Forget 3-D Chess; Here’s My 1-D Chess Rules

3dchessChess is sometimes held up as the embodiment of strategy and brilliance — if you’re playing chess while your opponent is playing checkers, you’re out-thinking them. Those even smarter can play chess in higher dimensions, with 3-D chess often used as a metaphor for politics. (There’s even a 5-D chess game on Steam which looks mind-bending.)

But going the other direction, the existence of 5-D, 3-D, and 2-D chess made me wonder: is there a way 1-D chess could work? And be fun, that is.

I’m not the first to have this thought; many people have tried their hand at designing one-dimensional chess including the late great Martin Gardner. His approach was for each side to have a single King, Knight, and Rook at the ends of an eight-tile long board. With so few pieces and spaces it’s fairly easy to “solve” the game, mapping out every possible move the same way we can solve tic-tac-toe.

I set out to create 1-D Chess which kept the spirit of the game as much as possible. It was initially inspired by conversations with Brienne years ago about designing mobius chess (which is topologically identical to playing on a loop, but is *obviously* cooler.)

Values to Preserve

  1. Low complexity – Piece moves are simple, there are few rules
  2. High depth – Many games are possible, with a mix of strategy and tactics
  3. Full information – No fog of war, no hidden cards, no randomness
  4. Personalized openings – Different opening play/counter-play options to match your aesthetics and strengths.

The last one is contentious — I know many people bemoan the amount of memorization required to learn the various chess openings. Bobby Fischer even famously proposed Fischer Random Chess which randomized the back row each game, thus stripping the game down to a player’s ability to understand the situation and respond.

However, I happen to enjoy the way you can study various opening strategies and say “I prefer to use the Alapin Variation to counter the Accelerated Dragon Sicilian Defense — I hate ceding the middle of the board.” Being able to steer the game toward your preferred style before getting into tactical elements of the game is a key part of what makes a game feel like *chess* to me.

So, after a lot of brainstorming and a lot of rejected ideas — see the last section — I whittled it down to a few core concepts. Pictures are worth a thousand words (although I’m sure there are opportunities for arbitrage somewhere…) so here’s a screenshot of the game I started building in Tabletop Simulator:

My Proposal for 1D Chess

RingChessScreenShot

  1. Ring Board – 28 squares; the outside of a standard chess board
  2. 12 Pieces per side – 4 fewer pawns, but otherwise the same pieces
  3. Placement Control – Players take turns placing non-pawns in their region to set up

Ring Board

Look, nobody said it had to be a line segment. Since each square has exactly two neighbors and the entire board is connected, it counts as 1-D.  Put it into polar coordinates if you have to.

Using a 28-square ring allows us to keep the standard chess board, but it also allows much more depth of play without adding complexity to the rules. Like in 2-D chess, you can focus your attack on one side or the other, and you have the ability to try interrupting your opponent’s plans by striking and causing havoc on the other side of the fight.

12 Pieces, Simple Moves

Similarly, I stuck with the original pieces and kept their movement as close in spirit as I could:

  • Pawn: Move forward one or capture two spaces ahead, ignoring the square in front. Cannot turn around.
  • Bishop: Moves up to 6 spaces, 2 at a time (hopping over every other square).
  • Rook: Moves up to 3 spaces forward, 1 at a time. [EDIT: Because the Rooks slide instead of hop, they get stuck easily. My current solution is that they can move *though* the King.]
  • Knight: Jumps either 3 or 5 squares
  • Queen: Can move like the Rook or Bishop
  • King: Moves one square.

This move set creates parallels to the 2-D version: Bishops stay on their color, pawns can get locked together, and Knights have a unique move (5 squares) that not even the Queen has.

The moves themselves stay fairly simple, but allow the kind of interplay that I like in 2-D chess with pieces defending each other and getting in each other’s way.

Opening Placement

Each player has 12 opposite squares to start, with 2 on each end filled by pawns. The remaining 8 squares are up to the players to arrange.

Starting with White, the players take turns placing one of their pieces on an empty square between their pawns.

It’s up to you: You can choose to create an unbalanced attack with both Knights on one side, ready to jump over the pawns and storm the enemy. You can choose to put your Bishops on the inside, where they have an easier time of getting out, or on the outside so that the Rooks are the last line of defense to mop up any attacks. You can leave the King with the Queen — your strongest piece — or between two Rooks…

There are lots of possibilities which rely on how you enjoy playing and how your opponent seems to be setting up. While the complexity of this rule is low, it adds immense depth to the game and prevents it from being quite so easily “solved”.

By requiring the pawns to take up the outermost two spaces, initial move choices are limited to advancing a pawn or using a Knight to hop over them. Moving one pawn can give your Bishops or Queen a way to move through them and enter the fray.  This is all just like in the 2-D version in a way I find aesthetically very pleasing.

If you prefer to just focus on the tactical side of things, you can use the normal ordering or give both players mirrored random arrangements.

Ideas that I considered but didn’t use:

Here are some snippets of ideas that I had but rejected because the complexity/depth tradeoff wasn’t good enough, or the game strayed too far and stopped being recognizable as “Chess”.

  • Making pieces face a direction, limiting them to moving forward
    • Allowed to turn around if the square immediately in front of them is filled
    • Might allow rules that make it easier to capture pieces from the back
  • Pieces can only capture certain types of pieces (in either a rock-paper-scissors style or Stratego style)
  • Ranged attacks without moving
  • Allow pieces to swap with each other
    • Either upon landing on your own, or as a type of movement
  • Pieces that push or pull rather than capture
  • Pieces that move differently when next to certain others
    • Rooks launch pawns, for example
    • The Queen could move in the pattern of any piece in a contiguous chain with her
  • Different terrain
    • Mud tiles which must be stopped on
    • Rocky terrain which prevents knights from landing on it
  • Pieces spawn new pieces next to them as an action

What do you think? Ideas and opinions are welcome!

 

4 Responses to Forget 3-D Chess; Here’s My 1-D Chess Rules

  1. Barry Galef says:

    Very creative! I have a question: if pawns can’t go backwards, do they stop somewhere, or loop-de-loop? If the latter. how do you identify deosil v. widdershins pawns? Oh, and another: Is castling allowed?

    On Sun, Aug 16, 2020 at 4:44 PM Measure of Doubt wrote:

    > Jesse Galef posted: “Chess is sometimes held up as the embodiment of > strategy and brilliance — if you’re playing chess while your opponent is > playing checkers, you’re out-thinking them. Those even smarter can play > chess in higher dimensions, with 3-D chess often used as a me” >

    • Jesse Galef says:

      I was ambivalent on promoting! My intuition is that the pawns are so unlikely to survive very long that the rule is unneccessary. But I would love to be proven wrong!

      Castling seemed tricky given that I wanted the back row customizable — if anything, it might work to say “If the King is next to a Rook, once per game you can switch” but I’m not convinced it’s necessary.

  2. Jesse Galef says:

    Oh, and since the King must be placed in the middle of his 4 pawns and the pawns must move away from their King, there shouldn’t be much confusion.
    Pawns and Kings move one space at a time so they don’t have much opportunity to go past each other*.

    *That said, there IS an edge case in which a pawn is next to the opposing king, captures PAST it, and ends up on the other side. No idea what should happen then!

    • Maybe promote the pawn in that edge case? Then you eliminate memory issues in the rare cases, while also avoiding adding any unnecessary complexity the more normal cases.

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