Balancing Act

I’m a lousy chess player, but I’m endlessly intrigued by the game as a field of far-reaching possibilities. Not just for game-play, but as a source of ideas for game design. I’ve designed a few chess variants, and I’m not alone. On the website you’ll find literally hundreds of variants, some of them quite clever and some not only weird but rather dumb.

No chess variant has made it into the mainstream, however, not in recent years. Distinctly different types of chess were developed in both China and Japan, but that was centuries ago. In the 1920s, world chess champion José Raúl Capablanca proposed a variant, reportedly because he was frustrated that high-level players had no choice but to memorize a couple of hundred variations on the opening moves. Capablanca’s design was a simple add-on, with two new pieces on a 10×8 board. Eminently sensible, but while you can buy handsome pieces (a set that includes the marshal and archbishop) and even a 10×8 board, it has never caught on.

This may be primarily due to the installed base problem. There are millions of chess sets already, so when people want to play chess, that’s what they’re going to use. In that sense, it’s not much different from the tuning system used in European/American music: There are many other tuning systems, and ours has some deficiencies, but musicians already own millions of instruments that are built to use it, so anyone who tries to do anything different faces enormous inertia.

Beyond that factor, though, European chess remains unchanged because it provides an almost perfect balance of complexity with economy. Quite a lot of the variants on the chessvariants website are large. Some of them are very large indeed. Armies of pieces with oddball names and movement types face off against one another, so a game becomes less an intellectual puzzle than an exercise in brute force. It’s too hard to keep track of what’s going on. Conversely, making chess smaller makes it too trivial to sustain interest.

The size problem also rears its head when we consider 3-dimensional chess. The smallest playing area (we can’t call it a board) that makes sense for 3D chess is 5x5x5. That’s 125 cells (can’t call them squares), which is already a lot. And the connectivity among the cells is much greater. On a standard board, each square is adjacent to eight others. On a 3D board, each cell is adjacent to 26 others! Keeping track of what’s going on is a mental challenge because of the extra dimension and the high level of connectivity. Yet the pieces on a 5x5x5 matrix are almost too close to one another for comfort.

A hundred years ago, a German fellow named Ferdinand Maack proposed a 5x5x5 variant called Raumschach. I feel it has some weaknesses, so a few years back I proposed a variation I called Five Up. Both of these can be found on the website. The site is kind of a mess, but it’s a good archive of ideas, if you’re interested in such things.

One possible change in chess would be to make some of the pieces more powerful. Yesterday I ran into a neat object lesson that illustrates why this can be difficult. Let’s turn the bishops into archers, I said to myself. In its travel a bishop can leap over one or more contiguous pieces that are in its path. Sounds spiffy, right? Well, here’s a transcript of a complete game that shows why it doesn’t work.


Yes, the white bishop can now checkmate the black king on the very first move of the game. We could change the new rule in various ways to prevent this. Maybe the bishop can leap over only a single piece. But this illustrates why making changes in a design that is already well balanced can lead straight to disaster. At the very least, a lot of play-testing will be needed to determine whether a proposed change leads to a good game.

When I was in high school (more years ago than I’d prefer to recall), it occurred to me that it would be great to be able to play chess with three players rather than two. I acquired a piece of plywood and painted up the board with white, black, and green hexagons, bought a couple of chess sets, and painted one set of pieces green. Great idea, right?

Nope. Terrible idea. Three-player chess is a complete loser as a game. A game of standard chess proceeds through the exchange of pieces of similar value: You capture my knight, and then I capture your bishop. Later, we trade rooks. Each player tries to gain an edge during the exchange — an extra pawn, for instance — and that’s the basic mechanism of the game. In a three-way contest, however, if two players exchange pieces, the third player gains an advantage. That being the case, there’s a profound disincentive to capturing any pieces at all, unless an opponent has foolishly left one unguarded. The game just plain doesn’t work.

I’ve ordered a Paco Ŝako set. (The Ŝ is pronounced “sh.” It’s Esperanto. Whatever.) This is a new variant in which capture is replaced by “union.” No pieces ever leave the board. Instead, they embrace the opponent’s pieces. This may be a viable new variant, though it requires a special set of pieces. It’s vaguely possible that three-player Paco Ŝako would work, but I’ll want to try out the two-player version before I start dreaming about that.

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3 Responses to Balancing Act

  1. mfidelman says:

    And then there are those of us who turn to Go – which seems to require a radically different state-of-mind to play. Still can’t wrap my head around it.

    • midiguru says:

      I used to be vaguely competent at go, but I haven’t played much in recent years. It’s another example of a perfectly designed game — and unlike chess, there’s almost no way to create a go variant that makes any sense. The rules are too simple.

      • mfidelman says:

        Except… there ARE variants to go, that are actually played. Starting with several different scoring systems. And there do seem to be some additional variants that people play. As to the rules, they may look simple, but “subtle” is probably more accurate, or perhaps, “chaotic” – in that very slight changes have a major impact on play (consider Ko, and suicide rules).

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