1D Chess

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bburnt-resistor 3 days ago 172 commentsRead Article on rowan441.github.io

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Discussion (172 Comments)Read Original on HackerNews

hackyhacky•3 days ago

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

anyfoo•3 days ago

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 their long streak in the game.

mckirk•3 days ago

Damnit, I am pretty sure I had a few-year-streak going until just now. Welp, off to the grind again, I suppose.

lamasery•3 days ago

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.

djsavvy•3 days ago

Same here, oddly enough, and every time besides this one was without anyone else mentioning it.

edanm•3 days ago

Yep, just lost after I think >5 years. But not because of your comment, because of GP comment.

jaeh•3 days ago

damn. multiyear streak ruined. i even managed to forget i was playing.

i just lost the game.

olelele•1 day ago

Wow maybe 10+years running here since i lost last..

shmeeed•3 days ago

Nah, I won't be fooled again. I won a long time ago and never looked back.

https://xkcd.com/391

ponkpanda•1 day ago

Damn!

CGMthrowaway•3 days ago

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"

benleejamin•3 days ago

And if you like Mind Chess, you might enjoy Mornington Crescent, which has a similar flavor to it! [1]

[1] https://www.youtube.com/watch?v=lziCsPmlbZI

Mordisquitos•2 days ago

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!

traderj0e•3 days ago

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)

wat10000•2 days ago

This sounds like an inferior, diminished version of Mornington Crescent.

stavros•3 days ago

Wait, how is the "put off checkmate" objective scored? Turns before checkmate? Or what?

Is it just a joke?

hackyhacky•3 days ago

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.

bombcar•3 days ago

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.

contraposit•3 days ago

The Search for the Longest Infinite Chess Game

https://youtu.be/b-Bb_TyhC1A

tylervigen•3 days ago

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."

zeroonetwothree•3 days ago

Isn't the optimal strategy just to say "checkmate" immediately? That dominates anything else.

zadikian•3 days ago

It only works if there are more than two players

jamie_ca•2 days ago

Give two players cards, "Check" and "Checkmate".

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.

stavros•2 days ago

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.

oever•2 days ago

Working at the Mind Chess Café is an interesting job.

rbits•2 days ago

Reminds me of The Button[1]

[1] https://en.wikipedia.org/wiki/The_Button_(Reddit)

adam_patarino•2 days ago

I did not enjoy this

quuxplusone•3 days ago

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.

al_borland•3 days ago

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.

teiferer•3 days ago

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)

pedrosorio•about 13 hours ago

I had claude code implement minimax (w/ alpha-beta pruning) for the general n cells version of the game.

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%.

tromp•3 days ago

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

aktenlage•3 days ago

Very cool. Reminds me of 1D Pacman: https://abagames.itch.io/paku-paku

wes-k•3 days ago

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.

https://megami.starcreator.com/nanaca-crash/

(Failing to find an online version of SFCave a.t.m :'()

aaaasmile•3 days ago

Very cool!

freetime2•3 days ago

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.

forrestthewoods•2 days ago

I still don’t understand the notation. What does N4 N5 mean? The knight can’t move one space? I’m so confused.

slumberlust•2 days ago

First number in the set is your move; Second is Opponents move.

jojobas•2 days ago

Odd moves for white, even for black.

j2kun•3 days ago

How often are you playing as black?

freetime2•3 days ago

As often as the system decides that I should play as black.

SV_BubbleTime•3 days ago

Ha. I thought mine was broken on iPhone for a second.

asibahi•3 days ago

This is really nice.

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

zniturah•3 days ago

Good observation. Considering stacking of pieces maybe 1.5D though.

a3w•3 days ago

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.

traderj0e•3 days ago

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.

moffkalast•3 days ago

Backgammon, the game everyone's seen and at the same time nobody knows how to play :P

dhosek•3 days ago

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).

vscode-rest•2 days ago

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!)

traderj0e•3 days ago

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"

Sharlin•3 days ago

I learned to play backgammon because it was one of the three games on my Nokia phone circa 2001 :P

pessimizer•3 days ago

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.

anthk•2 days ago

Goose/ Snakes and Ladders can be played with no human players at all. There is no interaction, just randomness.

etskinner•3 days ago

Mancala is roughly 1D too!

anthk•2 days ago

Ludo/Parcheese could have been more played among Southern Europe/Latin American people.

gef•3 days ago

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 :)

ctool•about 3 hours ago

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).

xg15•about 18 hours ago

(Chess noob here)

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.

sieste•3 days ago

It took me an embarrassing number of attempts to win.

northfield27•3 days ago

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.

aNapierkowski•3 days ago

you could also just move your king on that move same result knight cant move, only king can, so it has to back away

chedoku•3 days ago

If you like 1D chess, you'll probably like other chess-themed puzzles as well: https://chedoku.com/blog/chessPuzzles

juleiie•3 days ago

That finally confirmed that I am too regarded for chess if even 1D is too hard yay

amrrs•3 days ago

is that str.replace(g,t) ?

juleiie•3 days ago

No. I am actually too highly regarded for measly single dimensional game

MinimalAction•3 days ago

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#

dwa3592•3 days ago

I am ashamed to admit that i could not solve that even though i consider myself a decent player.

keeganpoppen•3 days ago

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.

schmeichel•3 days ago

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

palata•3 days ago

It was a lot more fun than I first thought!

splonk•1 day ago

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.

daynthelife•about 12 hours ago

It clearly doesn't use minimax, since it doesn't play the best move for black in the critical line, leading to a mate in 5 instead if a mate in 6.

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.

topce•3 days ago

I went in other direction ;-) https://topce.github.io/chess960x32/

bdcs•2 days ago

Trying to lose is also fun (as white)

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!)

quuxplusone•2 days ago

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.

mcdeltat•2 days ago

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.

aidenn0•2 days ago

This is part of why so many games on a competitive level end in a draw; the player that lacks a path to victory will try to force a stalemate.

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.

rbits•2 days ago

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.

yuppiepuppie•2 days ago

This is my kind of chess :) I’ve added it to the HN Arcade https://hnarcade.com/games/games/1d-chess

slopinthebag•3 days ago

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.

hart_russell•3 days ago

I don’t know why this is stalemate: N4 N5, N6 K7, R5. Wouldn’t rook have the king in checkmate?

_air•3 days ago

Black has no legal moves because of the knight but they aren't in check

Scarblac•3 days ago

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.

superxpro12•3 days ago

Isnt that a forced move to K8? The king is forced to take N6 or move to K8, either of which results in a capture.

Isn't this the definition of checkmate, not stalemate?

systoll•3 days ago

The relevant rule from standard chess:

> 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.

non-•3 days ago

King isn't allowed to move to a square that would put him in check, so there are no legal moves available. Chess rules.

frunkp•3 days ago

Those who play go may enjoy the variants: https://www.govariants.com/variants/rules-list Tetris is a fun one to try!

ergocoder•2 days ago

There aren't that many combinations. I finally won hahaha

igor47•2 days ago

Oh I made one of these once! In mine you play against other people. https://1dchess.igor47.com/

kkaske•3 days ago

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

anotheryou•2 days ago

Is this stalemate correct? https://imgur.com/a/Z7in8sl

Have not even lost a piece yet!

pbardea•2 days ago

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.

anotheryou•2 days ago

ahhh thanks

daynthelife•2 days ago

It frustrates me that the site does not give the strongest defense for black. The position is mate in 6, not 5:

1. N4 N5

2. Nx6+ K7

3. R4 N3+!

4. K2 N5

5. N8! Kx8

6. Rx5#

otherme123•2 days ago

You give "3 ... N3" a !, when it is literally the only legal move the black has.

hypendev•3 days ago

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.

MagicMoonlight•3 days ago

Why does it end in a stalemate if all my pieces are alive and they have none? That’s not a stalemate, I can move freely and get them.

dargscisyhp•3 days ago

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.

jpablo•3 days ago

https://en.wikipedia.org/wiki/Stalemate#History_of_the_stale...

chris_va•3 days ago

In chess they cannot move onto a spot that would put them in check. If they can make no legal moves, it's a stalemate.

bbx•3 days ago

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

darepublic•3 days ago

I won after four attempts. Pretty sure it was perfect play so yes white has forced win

sdthjbvuiiijbb•3 days ago

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.

sjdv1982•3 days ago

Zugzwang!

vdelpuerto•2 days ago

Took me like 4 resets to solve it.

armanhq•2 days ago

More fun than I expected! Thank you :)

lschueller•3 days ago

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

DemocracyFTW2•about 23 hours ago

0D chess is where real masters shine!

jibal•3 days ago

N4 N5 Nx6+ K7 R4 Kx6 R2 (or K2) K7 Rx5#

tempestn•3 days ago

That's actually a fun little puzzle.

tom-blk•2 days ago

Hehe cool idea, approved!

gcheong•3 days ago

Minor typo: assming -> assuming :)

hybirdss•2 days ago

spent way too long on this before realizing the knight is basically the whole game in 1d

rOOmbambar9•3 days ago

It's very interesting and fun!)

GKakhiani•2 days ago

Haha had a lotta fun

deadlypointer•2 days ago

Even in the winning line black can force stalemate in multiple ways,how is it a forced win?

otherme123•2 days ago

N4, black has three legal moves:

- 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)

keeganpoppen•3 days ago

that took me way longer than i thought it would, but made me all the happier for it

uvdn7•3 days ago

This is something AI would never take away from us.

Dante77711•3 days ago

Nice, fun and interesting! :)

GKakhiani•2 days ago

Haha had some fun

jaani090•about 23 hours ago

interesting game

addybojangles•3 days ago

Silly nice brain teaser

mememememememo•2 days ago

Nice little puzzle!

phplovesong•2 days ago

Basically tictactoe. Ends in a draw every time.

jibal•1 day ago

White has a forced win.

Computer0•3 days ago

I was expecting a blog post regarding Iran strategy...

tkapin•3 days ago

Nice! :)

neverkn0wsb357•1 day ago

This might have a bug. I have the following configuration.

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.

MegaSec•1 day ago

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.

sillyfluke•3 days ago

I honestly thought this post was going to be about the Iran war.

naorz•3 days ago

Fun stuff, love it!

abhinaystha•2 days ago

creative!!!

chatmasta•2 days ago

Wow, Trump’s job is harder than I thought.

Keyframe•3 days ago

This is stupid. I like it!

Nevermark•3 days ago

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.)

BiraIgnacio•3 days ago

love it!

vladde•3 days ago

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

thesuitonym•3 days ago

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...

burnt-resistor•3 days ago

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.

qup•3 days ago

The first move after the comma is yours (open with kNight to 4), and the second move is apparently predetermined or always chosen.

DrammBA•3 days ago

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>

tintor•3 days ago

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.

nippoo•3 days ago

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

Fabricio20•3 days ago

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.

rokkamokka•3 days ago

There is an explanation further down. A stalemate is if the enemy has no valid loves and is not in check

al_borland•3 days ago

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.

umanwizard•3 days ago

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.

jibal•1 day ago

> The first move is always: white rook takes black rook

No. N4 leads to a forced win.