Zendo is one of those creations that makes people slap their foreheads and say “why didn’t I think of that?” It’s just so darned simple. Surely the idea must have sprung fully-formed into its designer’s brain, just ready to be played? What else could possibly have been required? A weekend of tinkering, perhaps, but certainly no more than that?

Of course, that’s not really how the creative process works. Hindsight, as they say, is 20/20. Ideas that seem obvious later on are not so obvious at the beginning of a project, when you’re stranded in the vastness of design-space without even a signpost in sight. The first versions of Zendo were clunky, ugly, and complex. The playtesting team and I spent literally hundreds of hours, over a period of many months, molding the game into its final form. This essay tells the story of that process—sometimes in excruciating detail.

Why the detail? Quite simply, I’m obsessed with game design, and with the process of creation in general. My view of design is evolutionary—a wild spinning-out of variations to be tested, selected, and mutated, over and over again, to the nth power. The details of this process, the twisted trees of possibility explored during creation, are endlessly fascinating to me. Rather than paper-over these details in favor of a pristine, cleaned up vision of how Zendo actually came to be, I want to emphasize the messy details. I revel in them. This evolutionary process is where the fun really lies. I’m a staunch disbeliever in the magical view of creativity. Ideas don’t just spring fully-formed into their creators’ brains—at least, not without a lot of unconscious, non-magical evolutionary work leading up to them. The ideas that led to Zendo were bubbling around in my head for over ten years before they finally began to boil over.

Initial Inspiration

Many years ago, while I was browsing around at my local library, an interesting-looking bright orange book caught my eye. It was called A Gamut of Games, and it was full of the most inventive and fascinating games I’d ever seen. Its author, Sid Sackson, described himself as “the president and chief archivist of a very informal group with a very formal name: New York Gaming Associates, or N.Y.G.A., for short.” The group met at irregular intervals to play and criticize games that they’d designed themselves. Most of the games in the book had been designed by Sackson and his friends. I’d never heard of anyone doing such a thing before. I was fascinated, and a bit envious.

One of Sackson’s creations was an “induction game” called Patterns II, in which one player creates a secret pattern of symbols in a grid, and other players attempt to figure out the pattern by doing “experiments”—i.e., selecting small bits of the pattern to view. In his introduction to the game, Sackson made reference to another induction game called Eleusis, which was designed by N.Y.G.A. member Robert Abbott. Eleusis sounded even more fascinating than Patterns II. I had to know more.

A version of Eleusis had been featured in the October 1977 issue of Scientific American, in Martin Gardner’s classic “Mathematical Games” column. Eventually, I tracked down a reprint of the article in Gardner’s book Penrose Tiles to Trapdoor Ciphers and found out how this game actually worked. In Eleusis, one player (“God”, or “Nature”) comes up with a secret rule that dictates how standard playing-cards must be played in a sequence. For instance, “A red card must be played after a black card, and a black card after a red card”. Players (“scientists”) take turns playing cards from their hands onto the global sequence. They are rewarded for following the rule, and are penalized for breaking it. At some point in the game, a player may become the “Prophet”, and must correctly judge the plays that other players make, while the other players attempt to “overthrow” the Prophet by making plays that they think the Prophet will misjudge. Players never actually guess the rule out loud in Eleusis. They simply figure out as much of the rule as they can, and try to use that knowledge to achieve the highest score.

This all sounded fascinating to me. I carefully copied all of the rules onto a sheet of binder paper, and tucked it away safely in a drawer. I kept that sheet of paper for years, always hoping I’d get a chance to play the game. I never did.

In the meantime, however, a new shape had been created in my head: the Induction Game. I wanted to find more of them, but, as both Sackson and Gardner had pointed out, true induction games such as Eleusis and Patterns II were few and far between. Somehow, in the zealous naiveté of youth, I took these statements as a personal challenge. I will invent my own induction game, I thought to myself. The next ingenious induction game featured in Scientific American will be mine. Oh yes, I thought. It will be mine.

Inductive Parlor Games

Well, the years passed (as they often do), and my induction game didn’t just magically invent itself (as they often don’t). I went on with the normal business of life, shoving the project onto the back-burner along with a hundred others that I didn’t know what to do with. But the seed had been planted, and some part of my unconscious mind began chewing away on the problem. This lateral-drift process lasted for years. Every once in a while, a new piece of the puzzle would click into place, and the thing would surface in my consciousness for a while before submerging again.

For instance, at one point I realized that I already knew a number of common parlor-games that qualified as bona-fide induction games. I’d played a game called “Crossed and Uncrossed”, in which everyone sits in a circle and passes around a pair of scissors, and as each player passes them he or she says something like “I’m taking these crossed, and passing them uncrossed“. However, the “correct” answer doesn’t always match the state of the scissors, and the object of the game is to figure out what the pattern really is. The players who’ve already figured it out tell the other players when they’re correct or incorrect, and show them many examples of correct statements, until eventually everyone’s caught on to the secret rule. Similarly, in “Bang Bang”, one person points at someone else and says “bang bang!” (or some other variation on that theme), and the players have to figure out who just got shot (and it’s usually not the person who was just pointed at). Once again, there’s a pattern behind it all, and the game continues until all the players have figured it out. An unfortunate aspect of these puzzle-games (spoilers ahead) is that, unlike Eleusis, they can only be played once per group, because the solution to the puzzle always turns out to be a special kind of “trick” around which the game was obviously designed, and which has nothing to do with the ostensible focus of the activity. For instance, in Crossed and Uncrossed, you’re supposed to answer based on whether or not your legs are crossed when you receive and pass the scissors. In Bang Bang, the first person to speak after someone says “bang bang” becomes the one who gets shot. I sometimes refer to these puzzles as “shaggy-dog puzzles”, because players often feel like they’ve been lead on a mental wild-goose-chase, searching for something much more complex than the actual answer turns out to be. But of course, part of the whole fun of these problems is that they provide such great “ah-ha!” moments for the players who finally “jump out of the box” and realize what the answer is. And, “tricks” or not, these puzzles still capture the juicy essence of inductive reasoning, since solving them requires at least rudimentary forms of theory-building, experimentation, and falsification.

One of these games in particular had a profound influence on my own later thoughts about Zendo. I don’t even know the name of the game. Let’s call it “The Five Pencils Game”. I first encountered it when I was in high-school. One evening, for no particular reason, an older friend of mine showed it to me and a bunch of my friends. He started by nonchalantly laying five pencils out on a table and asking “what’s this?” We had no idea what he meant, so he said “well, this is a five.” Then he picked up one of the pencils and laid it across the other four, and asked “what’s this?” We still didn’t know, so he told us “this is a four.” We started to get the idea, and began making our own tentative guesses as he set up different configurations: “Is that a three?” “No, that’s actually a two.” The numbers were always between zero and five, which suggested that the answer was always equal to the number of pencils which were doing… something. (Touching the table? Pointing at another pencil? Touching another pencil?) But the longer the game went on, the more random the answers seemed. We started taking turns setting up our own experiments with the pencils, and grumbling as the answers failed to support our theories. At some point my friend started randomly tossing the pencils down onto the table and letting them lie wherever they fell, asking “what’s that?” And then things got really confusing when we made him set up some of the configurations we’d already seen, and the answers were different. Very suspicious! Yet I was certain that there was a pattern, because some of the players had already figured it out—they were able to state each answer correctly, in unison, even before my friend did. By that time I’d gathered enough evidence (including the amused expressions I saw on player’s faces when they figured it out) to convince me that the answer didn’t have anything to do with the pencils at all. Eventually I figured out the real secret: the “answer” to each configuration was simply equal to whatever number of fingers my friend was quietly displaying with his left hand!

Well, this was all very amusing, and in fact, the little exercise had some genuinely interesting things to say about the mental mechanisms involved in solving problems, getting “stuck”, questioning assumptions, performing mental paradigm-shifts, thinking-outside-the-box, and so on. Nevertheless, I couldn’t help feeling disappointed that the secret didn’t have anything to do with the pencils themselves, because the process of trying to figure out that problem had been so much fun! My encounter with this puzzle occurred years before I’d discovered A Gamut of Games, so it didn’t occur to me then to try to make a real game out of it. Nevertheless, my subconscious mind had taken a deep and lasting imprint on an important fact: there’s something extremely compelling about the activity of setting up configurations of objects and trying to figure out some underlying pattern based on them.

Bongard Problems

A second piece of the puzzle that I stumbled onto during these years was Douglas Hofstadter’s discussion of “Bongard problems” in his classic work Godel, Escher, Bach. The original Bongard problems were invented by a Russian computer scientist named Mikhail Bongard, and were featured in his book Pattern Recognition. Each problem consists of a number of simple diagrams. They can be of virtually anything, but most of the time they’re abstract collections of lines and geometric shapes. The diagrams are divided into two groups—half on the left, and half on the right. There’s something that’s true about each diagram on the left that’s not true about any of the diagrams on the right. The object of the problem is to discover what this distinction is.

Not only were Bongard problems fascinating in their own right, but they resonated deeply with the ideas that I’d been sub-consciously toying with. Here again I’d come across the central idea of searching for patterns among static configurations of “stuff”. Indeed, some of the diagrams in the Bongard problems reprinted in GEB even resembled jumbles of pencils! But, unlike the old Five Pencils Game, the answers to these problems were not “tricks”, but were actually based on the diagrams themselves. Furthermore, the Bongard problems suggested a nice simplification of the “zero-to-five” scale. Bongard problems are “binary”—each diagram either follows the rule or it doesn’t. Finally, the Bongard problems introduced the key idea of laying out many different configurations at the same time, some of which followed the rule and some which did not.

Nevertheless, the Five Pencils Game did have one key thing going for it: it was interactive. Players actually got to set up their own configurations and test their developing theories. Bongard problems, on the other hand, consist of carefully pre-designed diagrams, and all you can do is study them until you see the pattern. They’re puzzles, not games. Of course, it’s easy to see in hindsight where this thought leads, but it took me a long time to see it. Had I clearly formulated the concept of “Interactive Bongard Problems” back when I first read Godel, Escher, Bach, Zendo (in some form) may have been born years earlier than it actually was.

The Internet

Something else of staggering importance occurred during these years of lateral-drift: the Internet was born. I vividly remember the day when I finally tossed out my weathered sheet of binder-paper containing the rules to Eleusis. Why hang on to something so archaic as a piece of paper, when I knew I would be able to locate that information any time I wanted simply by typing “eleusis game” into the nearest Internet search engine?

At some point, I also came across Harry Foundalis’ fabulous web pages about Bongard problems, which include all of Bongard’s original 100 from Pattern Recognition, as well as many more creations by Hofstadter and others. (Foundalis is working on a computer program to solve these kinds of problems.) This site proved to be an invaluable resource during the design of Zendo, when I was doing a lot of thinking about what kinds of rules and puzzles could be constructed, and about terminology problems, and so on.

Jewels in the Sand

During these years I made a couple of other Internet discoveries worth mentioning. One was Stanley Anderson’s game “Jewels in the Sand“, which is somewhat like the Five Pencils Game or Bongard problems, but uses words rather than configurations of stuff. In this game, the “Sultan” comes up with a rule which divides all words into two categories: “jewels” and “sand”. (An example rule is “all words that describe objects with wheels are jewels. All other words are sand”.) The Sultan begins the game by providing an example “jewel” word and and an example “sand” word. Then the actual play of the game begins. But the interesting twist is that the players don’t propose new words to test—instead, they propose rules. After each proposal, the Sultan provides (if possible) two counter-examples: a “jewel” word that the proposed rule says should be “sand”, and a “sand” word that the proposed rule says should be a “jewel”. Sometimes only one of these can be provided, indicating that the player has discovered a subset or superset of the correct rule. When neither can be provided, this indicates that the player has discovered the correct rule, and has won the game.

My friend Dave Bender and I played this game a few times, but it wasn’t long before we ran into problems. First of all, there was the “form/content” issue. Most rules revolve around categories or meanings (content)—i.e. “any word that describes an animal is a jewel”, or “any word that describes a thing that has a lid is a jewel”. However, it’s also legal to make rules that revolve around the form of the word—”any word that has five letters is a jewel”, or “any word that ends in a vowel is a jewel”. A rule like this can be interesting if you’re unaware that it’s allowed. Solving it will probably produce a nice little “ah-ha!” moment. However, once you’re aware that these kinds of rules are allowed, they become somewhat mundane, and (to me) even slightly annoying. In every new game, you have to figure out whether the rule involves “form” or “content” (or a combination of both). However, this is no longer an interesting problem—in fact, it feels more like drudgery than anything else. Since Dave and I found “content” rules to be more interesting, we simply agreed not to use rules that referred to “form”.

However, our focus on “content” rules uncovered a much more serious problem—the inescapable fuzziness and ambiguity of all concepts and categories. This came through quite clearly in my very first game as the Sultan. I used the rule “any word that describes something that explodes is a jewel”. Almost immediately, I ran into problems—what, exactly, should count as something that explodes? Dynamite? Certainly. A volcano? Probably. A car? Uh… possibly. A balloon? A can of soda? An angry person? A political crisis? Well… obviously it depends on how loosely you use the word “explode”. But virtually every word in the English language has a similar halo of meanings surrounding it, and any binary division like the one this game demands is bound to be arbitrary. Furthermore, the whole idea runs up against the vast world of physical fact. Do we even know exactly what does and doesn’t explode? Does spontaneous human combustion actually occur? Probably not, but the players may not all agree on this “fact”. From the point of view of statistical or quantum mechanics, it’s “possible” for even relatively inert substances to explode—it’s just extremely unlikely. So perhaps the rule should be “things that commonly explode”—but what counts as “commonly”? Where do you draw the line? This whole issue was so annoying, and so all-pervasive, that it undercut any interest we had in playing the game.

Nevertheless, “Jewels in the Sand” planted some important seeds in my mind. For one thing, it introduced the idea of starting a game off with two initial examples, and it also introduced the idea of providing counter-examples to player’s guesses. (As you’ll see, I resisted applying these ideas to Zendo for a surprisingly long time.) “Jewels in the Sand” also gave me an early heads-up about ambiguity problems in these kinds of games.

Those Protean Pyramid-Shaped Pieces

After “Jewels in the Sand”, I made one further discovery relevant to my hypothetical induction game: I learned about the Icehouse pieces.

I first heard about the pieces late in 1997, when I came across some of Andy Looney’s web pages. Andy was a game designer who’d invented a card game called Fluxx. He and his wife Kristin were running an independent game-publishing company named Looney Labs, with Fluxx as their flagship product. In addition, his pages also contained information about a game called “Icehouse” that he and his friend John Cooper had invented years ago. Icehouse was played with a set of pyramid-shaped pieces of four different colors and three sizes. The play involved placing these pyramids in positions of attack and defense, with upright pieces as defenders and pieces lying on their sides as attackers. The interesting twist was that the game was played with no board and no turns—it was a totally free-form game played on any flat surface, with players playing whenever they wanted and placing their pieces however they wanted. I’d never heard of anything quite like it before.

Truth be told, I wasn’t particularly excited by the game itself—I generally don’t like real-time games, so it didn’t sound like my kind of thing. However, I was immediately captivated by the pieces. I immediately understood the deep generality of the design—an Icehouse set was like a deck of standard playing cards for piece-based games. I envisioned that countless other fascinating games could be designed for them. Indeed, Andy and John and others had already begun inventing them. I was particularly intrigued by John’s magnum-opus, Zarcana—an intricate territorial game of war and magic played with Icehouse pieces on a board of Tarot cards. But beyond all of this, I was excited by the mere existence of this fascinating group of game-designers and players that had collected around these pyramid-shaped pieces—an informal group with a very formal-sounding name: The Wunderland Toast Society. I envisioned the possibility of a book like Sackson’s, filled with Icehouse games designed by members of the WTS (a vision which has since become a reality).

In those days, if you wanted a nice Icehouse set, you had to make it yourself out of wood, clay, or melted plastic. However, if you didn’t have the time, patience, or know-how to tackle a project like that, there was a commercial option available: “Origami Icehouse”, a set of fold-up, colored-paper pyramids that Looney Labs sold for about two dollars. I settled for the paper set. Throughout 1998, I faithfully read Andy Looney’s weekly news page at wunderland.com, watching as members of the WTS continued to add more and more great content to the site, and Looney Labs itself continued to grow as a game company. I initiated email conversations with John about Zarcana, and about game design in general. Late that year, John released the rules to a new game called IceTraders—a planetary space-battle game that introduced some fascinating new concepts of Icehouse game design. I was excited, but also frustrated—my friend Dave was about the only person I knew who was interested in playing games like this, or helping me design some of my own. Finally, in the spring of 1999, I couldn’t stand it any more—I started designing Pantopia, a territory-based Icehouse game inspired by Zarcana, but using Aquarius cards instead of Tarot cards. (Aquarius was Andy’s second card game, and had been recently released by Looney Labs.) In addition, I decided I wanted to learn the Java programming language, and, as a starter project, I began working on a Java version of Aquarius. In the meantime, an exiting new development loomed on the horizon: the Looneys were in the process of manufacturing beautiful new sets of translucent plastic Icehouse pieces. The new pieces were going to be hollow and open at their bases—a feature that began as a financial necessity, but quickly turned into a blessing in disguise, since the ability to stack and nest the pieces opened up whole new dimensions of design-space to explore.

As the year wore on, I grew more and more bored with my job, the Bay Area, and my life—it was time to try something different. I finished just enough of Javaquarius to feel comfortable unveiling it to the Looneys. They liked it, and we began talking about putting it up on the Wunderland site. In the meantime, one of the members of the WTS, Jacob Davenport, had taken an interest in Pantopia, and (to my delight) had talked other people into playing at Wunderland. He had a lot of great feedback, and we had long email discussions about how we might make the game better.

Throwing caution to the wind, I invited myself out to Maryland for a visit. There, I got a chance to play Pantopia with Jake (and lose), demo Javaquarius for Andy and Kristin, play some late-night Aquarius with John and his wife Gina, and drive around the shady, quiet streets of Greenbelt, MD. It was a terrific trip, and I returned to the Bay Area—with a plan beginning to form.

Zendo is Born

Shockingly, it wasn’t until around this time that I finally realized that the Icehouse pieces were perfect for the induction game that I’d been imagining all those years. The moment I thought about it, my mind was flooded with possibilities. The attributes of color, size, orientation, pip-count, pointing, touching, stacking, and nesting suggested an endless number of interesting rules to try. These colorful pieces would be so much more interesting to fiddle around with than a bunch of pencils!

The idea of using Zen as a central theme occurred to me soon after the revelation about the Icehouse pieces. Although I knew that Zen had nothing to do with colored pyramids or inductive logic, something about the activity of building and studying these little crystal-like groups of pieces seemed quiet, meditative, and mystical. I’d already envisioned using black and white markers to represent the two different “states” that a configuration of pieces might be in. The image of the yin-yang sprang to mind. I thought of all the strange Zen koans that I’d read over the years, in which students were always asking Zen Masters whether or not things had the “Buddha-nature”, and achieving sudden enlightenment. Similarly, I envisioned players asking a “Master” whether or not different configurations of Icehouse pieces had the Buddha-nature, and experiencing the “enlightenment” of figuring out a rule. I started calling the configurations themselves “koans”—after all, each of them seemed to present its own little riddle for the players to meditate upon. (Although I didn’t think about it at the time, I was undoubtedly influenced by Hofstadter’s fascinating “MU Offering” dialog in GEB, in which Achilles and the Tortoise discuss a method of determining whether or not certain koans have Buddha-nature.) I started calling the game “Zendo”, which is simply the Zen term for a meditation hall. The name stuck.

Proof of Concept

The obvious next step was to talk Dave into to helping me try a few rules. We decided that we’d take turns being the Master. On my turn, I’d come up with a rule, and Dave would simply start building whatever koans he wanted, changing or destroying existing ones as desired. I’d tell him whether each koan had Buddha-nature or not, and he’d keep playing until he figured out the rule. For the truly detail-obsessed reader, I can still remember the very first Zendo rule ever played: “a koan has Buddha-nature if all of its pieces are pointing in different directions.” I watched as Dave struggled to figure out this seemingly simple rule, creating “superstitions” and false patterns for himself. Then he tried a rule on me, and watched as I struggled. Clearly, there was a whole world here to be explored.

I started to get excited.

Of course, I knew that there was no game here yet. All I had so far was a fascinating little single-player puzzle. I wanted to turn the concept into something more than simply setting up koans and trying to guess the rule, but I had no clear idea of what this “something more” should be. However, after all those years of keeping the thing on the back-burner, I was finally onto something, and I was happy to be patient and let the idea simmer a little while longer.

Joining the WTS

And it was going to have to simmer a little while longer, because I’d decided to move across the country to join the ranks of the WTS itself. I packed up everything I could fit into my two-seater, shipped it to Charleston, South Carolina (don’t ask), flew in ahead of it, and, finally, made my way up the coast to Greenbelt, MD. John and Gina were nice enough to let me crash at their place for the weekend, while my little one-room apartment was being prepared.

By the end of that first weekend, John and I had already started on our first collaborative design project—an Icehouse game of evolving microbes that eventually turned into Zagami. Only a handful of weeks later, I started in on yet another design—a game of robot programming called RAMbots. I learned a hell of a lot about Icehouse design, and game design in general, in those initial months. My confidence was growing. John and I talked about this Zendo idea of mine on and off, but I never felt the urge to rush it. When it was ready, I thought, it would come. Finally, in late January of 2000, it did. I remember sitting in my warm little apartment, watching the first real snow of the season drift down through the trees outside my window, thinking: “It’s time.” I was ready to start designing Zendo.

Building a Better Eleusis

Although I still didn’t have a clear picture of how the mechanisms of the game would work, by this time I definitely had a nebulous “vision” of what I wanted (and didn’t want) Zendo to be like. I’m going to try, to the best of my ability, to reconstruct that vision here.

But first, I should say a few words about the influence of Eleusis on the evolution of Zendo. People often characterize Zendo as “Eleusis with Icehouse pieces”. This is understandable—Eleusis is without a doubt Zendo’s closest relative within the family of abstract strategy games. However, it’s important to note that, at this point in time, my attitude toward Eleusis was almost wholly critical. After years of thinking about the game and analyzing it, I’d come up with more and more things that I didn’t like about it. Far from wanting to create a direct translation of Eleusis into the “medium” of the Icehouse pieces, my goal was to create a game that was deeply different in important ways, and which didn’t inherit what I considered to be Eleusis’s flaws—in short, to create my own vision of the perfect induction game. This is not to disparage Eleusis itself, which is a landmark game, but to clarify my motivations during this period of time. For what it’s worth, my own characterization of Zendo is “Icehouse Bongard problems for multiple players”, but that description doesn’t mean a whole lot to most people.

The Vision

So here’s the vision of Zendo that existed in my mind at that time:

For each game, one person would take on the role of the Zen Master, and come up with a rule for the other players to try to figure out. I felt strongly that the Master should not be in any kind of competition with the rest of the players. The Master should be a facilitator whose only goal would be to provide an enjoyable experience for everyone involved. This is in contrast to both Eleusis and Patterns II, in which the Master receives a score based on formulas that are supposed to reward rules or patterns which are neither too easy nor too hard. I felt that these systems were arbitrary and unnecessary—arbitrary, because I didn’t feel that the score one received as Master could be sensibly compared to the score one received as a player (it was an apples-and-oranges problem), and unnecessary, because I believed that most people would jump at the chance to be Master, simply for the fun of trying out their latest rules. Masters would motivate themselves not to choose rules that were too hard, because those rules would result in games that were frustrating and boring, even for the Master.

I envisioned that the main activity of the game would revolve around players setting up and rearranging different “koans” (configurations of Icehouse pieces). I wanted players to be able to set up these configurations in whatever way they chose. They would be allowed to lean pieces at odd angles, or balance them precariously on top of each other if they wanted to. No Icehouse game existing at that time allowed this kind of free-form structure-building, and I expected this to be a distinguishing feature of the game.

For a brief moment, I considered the possibility suggested by “Jewels in the Sand”, that the students would simply propose rules, and the Master would be the one who builds new koans, as counter-examples. However, it was immediately obvious that the game would lose nearly all of its appeal if the students were never allowed to build their own koans, so I stuck with my initial vision. As it turns out, the idea of having the Master build koans resurfaced later in a couple of important ways, so, in fact, Zendo in its final form really represents a mix of these two visions.

I knew that there would need to be some way of visually distinguishing which koans had Buddha-nature and which didn’t. The most obvious approach was simply to use black and white stones or markers of some kind. However, John and I had become enamored with the idea of “pure” Icehouse games—games that required nothing more than Icehouse set and a flat playing surface. I came up with the idea of dividing the table into two halves to indicate which koans had Buddha-nature and which didn’t. When you built a koan that had Buddha-nature, the Master would move it to one half of the table, and when you built a koan that didn’t have Buddha-nature, the Master would move it to the other side. I was obviously influenced here by the Bongard problems, in which the diagrams on the left all follow the rule, and those on the right do not. Needless to say, this was a horrible idea—trying to move koans around while retaining their initial structures is just a pain in the neck. This system lasted about two minutes into our first Wunderland playtesting session, at which point Jake insisted that we scrap the idea, and just mark koans with Black Ice pieces or something. I gave in gracefully. For the sake of clarity, I’m going to pretend, for the duration of this essay, that we always just marked koans with black and white stones. But this early misstep is worth mentioning here as a historical curiosity.

One thing that I wasn’t clear on at this point was whether it would be better for each player to “own” their own set of koans, or whether koans should simply be spread across the table, with no one “owning” anything. This question really delved into the nitty-gritty of how the game ought to actually work, and I knew I couldn’t really answer it without actually designing some rule-sets and trying them out. I had a vague aesthetic preference for the the “no player owns koans” idea, but I felt that allowing players to own koans might create more potential for a competitive multiplayer game.

I had no doubt that the ultimate goal of the game should be to correctly state the Master’s rule. I felt that this was the only goal that players would find truly satisfying, and I was surprised at how steadfastly Robert Abbott resisted the idea all the way though the design of Eleusis. In his own essay describing that game’s history, he reports that he rejected the suggestion for two reasons: “first because it violated the scientific analogy (you normally acquire knowledge because it will be useful, not to get the right answer on a test), but chiefly because it turned the game psychologically into a teacher-student relationship.” I don’t find either of these reasons to be persuasive. It seems silly to rob players of the deep satisfaction that results from announcing the correct answer, solely on the grounds that scientists in the real world never receive such unambiguous validation from Nature. As a designer, my primary concern is to make my games as compelling as possible for the players. Thematic concerns are subordinate to that goal. As for his statement that the game might turn into “a teacher-student relationship”, I’m not sure I even understand what he means, or why that would be a bad thing. Perhaps he was afraid that the game would devolve into a bunch of isolated players who interacted only with the Master and not with each other. I agreed that this would be bad, but I felt that the solution would not be to disallow explicit rule-guessing. It would be to add some other mechanism to the game which created player interaction.

My conception so far amounted to something very much like the Five Pencils Game with Icehouse pieces—an interesting multiplayer puzzle, to be sure, but I wanted something more than that: I wanted a multiplayer game. I knew that I was going to need two things: some form of player interaction, and some way of providing intermediate rewards in addition to the ultimate goal of guessing the rule correctly. I figured that these two things would probably go hand in hand—whatever the reward system would be, it would probably involve some kind of interaction or competition between players. So the challenge was to come up with some mechanism that fit these criteria.

Eleusis has a simple mechanism for providing rewards as the game progresses: players are rewarded for playing cards that follow the rule (they get rid of cards) and penalized for breaking it (they have to draw extra cards). However, I couldn’t see any good way to apply this idea to my game. If players were rewarded for simply building koans that had the Buddha-nature, it would be trivially easy to receive this reward simply by copying existing koans that had the Buddha-nature. This mechanism works in Eleusis because players play to a central sequence which is never in the exact same state twice, and they have hands of cards which restrict their options, so it’s rarely possible to simply duplicate some previous play. Anyway, the more I thought about it, the more I realized that I didn’t like the idea of rewarding “white” plays and penalizing “black” plays in Zendo, even if I could think of some way to make it work. I didn’t want white and black to represent “good” and “bad”. After all, this was supposed to be Eastern philosophy, not Western! I felt that the symbol of the yin-yang perfectly captured the ebb and flow that I wanted to see in the game: the pair of opposites swirling around each other, each containing within it the seeds of the other. Of course, the real point was pragmatic: I knew that, in the course of solving a Zendo problem, players would need to see many examples of both kinds of koans, and that good players, in the process of testing their theories, would often build koans that they expect to be black. It seemed arbitrary to penalize one kind of play and reward the other. Indeed, I knew that “black” and “white” could just as easily be replaced by “purple” and “orange” without changing the game at all. I wanted to come up with some reward mechanism that didn’t favor black or white.

This leads me to yet another problem with Eleusis: the game doesn’t work well when the dealer creates a rule that’s too “wide” or too “narrow”—i.e. that rewards most plays, or penalizes most of them. This is an obvious side effect of the game’s reward system. When the rule is too wide, players will make “good” plays without even trying, and the game will be over before anyone has a clue what the rule is. When the rule is too narrow, player’s hand-sizes will become unwieldy as the penalties pile up. In my opinion, this is a defect of the mechanism—it invalidates a vast number of otherwise perfectly good rules. I was determined to come up with a reward mechanism for Zendo that wouldn’t invalidate certain kinds of rules in this fashion.

There were still other questions that arose in conjunction with the idea of intermediate rewards. For instance, what form would these rewards take? Since I was still interested in making as “pure” an Icehouse game as possible, I envisioned that the Icehouse pieces themselves could be used to represent player’s scores. As a game progressed, you’d collect rewards in the form of Icehouse pieces, with each piece representing a “point”. That seemed reasonable. But now an even more important question arose: what did this score mean? Since the object of the game was simply to be the first to figure out the rule, why would it matter how many “points” you’d collected during the game? My answer to this involved two other, seemingly unrelated questions: how many guesses should a player get during a game, and what happens when none of the players end up being able to figure out the rule? My feeling at the time was that players should only get one guess per game. I’m not sure now why I was so stuck on this idea. Perhaps I was still under the influence of Eleusis, in which each player is only allowed to become the Prophet once per game. I knew that I wanted rule-guessing to be a tense affair, and I certainly didn’t want to allow an unlimited number of attempts. And I knew that if I chose some arbitrary number (say, three guesses per player), then we’d have to have some way of keeping track of how many guesses each player had used. So, for the moment, I preferred the idea of one guess per player—and this is where my idea of keeping score came in. I figured that if you guessed the rule incorrectly, you could still continue to try to get the highest score. Of course, if some other player guessed the rule correctly, your score would be worthless, but if all players guessed incorrectly, the player with the highest score would win. Again following the lead of Eleusis, I felt that the game needed a guaranteed ending and winner, even if the rule turned out to be way too hard. I also figured that, if Icehouse pieces were used to keep score, the stash would be gradually depleted as player’s scores grew, and this would be a way to drive the game to a close.

Lastly, and perhaps most importantly, I had one crucial overarching goal: I wanted Zendo to be simple. At the end of Robert Abbott’s essay, he claims that the scoring system “produced the desired result and was not too complicated”. I tend to agree more with Kevin Maroney’s remark on the Icehouse list that Eleusis’s scoring system is “endlessly fiddly”. I’ve read and re-read the rules to Eleusis countless times over the years, but I still cannot remember all of the details of its scoring system. My goal was to create a game that was so simple that you could read through the instructions once and then not have to refer to them again. This was a tall order, I knew, but one worth shooting for.

The First Rule-set

So, with all of these thoughts jostling around in my head (and believe me, they weren’t nearly as organized or coherent as the above list makes them sound), I sat down to create my first trial rule-set. The obvious issue to focus on was that pesky reward mechanism. I needed to come up with some kind of action that a player could perform to score points—preferably something which would tend to reward the students who’d figured out the most. After thinking about this for a while, I came up with the following idea: a student could score points for causing a koan’s status to change, either from white to black or from black to white. My thought was that the dividing line between white and black—between Buddha-nature and non-Buddha-nature—would be a perfect focus for the game, and the players who’d figured out the most about the rule would be the ones in the best position to determine how to cause any given koan’s status to change. And, of course, this reward criteria did not in any way favor white koans over black ones.

However, it did have a couple of obvious problems. For one thing, it still seemed as though earning rewards would be trivially easy, since if one player changes a koan’s status and gets a reward, the next player can simply reverse that change to get another reward, and so on. Not only that, but it became clear that I was going to have to somehow limit the number of changes allowed to a koan, since obviously any koan can be changed into any other koan, given unlimited additions and removals of pieces. This wasn’t looking so good. But rather than keep rooting around for a better idea, I decided to forge ahead and see if I could somehow make this thing work. Over the course of a weekend, I managed to cobble together the following rule-set:

At the beginning of the game, divide up the stash of Icehouse pieces as evenly as possible among all the students.

On your turn as a student, you may do one of three things: build a new koan in front of yourself using your own pieces, change one of your own koans, or change another student’s koan.

When you build or change one of your own koans, the Master will simply declare whether or not it has Buddha-nature, and will mark it accordingly.

When you alter another student’s koan, you are only allowed to make a single change to it. That is, you may add, remove, or move a single piece. (This required some truly ugly rules about how to remove pieces that were underneath other pieces, etc.) If you manage to change the status of that koan from white to black or from black to white, you get to take all of that koan’s pieces and add them to your own stash. If you don’t manage to change its status, that player gets to take one of your koans.

Once per game, you’re allowed to guess the Master’s rule. If you guess correctly, you win. If all students guess incorrectly, the game ends, and the player with the most pieces in his or her scoring stash wins.

What I envisioned was that players would use their own koans for experimentation, but they would attempt to build them “defensively”—that is, they’d try to build them in such a way that no single change would cause any of them to switch status. Of course, the more a player learns about the Master’s rule, the easier it becomes to build koans defensively. This provided a basic framework of play, as well as some sub-goals and smaller rewards to go along with the ultimate task of guessing the Master’s rule. It seemed simple enough. But how would it play?

The First Playtest

I wasn’t ready to unveil Zendo to the group at Wunderland yet. I wanted to do some basic playtesting first. So, on the following Tuesday, John and Gina and I sat down to try the very first games of Zendo. We played three games that night, each of us taking a turn as Master. I kept a log of that session, and am therefore still able to remember the rules that we used. I was the Master for the first game, and I used “A koan has Buddha-nature if it contains exactly two sizes of pieces.” John then tried “A koan has Buddha-nature if it contains at least two pieces of the same size or color.” Gina’s rule was “A koan has Buddha-nature if any piece is stacked directly on top of a smaller piece.”

Although I had a terrific time playing, it was clear by the end of the second game that there were some serious problems. Under John’s rule (“a koan has Buddha-nature if it contains at least two pieces of the same size or color”), Gina and I both quickly discovered that no single-piece koans had the Buddha-nature, and soon afterward we both figured out that any koan that had at least two pieces of the same size always had the Buddha-nature. We used this knowledge to steal koans from each other for a couple of turns, but I soon grew impatient and took my chance on the obvious guess. John informed me that my guess was incorrect, and the game continued.

At this point, things bogged down badly. Both of us realized that we could “protect” our own koans by making sure each one contained at least three pieces of the same size, so that any single change would fail to change the status of the koan. However, we also both knew that there was something else that we hadn’t yet discovered about John’s rule (since my guess was incorrect), and it was pretty clear that we were going to have to build some easily-stealable two-piece koans in order to discover it. Since I’d already spent my guess, I had very little motivation to perform good experiments. Not only would those koans be easy to steal, but the good experiments might give Gina enough information to guess the rule correctly and win. On the other hand, Gina wasn’t especially motivated to do those experiments herself, since I was waiting to snatch up any two-piece koans she built, and after a few rounds of that she’d be out of pieces entirely. So the game more or less ground to a halt. Eventually, I got bored, and played out a random two-piece koan (a medium blue and a small blue), which turned out to be exactly the thing Gina needed to see to help her figure out the rule and win. Neither of us felt at all satisfied by that turn of events. Even so, I went home that night filled with excitement, wondering what to try next.

The Second Rule-set

Clearly, the mechanism of koan-stealing was conflicting with the ultimate goal of solving the Master’s rule, creating an uncomfortable kind of dissonance in the motivations of the players. What could I do to eliminate this?

Well, first of all, based on that playtesting session, I was now certain that I didn’t want players to own koans. My initial aesthetic preference was to have all koans be “communal property”. I’d strayed from this vision in order to try to introduce a level of player interaction, but now I became convinced that my initial preference was correct.

Of course, this only served to exacerbate the difficulties presented by my reward mechanism. What reward should a player receive for causing a koan to change status? And, even more seriously, what’s to stop the next player from simply undoing the previous move and scoring again? John was in favor of retaining the mechanism of our initial playtest: when you change a koan’s status, you take all of its pieces as a reward (solving both of the above problems at once). However, the more I thought about this, the more I didn’t like it. First of all, it didn’t seem right to me that a player would score more points for changing the status of a five-piece koan than a two-piece koan. Why should a koan’s size have anything to do with how many points you receive if you change it? But even more seriously, this mechanism would favor players with very good memories. Important koans would constantly be disappearing from the table. I don’t particularly like memory-games, and I didn’t want Zendo to become one. I wanted as much data to stay out on the table as possible. I felt that a better system would allow the koans to remain on the table. A player’s reward would simply be a single piece from the global stash. At the end of the game, if no one was able to guess the Master’s rule, the player with the most pieces would be the winner.

Of course, this completely failed to address the problem of how to keep people from scoring simply by reversing previous moves. That turned out to be quite a quandary, and I did nothing but beat my head against it for the next couple of days. The weekly Wunderland game night was fast approaching, and I desperately wanted to have a working version of Zendo ready to test. But, try as I might, I couldn’t figure out how to solve this problem. I played around with some rather desperate ideas relating to “balance”—i.e. if the majority of the koans on the table were white, you’d only score for changing a white koan to black, and so on. These ideas never quite worked, and they grew more and more elaborate until they finally collapsed under their own weight. I had to try something else.

On the morning of the next game-night, after a sleepless night of fruitless brainstorming, I’d finally given up on the hope of playing Zendo that evening. But then, as I was preparing to collapse into unconsciousness, a new idea bubbled up in my brain. What if you only scored a point when you caused a koan’s status to change by adding a piece? And what if you were never allowed to remove pieces from koans? Then it would be impossible to win points simply by reversing a previous play, since piece additions couldn’t be undone. Repositioning a piece within a koan would still be allowed, but you couldn’t score points by doing so. This created what I hoped would be a nice little distinction between purely “experimental” plays, and attempts to gain points.

Here’s the full rule-set for Zendo as I then envisioned it:

At the beginning of the game, all of the Icehouse pieces are placed to one side of the playing surface.

On your turn as a student, you may create a new single-piece koan, reposition a single piece within an existing koan, or add a piece to an existing koan. The Master marks the koan. If you add a piece to an existing koan and its status changes from black to white or from white to black, you make take any piece from the global stash as a reward.

Once per game, you’re allowed to guess the Master’s rule. If you guess correctly, you win. If all students guess incorrectly, the game ends, and the player with the most pieces in his or her scoring stash wins.

At any time during the game, anyone can suggest that the group break down a specific koan. If all players concur, the koan’s pieces are returned to the global stash.

If the global stash runs out of pieces, the players are allowed to break down existing koans and keep playing, but if even one player is not willing to do so, the game ends.

I wrote up an excited email to John and Gina outlining my new ideas, and then I collapsed into bed. I slept like a baby. The next afternoon, on our daily walk through the woods, John expressed a few misgivings about these ideas, and we debated about whether it was wise to unleash it on the WTS. Back at his place, we tried a few two-player tests to see how it all felt.

“Okay,” he said, after about five minutes. “We should play this tonight.”

The Second Playtest

I’ll never forget my excitement as we headed in to Wunderland that evening. After a few minutes of standing around in the front room, jawing with the WTS regulars amid the neon buzz and the hum of old coin-op machines, John pointed to me and said “Kory has created an Icehouse game to beat all Icehouse games.”

A circle of expectant faces turned toward me. Only a week earlier, we’d done the first playtest of RAMbots at Wunderland. Surely that’s what John was referring to…?

“Well,” I said, “it’s called Zendo. One person is the Zen Master, and the rest of the players are students, and they set up groups of Icehouse pieces called ‘koans’. And the Master tells them whether those koans have the Buddha-nature or not…” People started smiling. Pretty soon we tromped into the Zarcana lounge and started up the first game.

By any reasonable standards, the playtest that evening was a terrific success. My new reward mechanism seemed to be working. The thing really felt like a game, not just a multiplayer puzzle. After waiting so many years to play a good version of the Five Pencils Game, here I was playing one that I’d designed myself. It was glorious. At one point, in the kitchen, between games, I told John “I’m on a major high right now.”

He smiled. “You did it,” he said simply.

Later, Andy Looney, in his best “so-my-old-nemesis-we-meet-again” voice, said “You realize that we’re going to have to kill you. Not right away, of course—we need to get some important information out of you first. But eventually, we’re going to have to kill you.”

The whole Zen theme was clearly a huge hit, and we had no end of fun asking “Master, does this have the Buddha-nature?” There was a full lunar eclipse that evening, and our games were constantly being interrupted as people went trudging out into the snow to watch its progress. In a scene which will be forever etched in my memory, John called out in frustration to a group of players who were heading for the door yet again: “The students are not allowed to leave the classroom!”

“But Master,” replied Andy as he shuffled out with the rest, “there is a demon eating the moon!”

Of the other playtesters present that evening, Kristin Matherly was the most obviously enthusiastic about Zendo. John and I were, of course, already sold on the idea. Jake’s initial reaction to the game was a bit more ambivalent. He seemed interested, but not overly so. However, over the next couple of weeks, he warmed up to it, and soon the four of us were spending just about every minute we had together playing, thinking about, and talking about Zendo. (Jake later explained his initial ambivalence: he’d felt that he wouldn’t be very good at the game, and—more importantly—that it would be impossible for anyone to get better at such a game. We soon discovered that it was possible to get much, much better at Zendo. He proceeded to become the best Zendo player around.) Other members of the WTS showed interest in the game and were willing to help, but it was clear from early on that the core playtesting and design group was made up of the Four.

The next few weeks were some of the most manic weeks of my life. I slept little, wrote a lot, thought incessantly. John and I took long walks through the snowy woods with his dog (whose name happened to be Booda) and discussed the game from every angle. It was a magic time.

Terminology

Nevertheless, it wasn’t long before the inevitable issues began to arise. For instance, it became clear almost immediately that we were going to need to come up with some standard terminology. What counted as “pointing”? Do pieces point through other pieces? Should an upright piece be said to be pointing at a piece stacked on top of it? What counts as a “stack”? Does a single piece count as a stack of one? Does a nest of pieces lying on its side count as a stack? We didn’t come up with answers to these questions all at once. In fact, we were still wrangling with some of them over a year later. However, it didn’t take us long to settle on definitions for a couple of the most important concepts. We came up with precise definitions for “upright” (a piece whose base is parallel to the table) and “flat” (a piece whose lowest triangular side is parallel to the table). We made certain to disassociate the concept of “touching or not touching the table” from these definitions—we reserved the terms “grounded” and “ungrounded” for that. One of the most important and satisfying breakthroughs was Kristin’s idea to use the term “weird” to refer to any piece that’s neither upright nor flat. Another was Jake’s proposal of the “pointing line”, which shoots directly out of the tip of a piece, but bends and skims if it hits the surface of the table, thus capturing our intuitions about how pointing ought to work for flat, upright, and weird pieces. I always knew that these terminology issues were fundamentally tractable. In fact, I knew that other groups of players could even devise different standards and play Zendo perfectly well. I never worried that these issues of terminology would cause any deep problems for the game.

Ambiguity in Koans

Not so with a different but related issue: physical ambiguity within koans. Sure, we could come up with crystal-clear definitions for things like “pointing”, “weird”, and so on, but that didn’t change the fact that, in practice, it might be extremely difficult to tell what a piece is pointing at, or whether or not a piece is really weird. Is that red piece pointing at that yellow piece, or is it just barely missing it? Is that precariously balanced piece perfectly upright, or is it just barely leaning to the left? Of course, most of the time, a koan’s ambiguities had nothing to do with the current rule. But when they did, these problems threatened to undermine the whole enterprise. It didn’t seem right to expect the students to read the Master’s mind on these issues. On the other hand, it would give too much away if the Master was obliged to say things like “by the way, that red piece is pointing at that yellow piece”. What’s a Master to do?

Well, during the first few playtesting sessions, Masters didn’t do anything about it at all. They just made silent judgment calls, and hoped things would work out. When it finally became clear that we couldn’t ignore the problem any longer, we tried an experimental approach: in a borderline case, the Master should mark the koan with a white and a black stone, and call it “mu”. Mu is a Zen term which means something like “unask the question”. In this case, the question being unasked is “does this koan have Buddha-nature?”, since there’s no clear yes-or-no answer. Mu alerted the students to the fact that the koan was difficult to judge, without giving them obvious information about which features were important. Although this solution was better than none at all, I definitely wasn’t happy with it. For one thing, it essentially added a third “state”, which complicated the scoring rules—we had to specify that you couldn’t score by changing a koan into or out of mu. But, more seriously, it sometimes happened that the Master would judge a feature to be ambiguous when some students didn’t see it as ambiguous at all. And sometimes the Master thought a feature was totally unambiguous when it looked ambiguous to some students. In other words, the Master still ended up making subjective judgment calls about which koans to mark “mu”.

It took a surprisingly long time—at least a month—for a good solution to dawn on me: when a koan’s status is difficult to judge, the Master should make a silent judgment call, with the understanding that the students are allowed to ask about any features of the koan that they aren’t sure about. Now the Master will never “give the game away” by indicating which features are important, but the students will not be forced to read the Master’s mind about the features they think might be important. The more I thought about this, the more sense it made. Zendo isn’t about trying to determine what features a koan contains; it’s about determining which of those features is important. There’s no reason why the simple facts about a koan (as judged by the Master) shouldn’t be freely available to all students, if any of them chooses to ask. Asking the Master whether or not some piece is pointing at some other piece should be no different than asking the Master about the color of a piece that’s buried deep within a tower.

I think the reason it took me so long to come up with this idea was that, at the time, I was uncomfortable with anything that smacked of “conversation” between the Master and the students. I feared that there would be too much opportunity for the Master to give things away, or to otherwise give some kind of unfair advantage to the student whose turn it currently is. But once we actually tried it, not only did I find that my fears were unfounded, I found that I actually enjoyed this kind of interaction, and became interested in introducing even more of it. The solution to this problem therefore paved the way for solutions to some even knottier problems.

Ambiguous Guesses

One of these knottier problems was the dreaded Ambiguous Guess problem. What should the Master do when a student’s guess is clearly ambiguous? “A koan has Buddha-nature if the largest piece is red.” What if there’s more than one largest piece? How about when a student uses a vague or undefined term? “A koan has Buddha-nature if there’s a blue piece near another blue piece.” What counts as “near”? The worst case is when the Master misunderstands a guess without even knowing it. During one early game, I guessed (correctly) “a koan has the Buddha-nature if it contains exactly two flat pieces which are pointing at larger pieces”, but the Master heard “a koan has the Buddha-nature if it contains exactly two flat pieces, which are pointing at larger pieces”, and pronounced my guess incorrect. One misplaced comma can change everything! Clearly this was a serious problem.

Although the solution to the “ambiguity-in-koans” problem was a breakthrough, it wasn’t clear how to apply the same kind of solution here. In this case it would have to be the Master asking the questions, not the students, and that certainly seemed like a bad idea at the time. We made many attempts to address this problem, none of which were satisfying in the least. We tried having the Master simply say “incorrect” if a guess was vague or ambiguous in any way. We tried having the Master say “mu” in such a case, and allowing the student to guess again on a later turn. At one point, I became so desperate that I decided to try an Eleusis-style “Prophet” system, just to see how it felt. My early intuitions were correct. The game was not nearly as compelling without the thrill of guessing the rule out loud. (Incidentally, we ran into another problem that arises in this kind of system: if all of the players realize what the rule is while one player is Prophet, there’s no satisfying way to cut the game short. You just have to tediously play it out.)

Eventually we settled on a system that, while not ideal, seemed to work tolerably well—what we called the “testing” method. If a Master wasn’t certain about how to judge a student’s guess, the Master would set up a few koans which would be specifically designed to probe the ambiguity, and the student would mark each of them. If the student marked them all correctly, the Master would assume that the student’s guess was correct. If the student marked any incorrectly, the Master would break them down without indicating where the mistake was made, pronounce the guess incorrect, and continue the game. I was always deeply unhappy with this idea. For one thing, it was clunky, arbitrary, and inelegant. For another thing, it didn’t solve the problem of the Master misunderstanding a student without even realizing it. Furthermore, when the Master did choose to use the testing method, it was quite possible for a student to get lucky and mark all the test koans correctly without actually knowing the rule. Finally, it seemed to me that the testing process always threatened to give away too much information to the students. They could deduce a lot about the rule by observing the koans that the Master set up. Also, testing usually indicated that a student’s guess was in the right ballpark, which was an important bit of information for the following students. More than once, I tried to push the idea that this testing should happen after every guess, but people correctly pointed out that it would be sort of silly and time consuming in those cases when the guess was completely unambiguous. Still, this turned out to be a tantalizing foreshadowing of the solution we eventually came up with.

The Reward Mechanism Breaks Down

But that was still to come. In the meantime, I had to deal with an even more pressing problem: my “ingenious” reward mechanism had finally begun to show its flaws. In opposition to my early hopes, it had become clear that this system did not, in fact, reward the players who learned the most about the rule. Instead, it rewarded the players who learned only a tiny bit about the rule, and then ruthlessly exploited that information over and over again to score easy points, often ruining other player’s attempts at good experimentation in the process. No one ever wanted to start new single-piece koans, or to perform the crucial experiments necessary for solving a rule, because too often those plays would result in easy points for the following players. I’d hoped that this would create an interesting kind of player interaction. Instead, it was just annoying.

On top of all of this, I finally realized that my system suffered from a flaw that was very similar to the one I’d seen in Eleusis: it invalidated certain kinds of rules. Since points could only be earned by adding pieces to koans, some rules provided many scoring opportunities, and others, very few. For instance, a rule like “a koan has the Buddha-nature if it has three or more red pieces” provides one scoring opportunity per koan (whoever adds the third red piece to a koan will score a point). On the other hand, a perfectly good rule like “a koan has the Buddha-nature if it has an odd number of pieces” was hardly worth playing under this system, since players would score every time they added any piece to any koan. I’d criticized Eleusis rather harshly for this kind of problem, and here it was cropping up in my game as well. As disheartening as it was, I knew it was time to bite the bullet and start working on a new system.

Taking everything I’d learned so far, I went back to square-one and asked my original question: what action might students perform that would reliably indicate progress towards discovering the Master’s rule? It seemed clear that, one way or another, the answer revolved around the idea of prediction. The more you know about a rule, the better equipped you will be to predict whether a given koan will be black or white. I saw that this idea of prediction was actually implicit in both the Prophet mechanism of Eleusis and my own rewards mechanism, but neither of these was satisfactory. I needed something else.

At some point it occurred to me to try the direct approach: after you build or change a koan on your turn, you predict whether it will be marked white or black. I didn’t know yet whether this prediction ought to be optional or mandatory, but that was a minor issue. There was, of course, a serious problem here: what would keep you from simply building a copy of some existing koan and making the obvious “prediction”? It seemed to me that the solution was to get the other players involved in the prediction. What better way to determine whether or not an answer was “obvious” than to see how many players were able to predict it correctly? All I had to do was work this into some kind of mechanism that would provide the proper motivations for the players.

By the following Wunderland game-night, I’d cobbled together the following rule: after you build or change a koan on your turn, you can choose to call a “prediction round”. The player on your left may either predict or pass. If that player passes, next player on the left may predict or pass, and so on. If all players pass in succession then you yourself get to predict, and will gain or lose a point as a result. If any other player chooses to predict, the prediction round ends there. If the player predicts correctly, he or she wins a point, and you lose one. Otherwise, he or she loses a point and you win one. The idea here is that you’ll only want to call prediction rounds on koans that you think the other players will be unsure about. Calling prediction on an obvious koan will simply give an easy point to the player on your left. The mechanism would be nicely self-balancing, since what counts as “obvious” would be entirely dependent on the knowledge of all of the players at any given time. This certainly sounded promising.

Incidentally, it was around this time that we finally stopped using Icehouse pieces to keep score, and started using stones instead—an idea that Andy had been in favor of from the beginning. I was becoming more sensitive to the dangers of allowing the rewards mechanism to interfere with the normal play of the game. In this case, I’d grown uncomfortable with the way that the scoring system was tying up pieces that people wanted to use for koans. Again, I’d hoped that this tying-up of pieces would represent an interesting aspect of play, but it only turned out to be annoying. We were already using black and white stones for marking koans, so it seemed reasonable to simply add a third color of stones to represent points.

As another side note: since this new scoring mechanism no longer depended on the idea of adding pieces to cause koans to change status, we were able to start allowing the removal of single pieces from koans as well. (Actually, this new mechanism freed us up to allow multiple changes to a koan at once, but I didn’t understand that yet.)

The first time we tried the new prediction idea, it met with a rather lukewarm reception. One problem was caused by the fact that stones could be lost. We wrangled over how many stones players ought to start with, if any, and I wondered if players ought to be disallowed from predicting on other player’s turns if they had no stones to risk—an idea which just about everyone hated. We wrangled over whether the prediction rounds should happen on every turn, or only by choice of the player. But beyond all of this, the problem was that these prediction rounds had slowed the game to a crawl, resulting in a general lack of enthusiasm about the whole idea. I went home discouraged, but not beaten. I was convinced that prediction was the key. We just had to come up with a way to make it more natural.

The Origin Of Mondo

Actually, even then I’d had the spark of an idea, but for some reason I pushed it aside, thinking perhaps that it was “just too crazy”. However, it wouldn’t stop nagging at me, and finally, at some social gathering or other that weekend, I leaned over to John and said, “what if each of the students has a black stone and a white stone, and when a student calls a prediction-round, all students put their predictions in their fists and reveal simultaneously?”

John looked at me, almost with a kind of indignation. “I was going to suggest that to you,” he said, “but I thought you’d hate it!”

Well, I didn’t hate it. In fact, the more I thought about it, the more I liked it. I knew that it would significantly speed up the prediction process, and add a major dose of fun to the game as well. And I’d even found a name for it while poring over a bunch of Zen glossaries I’d found on the web: Mondo, a Zen term which referred to a question-and-answer session between a master and a group of students. It was perfect!

Of course, we now had to figure out how the mondo scoring should actually work. John and I tossed it around a bit, and eventually I decided I liked a “zero-sum-game” style of scoring. Everyone would start the game with a certain number of stones (say, twelve). When you call mondo on your turn, if you answer correctly, you may give a stone to every player who answered incorrectly, and if you answer incorrectly, you must take a stone from each player who answered correctly. When all players guess correctly or incorrectly, nothing happens. This seemed right to me.

Note that players lose stones when they win mondos instead of gain them, so the goal was to have as few stones as possible. Although this might seem counter-intuitive, there was a method to my madness: if players lost stones when they lost mondos, a player might run out of stones entirely, at which point the system of exchanging stones breaks down. However, if players have to take stones when they lose mondos, they always have more to lose, since they can always take more stones. Now the only way a player can run out of stones is by winning a lot of mondos. Therefore, I figured that running out of stones could signal the end of a game. This would provide a secondary goal, and a way to drive the game forward.

Unfortunately, it wasn’t guaranteed to drive the game forward—players might just mondo back and forth, exchanging stones here and there, with no player getting very far ahead. As long as even one player held off on guessing the rule, the game would never end. Remember, we were still only allowing each player to take one guess per game at this point! Therefore, we introduced the idea of “meditation”, which meant that you could “pass” your turn, and cause all players, including yourself, to discard a stone. This would be a way for the player with the best score to drive the game to a close if it was dragging on for too long.

This sounded okay. However, in the meantime, Kristin had begun to voice a very reasonable complaint: one guess per game just wasn’t good enough. She, Jake and I discussed what might be done about this, and after a while, we came up with the following idea: at the end of a game, whether it ended because all players had used their initial guess, or because one player ran out of stones, each player was given a free guess, starting with the player who had the best score. This allowed all players to feel like they were in the game until the end, and we hoped it would make the scoring a bit more crucial.

Well, at the next Wunderland game night, we tried out this new hodgepodge of ideas. As I expected, the mondo idea was an immediate hit. The excitement of the prediction-rounds really pulled players into the game, and there were great moments when one player managed to catch the rest in a bad guess. (Tip for game designers: any mechanism that periodically causes all the players to go “Ooooooo!” is probably on the right track.) I especially liked the way that the new mechanism actively involved all players during a single turn, giving the game a nice, almost intimate, group-dynamic. Unquestionably, we’d taken a step in the right direction.

Making Mondo Matter

So we played this rule-set for a couple of weeks, and I started feeling pretty good about the whole thing. However, after a while, Jake became more and more vocal about something he felt was a serious problem: mondo was fun, but when it came right down to it, it didn’t really mean much. The more we played, the less any of us really cared about scoring. The only satisfying way to win Zendo, as I’d always known, was to discover the Master’s rule. The fact that the player with the best score was allowed to guess first in the final guessing round turned out to be insignificant. In fact, sometimes it was a disadvantage to guess first in the final guessing round. It was often better to hear other player’s incorrect guesses first. I had to admit that Jake was right. Mondo, as fun as it was, was beginning to look like extraneous fluff.

There was a bit of talk about eliminating it completely, but I couldn’t bear it. Mondo was just too much fun to give up on that easily. After a few days, Jake and his friend Peter Hammond, who’d also recently become hooked on Zendo, came back with a suggestion—one which now seems so staggeringly obvious that I can’t believe we didn’t just start with it in the first place. You win stones for answering mondos correctly, and the stones that you win are used to buy guesses. There was no need for a final guessing round—no need, in fact, for a final round at all. Everyone simply played and mondoed and spent guessing stones until someone solved the rule. Beautiful!

After hashing it out some more, we settled on the following system: guesses cost three stones apiece, and each student begins the game with three guessing stones. If you call mondo and answer correctly, you get one stone for each player who answered incorrectly. If you call mondo and answer incorrectly, each player who answered correctly wins a single stone. We’d finally decided that it would be best if there was no way to lose stones during mondo, so that we wouldn’t be faced with the niggling issue of what to do when a player had no stones.

We playtested this idea, and it worked wonderfully. Kristin’s previous intuitions about allowing more guessing were completely vindicated—the game was simply more fun when players were able to guess many times during a game. We began to play with more interesting and complex Master’s rules, as these rules became solvable with the trial-and-error process of multiple guesses. Most importantly, we’d succeeded in making mondo matter. It was now tied in a very straightforward way to the one true goal of the game: to correctly guess the Master’s rule.

This is an important point. With the adoption of these new mondo rules, not only had we effectively eliminated the concept of “scoring”—a player’s stash of guessing stones did not measure progress, since good players would be spending their stones on guesses—but we’d also eliminated the mechanisms that might drive a game to a close if no one was able to figure out the rule. I worried a bit about this at first, but after a while I came to realize that it was simply not necessary. Players were perfectly free to give up on a game when they’d had enough—they didn’t need some mechanism involving depleting stashes of pieces or stones to tell them when they were allowed to do so. It was true that giving up was an unsatisfying way to end a game. However, we finally realized that it was every bit as unsatisfying to declare a winner based on some kind of score. Once we’d played with the new mondo rules for a while, we simply stopped caring about providing an alternate way to end the game, and we never worried about it again.

Niggling Issues

We continued to playtest, and now it was really starting to feel like we were homing in on it. Nevertheless, there were still some niggling issues that were bothering me. First of all, there was a somewhat obscure stalemate problem that occasionally arose under the new mondo system. It was possible for all of the players in a game to figure out the Master’s rule at a time when no player had enough stones to guess. At that point, no player would be able to win more stones, because everyone would answer all mondos correctly. This was a fairly rare occurrence, but nevertheless it was a real problem. It wasn’t just the stalemate aspect of it that I didn’t like. It was the fact that there was no real way to be certain that you were in stalemate. You wouldn’t want to give up on such a game until you’re convinced that everyone knows the rule—but how many mondos do you have to do before you’re convinced? It was frustrating. In order to address the problem, I suggested variations on the old meditation idea to give everyone free stones, but none of us liked these ideas much. As it turns out, it took us almost a year to come up with a good solution to this problem. More on that later.

Another problem was related to the fact that we were still only allowing a player to make one change to a koan per turn. I’d started to dislike the way that players were often hindered from doing the exact experiments that they wanted to do. Sometimes a player would even spend multiple turns working on a koan, only to see this work ruined by another player’s changes. John suggested that we allow all pieces within an existing koan to be rearranged on a single turn, while still only allowing a single piece to be added or removed. This would eliminate all of our fiddly rules about what counts as a single “change” to a koan, and give players more flexibility for experimentation. I saw the merit of this suggestion, but, for reasons that now seem extremely silly, I resisted it. I liked the evolutionary feel that resulted when all koans started as single pieces and changed only gradually. I also remember worrying that, if players didn’t have enough restrictions on their ability to build and change koans, the game would start feeling less like a game and more like a multiplayer puzzle. As you’ve seen, this worry haunted me throughout the design of Zendo, and it’s interesting to note that, for the most part, it did more harm than good. The final version of Zendo turned out to be surprisingly like that first puzzle-test I did with Dave Bender way back in the fall of ’99.

Anyway, during this period of time I did a lot of experimenting with some truly horrendous ideas involving “koan protection”—ways of locking up a koan for a round so that no other players could change it. Perhaps, I thought, you can pay a single stone to “protect” a koan for a round, or perhaps you can protect one koan per turn for free. And so on. I also experimented with the idea that every player could have one special koan in front of them that they “owned”, and that no one else could change.

The craziest idea I had during this period of time was that, when creating or changing a koan, the number of guessing stones you had in front of you would determine the number of pieces you would be allowed to add, remove, or reposition. (If you had no stones in front of you, you would still be allowed to make single changes.) This would eliminate the need for some kind of “protection” or owning of koans, and would also make winning mondos even more important. I actually talked people into playing this crazy idea. Needless to say, it wasn’t a hit. However, the experience was invaluable—it proved to me that the game didn’t fall apart or lose any of its “evolutionary feel” when players were allowed to make multiple changes to koans. I came away from that playtesting session with a complete reversal of my earlier position. I not only saw that John was entirely correct about allowing multiple repositionings as a matter of course. I was now willing to go him one better, and allow unlimited additions and removals of pieces as well—essentially, to give players free reign to build whatever koans they wanted. I’d finally realized that the “single change” idea was nothing more than a useless holdover from the obsolete rewards mechanism. Good riddance.

A New Solution to an Old Problem

That playtesting session turned out to be one of the most important in Zendo’s history, for on the same evening we achieved yet another startling breakthrough. It was during the last game of the evening. Jake was the Master, and he’d come up with a particularly devilish rule: “a koan has the Buddha-nature if the pip-count of the weird pieces is greater than the total number of pieces in the koan”. Needless to say, we struggled with this for quite some time. It wasn’t too long before we’d homed in on the right idea—that it had something to do with comparing the pip-count of weird pieces to something. But after many guesses, we couldn’t figure out what. As the game dragged on, it devolved into a cooperative effort, as such games often do, and we all began working together to try to crack the rule. One player spent some guessing stones on what sounded like a reasonable theory—something like “the pip count of weirds is greater than the number of non-weirds”. Jake pronounced the guess incorrect, but, frustratingly, it continued to work for every new koan we built. We became gripped with the existential fear that occurs at such moments—what if that guess was correct, but Jake had misunderstood it? Should someone try guessing it again, with a different wording?

Seeing our frustration, Jake told us that there were koans that would disprove that guess, but it might take us a while to stumble onto them. He offered to build one for us, and, of course, we jumped at the chance. After Jake built the koan, we remained stumped, but at least we had a clear example of why the recent guess had been wrong. We continued valiantly for a little while longer, and I believe Jake even built us another koan or two. But eventually, we threw in the towel, and he told us the rule.

Afterwards, we all sat around and talked about the way things had played out, and we agreed that this circumstance—that of an entire group of players being unable to find a counter-example to an incorrect guess—was likely to occur given any difficult rule, and was likely to cause the same kind of stagnation. We liked the way that Jake’s helpful koans broke up the stagnation. Jake therefore suggested that a group of students could always be allowed to “petition” the Master to build them a koan which showed why some guess was incorrect. When I heard this suggestion, something clicked in my head. Old memories of Jewels in the Sand resurfaced in my mind. “You know,” I said, “I’ve considered the possibility that this should happen after every guess. If your guess is incorrect, the Master must show you that it’s incorrect by building a koan which disproves it.” Jake’s eyes lit up. He added that he’d always felt disappointed and frustrated when he spent his stones on a brilliant guess, only to have the Master shoot it down with nothing more than head-shake. This idea promised to make the process of guessing much more interesting.

We didn’t get to try it that evening, but nevertheless I went home in great excitement. Over the next couple of days, after many emails among The Four, I became convinced that this was the answer to all of our rule-guessing problems. First of all, as Jake pointed out, it provided a psychologically satisfying response to an incorrect guess, while providing an influx of new information to keep the game moving forward. One particularly exciting result was that a player could now save up a bunch of guessing stones and then unleash them all at the end of a single turn, gaining new information after each guess until, hopefully, enlightenment was achieved. John later dubbed this process the “guess barrage”. This seemed so likely to improve the play of the game in general that John and I decided that we should reduce the cost of guesses to one-per-stone, and then tweak the mondo scoring system so that you can never win more than a single stone during mondo. Not only was our resulting mondo system simpler and more elegant, but it now increased the possibility of saving up three or four stones for a good barrage.

Furthermore, the new idea provided a beautiful solution to the “functional equivalence” problem—the fact that the same rule may be stated in many different but functionally equivalent ways. We used to have to tell every new Master: “Whenever you judge a guess, try to imagine any koan that your rule would mark white but that the student’s guess would mark black, or vice-versa. Don’t judge a student’s guess incorrect until you think of one.” With the new idea, the Master had to do this explicitly and publicly, rather than internally and silently. This virtually eliminated the possibility of the Master judging a guess incorrect when it was in fact correct.

I realized with excitement that we no longer needed our clunky “testing” mechanism requiring the Master to set up a number of test koans for the student. This elegant idea of providing counter-examples had subsumed and replaced it. We’d found our way to a solution of the dreaded ambiguity problem: simply allow Masters to ask clarifying questions about guesses. Now that we’d taken the crucial step of allowing the Master to be an active and creative participant in a game’s events, it suddenly seemed acceptable to allow this kind of Master/student interaction. And, as had happened so many times before during the design of Zendo, once I’d finally opened myself up to an idea I’d resisted for so long, I realized that my previous fears about it were totally unfounded. The Master doesn’t give away anything about a rule simply by explaining to a student that a guess is ambiguous and needs to be clarified. If a student guesses “a koan has Buddha-nature if the largest piece is flat”, the Master gives away nothing by pointing out that koans might have more than one “largest piece”. If a student guesses “a koan has Buddha-nature if it contains two red pieces”, the Master gives away nothing by asking “do you mean at least two, or exactly two?” The Master will ask this question even if the rule has nothing to do with red pieces. The Master simply needs to fully understand the guess in order to provide a counter-example to it. The wall between Master and student had finally collapsed, and with it, one of our most frustrating design problems!

To top it all off, the new change opened the door to yet another idea: the Master should start off each game by building a black and a white koan. Up until then, we’d been starting each game with an empty table, and spending the first part of each game searching for that initial black or white koan. During our first playtests, this process seemed amusing and exciting, but before long it began to feel like drudgery. When the Master’s rule was particularly “narrow” or “wide”, it could take a long time to find the first koan of the uncommon state, and it didn’t really feel like the game had started until we’d found it. This caused many rules to feel more difficult than they actually were. Here was yet another area where the game’s mechanics were interfering with the Master’s choice of rules. In hindsight, having the Master set up two initial koans, a-la Jewels in the Sand, was an obvious solution to the problem, but I’d been resisting it because, once again, I was worried about allowing the Master to have creative influence on the game. But now that we were actually allowing the Master to build koans during the game, allowing this extra bit of influence at the beginning of the game was a no-brainer.

I vividly remember the Saturday evening on which we tried out all of these new ideas—the Master builds initial black and white koans, mondo only gives a single stone, guessing only costs a single stone, and the Master builds counter-examples to incorrect guesses. The rule-set played like a dream. There was simply no question in my mind: we’d nailed it. As far as I was concerned, Zendo was done.

Tweaking Mondo

I’m shocked to report that this Saturday evening playtest occurred only about two months after the first playtest with John and Gina. And indeed, my assessment of the project at the end of this period turned out to be more or less correct. Zendo really had reached a state pretty close to its final form.

However, the fact is that Zendo continued to undergo brief flurries of design activity over the course of the following year. The first occurred a full six months after the above changes had solidified. In the fall of the year 2000, I got it into my head to try experimenting just a bit more with the mondo scoring system. Remember that, at this point, the rule was: when you call mondo, if you answer correctly and at least one other player answers incorrectly, you win a stone and no one else wins anything. If you answer incorrectly and at least one other player answers correctly, each correct player wins a stone. In an email to the Four, I laid out three complaints about this system:

It didn’t provide enough tension. Even if you had no clue how to answer a mondo, you still had a 50/50 chance of answering it correctly. Over the course of six or seven mondos, you could probably win a few stones just by flipping a coin. My old fear resurfaced. I started to worry once again that maybe mondo didn’t mechanically matter much at all—that it was just a psychologically pleasing way to dole out stones at a controlled rate. The system didn’t provide any gradation of value in the case when the mondo player answers correctly. If you answer a mondo correctly and three other students answer it incorrectly, that’s no better than having only one of those students answer it incorrectly. The system was just complex enough to confuse first-time players. The fact that there were different rules depending on whether or not the mondo player answered correctly was a tiny bit weird. Basically, the mondo system didn’t quite meet my initial criteria of simplicity—people weren’t likely to fully remember it after a single read-through or play-through of the rules.

In order to address these issues, I decided to experiment once again with the idea that players lose stones for answering mondos incorrectly. This would certainly address issue #1, since if you answered randomly, your number of guessing stones would tend to remain near zero. This idea also addressed issue #2 by providing a gradation of value when you call mondo—the more opponents answer incorrectly, the better. It even addressed issue #3, since the system was now simpler—if you answer correctly, you get a stone. If not, you lose one.

Well, we tried this “losing-stones” idea, and we found that it had a surprisingly negative impact on the feel of the game. The play lost its pleasant meditative and non-confrontational flavor. Psychologically, the game began to feel aggressive, stressful, and constrictive. The sense of being punished for taking an intuitive stab in the dark was an unpleasant and unwelcome addition. After a few games, we were all itching to return to the older system. However, our experiments hadn’t been a waste of time by any means. They’d reassured me that our old system did, in fact, provide a good balance between tension and reward. I now saw that, over the course of a single game, the difference between answering 50% of the mondos correctly and 90% was significant enough to provide the motivation and tension that I wanted.

Another good thing came out of these experiments: during our testing, we stumbled upon a simplification of the old mondo system. The new idea was: each player who answers a mondo correctly wins a stone, unless everyone answers it correctly, in which case no one wins a stone. This was easier to explain (thus addressing issue #3), and it provided a gradation of value, since it was now better to catch as many other players in incorrect guesses as possible (thus addressing issue #2). So after months of claiming “this game is done”, we decided to officially change mondo to this simpler version.

While we were solidifying this change, Jake asked a nonchalant question: do we need to say that if everyone answers a mondo correctly no one wins a stone? By this point in time, we’d all had a lot more experience with game design, and we’d become highly sensitive to little fiddly exceptions in our rules. Our policy was to eliminate them whenever possible. However, in this particular case, it seemed obvious that the exception was absolutely necessary—I mean, without it, you just call mondo on really obvious koans to win stones anytime you wanted. That would ruin the game, right? Jake agreed, and we let the matter drop.

Fixing the Stalemate Problem

But that wasn’t the last we’d heard of the issue. It resurfaced again many months later, in an unexpected context. By that time, Zendo had acquired a bit of a following, purely by word of mouth (since I hadn’t yet published it on the web or in any other form). I initiated an email discussion among the inner circle of players to discuss a number of outstanding issues, and one of the most prominent of these was the stalemate problem that had been plaguing the game since the introduction of mondo. There were two solutions that we’d been vacillating between for months:

If all players run out of guessing stones, the game ends immediately. If all players run out of guessing stones, the Master immediately gives a free stone to each player.

We debated the relative merits of these two ideas, and whether or not either of them was really good enough (nobody liked either of them much). We considered even more elaborate proposals, such as “if all players run out of guessing stones, the Master sets up a mondo, and gives a stone to each player who answers it correctly”. We discussed the possibility of simply allowing the occasional stalemate to occur. But there was one other idea that I’d tentatively proposed to the group: what if, when you call a mondo, anyone who answers it correctly wins a stone, period? That way, players could always win more stones, even if everyone knew the rule.

As expected, almost everyone disliked the idea. Hell, even I wasn’t crazy about it, and I was the one who proposed it. The one person who didn’t seem to dislike it was John. He wrote back that we ought to think very carefully before we tossed out this idea. Sure, it seemed too easy, but maybe that was just our pre-conceived prejudice based on some unquestioned assumptions. Perhaps players would adjust their motivations to take this new idea into account.

So I went back over it in my mind. Why, exactly, was this version of mondo—which we began referring to as “simple mondo”—bad? My knee-jerk reaction was that it just didn’t feel right to allow players to score when everyone answered a mondo correctly. In my initial concept of mondo, the other players’ answers were supposed to gauge the “obviousness” of mondos. I only wanted players to be rewarded for calling non-obvious mondos. However, as I thought about this, I realized that, under the new proposal, players would still be motivated to call non-obvious mondos, because they wouldn’t want to give free stones to all the other players. The previous mondo rules assumed the validity of this same logic—for the player who called mondo, the best result was when all other players answered incorrectly, not just one. If these motivations worked there, they ought to work just as well in the new system. Score one for John’s perspective!

This didn’t completely solve the problem, though. Let’s say that, during a game of Zendo, it comes around to my turn and I have no guessing stones, but I really want to guess on this turn. Won’t I just do an obvious mondo to guarantee that I will win a stone for my guess? This, I decided, was the deal-breaker—I just couldn’t stand the idea that it would sometimes be strategically correct to call an obvious mondo.

But hold on a minute. Was I really thinking this through properly? If I have no stones, and I really want one right now, it must be because I have a theory that I’m ready to spend a stone on. But if that’s true, I should be able to apply my theory to any koan I could possibly build. So why not build a complex, non-obvious mondo designed to confuse other players, and answer according to my theory? The reply to that question—which seemed intuitively obvious to everyone at the time, including me—was that my answer to my own non-obvious mondo might be incorrect, and then I wouldn’t get the stone that I need so badly.

It took a surprisingly lon