single dimension, it would just be that each pieces' movement rules would be more confusing
E.g. a pawn can move exactly 8 squares towards its opponents end (16 on its first move if no piece occupies 8 squares away), but can only capture 7 or 9 squares forward (with some extra modulo math to prevent wrapping)
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).
You’d be surprised – take a Backgammon board to a table in at a cafe in a popular area and chances are someone will sit down to play with you. Can be a good way of meeting people in a new area. (or new people in an old area!)
It was a good way to while away the time at jury duty back in the days when you had to physically be there until you were called. I encountered a tournament player who beat me maybe 4 times out of 5. I also played in a chess tournament where my opponent was considerably stronger and faster and quickly put me in a position where I had to think long and hard to try to avoid disaster (fruitlessly in the end). She would make her move, wait a few seconds to see if I would reply, and then get up and disappear into a back room where, I found out later, she was playing backgammon. I looked her up and learned that she was a rapidly rising women's chess star but was better known as a semi-pro backgammon player.
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.
I tried and failed a couple times before looking at the hint. And then I had to ask ChatGPT to explain the hint because I didn't understand chess notation. But with all of that out of the way, I am now winning 100% of my matches and feel it's not an overstatement to call myself a 1D chess grandmaster.
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 :)
Always found the "protect the king" rules in regular chess interesting but also somewhat strange. (The rules that make it impossible to actually take a king and instead let the game reason on the "possibility" that a king could be taken in the next turn - i.e. check and checkmate)
As long as only check and checkmate are considered, the rules are a bit weird, but should not change the game dynamics, as they only enforce the moves that any rational player would do anyway.
But adding stalemates to it seems to actually change the gameplay, and this 1D variant makes it even more obvious.
If you compared this chess variant with a 1D chess where the king would behave like a normal piece (except taking it would end the game) and any draw would have to be called manually, the game would behave completely different.
just work backward from the moves it allows you to make— it tells you when it’s hopeless, so thus if it lets you move, you’re onto something. took me like 9 or 10 tries easily.
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#
A workable minimalist variant is slimchess, which contains one of each piece on a 3x8 board. It's the smallest chess board that can preserve all the rules (including castling).
How do you mate with N+K? Surely your King can't give check, and if your Knight is giving check then the enemy king can just take a step toward it to get out of check.
It's interesting that the page actually uses minimax to determine black's play. I kind of assumed it would be a simple lookup table given the small state space of the game. I suppose it makes it easier to add more variants.
Ok seems like I don't understand and really dislike chess stalemate/draw rules. So if I make a move which is directly causative to my opponent having no moves which would not result in checkmate, this means the same is a draw?? That makes no sense to me.
I think it's because the rules of chess don't state that making a move that puts yourself in checkmate results in a loss, they state that you're straight up not allowed to make that move. So if the only moves you have left would put you in checkmate, they're not legal moves.
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.
If it's black's move then yep! The king is not in check and it cannot move right otherwise it's in check by the knight and it cannot take left since it'll be in check by the rook.
That is a standard rule in chess. If your opponent has no legal moves (i.e. no way to move without moving his king into check) and is not currently in check, it is considered stalemate, which is a draw.
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#.
I don’t think it is a bug, the enemy king can’t move back to X because the knight is attacking that space. Traditionally you can’t move into check in chess.
I thought for sure this article was going to be political commentary!
(I would pay a lot for some fat 1500 page, leather-bound tome of wisdom and anecdotes about historical foot guns, by Carl von Clausewitz, titled "1D Chess". And it's inevitable multi-authored, Harvard-published much thicker contemporary-world sequel.)
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.
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>
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.
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.
... 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.
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
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 their long streak in the game.
Like, five or so losses this year.
i just lost the game.
https://xkcd.com/391
[1] https://www.youtube.com/watch?v=lziCsPmlbZI
Is it just a joke?
https://youtu.be/b-Bb_TyhC1A
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."
Then the game at least has a chance to develop some mechanics. Players who delayed longer have a chance at winning more points. They also might be challenged more…
You can leave at any time by breaking the rule, but then you will be playing with other people who say checkmate immediately, and that would be much worse.
Being prosocial is in fact a stable equilibrium. As prophecized by gestures broadly at everything.
https://en.wikipedia.org/wiki/Camping_(video_games)
Both players choose a card. Players then in turns reveal their card, and if Check, make another choice. The player first revealing Checkmate wins if their opponent's currently-chosen card is also a Checkmate.
The player first revealing Checkmate ends the game. They win if their opponent's currently-chosen card is also a Checkmate, otherwise the opponent wins.
1: P1 selects 2: P2 selects 3: P1 reveals 4: P1 selects 5: P2 reveals 6: GOTO 2
I.e. each player always selects immediately before their opponent reveals.
If P2 picks check the first time, then they're done. At any point after if they pick checkmate, since P1 has checkmate selected they will reveal it and P2 will lose.
It seems like a poorly thought through game...
You're assume if someone picks 'checkmate' and the next player picks 'check' the games is over and the checkmate selector loses. I assumed that it means you treat it like 'check' 'check' and continue playing. But neither is actually specified in OPs post.
But let's assume it's your rules. Then winning is easy, just never pick checkmate. Literally never. As soon as your opponent picks it, they lose.
It's a terribly designed game as described.
I think the proposed game has that both of you lose, like tic tac toe. The only way to win is to checkmate as described. Although it is a memoryless game as proposed, so all options (restart, continue, end) are indistinguishable. Maybe if you win, you go again?
Anyways, the game seems to be described to be the equivalent to the political doctrine of mutually assured destruction. Also a terribly designed game.
[1] https://en.wikipedia.org/wiki/The_Button_(Reddit)
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)
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%.
[1] https://senseis.xmp.net/?Alak
[2] https://tromp.github.io/go/gostate.pdf
Reminds me of SFCave and Nanana Crash for the simplicity and surprising replay ability.
https://megami.starcreator.com/nanaca-crash/
(Failing to find an online version of SFCave a.t.m :'()
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.
I'm fine calling Backgammon 1.5-D. Physically you focus on a single dimension, and the second one matters too but it's not the same.
E.g. a pawn can move exactly 8 squares towards its opponents end (16 on its first move if no piece occupies 8 squares away), but can only capture 7 or 9 squares forward (with some extra modulo math to prevent wrapping)
Always found the "protect the king" rules in regular chess interesting but also somewhat strange. (The rules that make it impossible to actually take a king and instead let the game reason on the "possibility" that a king could be taken in the next turn - i.e. check and checkmate)
As long as only check and checkmate are considered, the rules are a bit weird, but should not change the game dynamics, as they only enforce the moves that any rational player would do anyway.
But adding stalemates to it seems to actually change the gameplay, and this 1D variant makes it even more obvious.
If you compared this chess variant with a 1D chess where the king would behave like a normal piece (except taking it would end the game) and any draw would have to be called manually, the game would behave completely different.
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.
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#
Some observations:
* Knights are color bound
* You can mate with Knight & King (K+K is still insufficient material)
* 3 fold repetition still applies (and has a popup!)
Best line is N4 N5, Nx6+ K7, R4 N3+!, K2 N5, N8! Kx8, Rx5#. The site has black instead play Kx6 on the third move, allowing a faster mate.
Since this makes it harder for the player with an early advantage to win (by constraining their moves), it is considered a feature, not a bug.
So black is not in check and has no legal moves, so stalemate.
Isn't this the definition of checkmate, not stalemate?
> Leaving one’s own king under attack, exposing one’s own king to attack and also ’capturing’ the opponent’s king are not allowed.
N6 and K8 both expose the black king to attack, so black is not allowed to make those moves. And with no other options, black has no legal move.
And since black isn't in check where they are right now – that's a stalemate.
Would enjoy so much if there were more of these, feels like an obligation-free chess puzzle.
1. N4 N5
2. Nx6+ K7
3. R4 N3+!
4. K2 N5
5. N8! Kx8
6. Rx5#
Have not even lost a piece yet!
There are probably other ways to win too.
- RxN RxR, N5 (unique), RxN 1-0
- R5, R2 RxN (if R6, NxR, 1-0), RxR N5 (unique), RxN, 1-0
... N5 NxR+ K7 (unique), R4 KxN (if N3+, K2 N5, N8 KxN, RxN 1-0), R2 K7 (or N3, RxN 1-0), RxN (1-0)
K - King H - Knight R - Rook E - Enemy King X - Empty
K X X X R K E X
But it indicates it’s a draw by stalemate.
There is only 1 legal move for black here. Which is to move back to X. If it takes my Knight rook gets it.
He moves back, I move my Knight out of the way. Checkmate.
Edit: oh wait nvm there’s no legal move for black.
(I would pay a lot for some fat 1500 page, leather-bound tome of wisdom and anecdotes about historical foot guns, by Carl von Clausewitz, titled "1D Chess". And it's inevitable multi-authored, Harvard-published much thicker contemporary-world sequel.)
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.
No. N4 leads to a forced win.