The Tao of Gaming

Boardgames and lesser pursuits

Does one dimensional chess work?

As a gedankenexperiment, can one dimensional chess work as a game? Would it scratch the same tactical (and positional) itch? My gut feeling is that it would not, but let me try to reason out why.

Chess works (as a tactical game) because you have a variety of threats, and most of the threats deal with interactions between pieces. Some things in chess just don’t really work. A fork threatens multiple pieces. That can strictly be done in one dimension (a rook or bishop can fork by moving). Discovered attacks by moving out of the way become more difficult, unless you have pieces that effectively move every N squares (skipping over the square in between). These are one-dimensional bishops, although an argument could be made that modular arrays create a second dimension I’ll let it slide, since developing a one-dimensional chess variant that’s interesting is probably a hard problem. Given that some very clever people (including Sid Sackson and Martin Gardner) have tried, I’m going to just go ahead and say that one dimensional chess doesn’t work.

Why? There’s some interaction between the various dimensions. As we’ve forks become much more common and interesting, pins, discoveries, etc proliferate. You need restrictions in a game (as we’ve noted before, letting people move every piece doesn’t work). There’s nothing particularly magical about a single move — double move chess can work — but letting every piece move means you can’t fork, pin, and the like. The game falls apart.

Now, in most games (non-chess) the term “dimension” is more abstract. There are constraints. Not necessarily spatial. They may be temporal (X actions per turn), economic (a literal cost). You may have random constraints (roll and move or other randomizers). You may have incomplete information. You can like big sprawling games (ahem), but if it isn’t just a salad … if the design is actually good, you pare and trim. As the man said…

A designer knows he has achieved perfection not when there is nothing left to add, but when there is nothing left to take away. — Antoine de Saint-Exupery

Star Trek got it wrong — 3D chess isn’t an improvement over chess, but neither is 1D. Two dimensions is enough for the game to express itself. 3D chess can exist, but it exists as an inferior product. Similarly, 1D chess is inferior.

I don’t think this is particularly controversial, but perhaps I am wrong. I suspect I may be wrong trying to generalize it to other (non-abstract) games, but non-abstracts live across a huge variety of dimensions. How do you compare Food Chain Magnate (which as spatial, temporal, economic, organizational, etc) with superficially similar 18xx — both games are about building and growing a business on a spatial map, but feel nothing alike (to me). They share a few dimensions, but the dimensions they differ on (the fact that the player is 100% owner in FCM and may suffer from agency issues in 1830, for example) make the games distinct.

It’s a complex issue.

All of this propelled by the thought I had earlier tonight — If Power Grid: The Card Game works as a game, does that mean that Power Grid (the board game) is 3D chess and we just didn’t know it?


Written by taogaming

January 3, 2017 at 12:50 am

Posted in Ramblings

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  1. I remember a Martin-Gardner-column about 1-dimensional chess and the discussion, how much of it is solved (as for checkers, I think).

    peer sylvester

    January 4, 2017 at 11:26 am

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