Civilization veteran Soren Johnson, one of the foremost designers of strategy games and AI today and certainly one of the best writers on the subject, often remarks that the theme of a game is not to be confused with its meaning (slides here). Diplomacy may cast its players as the great powers of pre-1914 Europe, but it’s about simultaneity. StarCraft may put you in charge of Heinlein-esque space marines and alien civilizations, but it’s about asymmetry. If the theme and mechanics harmoniously cohere, then the mechanics can shed light on the theme in the way that art sheds light on the world. Pre-war Europe is an intriguing setting for Diplomacy because in all their backroom double-dealing, the empires didn’t take turns. Aliens are a good fit for StarCraft because you can map anything onto aliens, be it the collectivist swarm-by-numbers ethos of the Zerg or the judicious high-tech investment of the Protoss.

I am partial to this view, predominantly for reasons of aesthetics. If we are to conceive of game design as an art form, it does not suffice to decompose games into the artistry of constituent parts—the music, the models and sprites, the cinematic sequences, on rare occasion the writing. The aesthetics have to come from the specific properties that make something a game, whether it is played with a board and dice, a deck of cards, or a mouse and keyboard—and those properties come from the mechanics.

But that’s neither here nor there; I won’t elaborate today. Instead I want to turn to my favourite of Johnson’s examples: the evolution game. For your fill of Darwinian game mechanics, look not to Spore (which Johnson worked on), a game that is nominally about evolution from microbe to intergalactic juggernaut, but is actually about special creation. Back when I first played it, I wrote, perhaps a tad generously:

Let’s not bury our heads in the sand: by placing creature design into the player’s hands instead of leaving it up to random mutation, Spore inherently owes a lot to intelligent design. There’s still room for a real game about evolution in the Darwinian sense, where you set certain environmental constraints and preconditions, let a species run loose, and see if it survives in an ecosystem full of other models—kind of like how some engineers pit robots in mortal battle, but with adaptation.

Spore is a lot more creationistic than I gave it credit for; consider that the functional components of your custom-made species—the mouths, the horns, the flagella—are interchangeable parts from a specified, modular set, which is precisely what we would expect from a designing agent but not at all what we would expect from natural selection. But never mind all that. The evolution game exists, says Johnson, and it’s called World of Warcraft.

I would contend, however, that the Darwinian features Johnson ascribes to WoW are equally prevalent in most games with competitive and highly interactive player populations, provided there is sufficient strategic depth worth talking about. WoW is an evolution game because its core mechanic is community. Where there is a community of players and a developed metagame of optimal practices, strategic decisions are memes that compete for survival. Let’s call them strategemes.

Strategemes include everything from chess openings to Scrabble vocabulary: they are transmissible units of knowledge that players learn, study, and adopt—and crucially, copy. Copying them is not seen as unfair, but as an advantageous and often essential behaviour. They leave room for mutation, and we can perceive a frequency distribution of variations over a population of players and games.

But where does natural selection come into play? Let’s look at the exemplar we get from Johnson: the WoW talent tree.

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In brief: The book’s alternate subtitle—”How 32 Carved Pieces on a Board Illuminated Our Understanding of War, Art, Science, and the Human Brain”—offers a hint of Shenk’s scope of thought. Full of colourful stories and painstaking research, this thoroughly accessible work probes into the mystery of how chess has endured for 1400 years and why it delights us still. Shenk guides us on a tour through everything from the intrigue of warring nations to the play-by-play thrill of a historic game, and muses as much about how chess has shaped humanity as how humanity has shaped chess. A must-read for hobbyists and serious players alike.

(The Wednesday Book Club is an ongoing initiative of mine to write a book review every week. I invite you to peruse the index. For more on The Immortal Game, keep reading below.)

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This caught my attention:

In 2006, Brian Reynolds, a founder of Maryland software company Big Huge Games and the programmer who developed the AI behind the addictive computer classic Sid Meier’s Civilization II, set out to make an Xbox 360 version of Settlers. To help programmers develop the game’s AI, Teuber spent months exploring the mathematics of his most famous creation, charting the probability of every event in the game. The odds of a six or eight being rolled are almost 1 in 3 for example, while the chance of a four being rolled is 1 in 12. There is a 2-in-25 chance of drawing a Year of Plenty development card. Teuber created elaborate logic chains and probability matrices in a complex Excel spreadsheet so the videogame developers could see how every possible move and roll of the dice—from the impact of the Robber to the odds of getting wheat in a given scenario—compared. The end result was a sort of blueprint for the game that gave Big Huge Games a head start and showed just how complex the underlying math was. “It was the biggest, gnarliest spreadsheet I had ever seen,” Reynolds says.

I want to see this.

One of the best things that happened to the Civilization series was how in Civilization IV, lead designer Soren Johnson laid the mathematics and AI bare for everyone to see, expanding on a series tradition in the Sid Meier games to make all the data easily accessible (and therefore modifiable).

Settlers is elegant enough that I’m sure people have already figured out the math through a spot of reverse engineering; it’s really not that hard. But I’d love to see Teuber’s spreadsheet for its immense historical value as a design document alone. Surely there was a calculated rationale to everything from the fifteen-road limit to the assignment of three ore/brick hexes instead of four—and I often wonder if the perpetual endgame glut of sheep is here as an intentional crimp.

Casablanca is one of those films that nobody really falls in love with the first time through, even if they think otherwise. Most of its enduring power emanates from multiple viewings, when the film truly demonstrates its uncanny ability to resonate with almost every conceivable romantic trauma, especially those of a triangular geometry (which is to say, practically all of them). You go through life-as-such and every time, there’s always a handful of scenes that you’ll never look at in the same way again.

I haven’t watched the film in months—I only pull it out once a year as a routine, emergencies notwithstanding—but I already expect to encounter these transformative moments with respect to two scenes in particular: a) when Victor Laszlo leads Rick’s Café in a stirring rendition of “La Marseillaise” (for reasons I’m not even going to bother explaining), and b) the first time we see Rick, brooding over a chessboard by himself.

So here’s the mystery du jour: why is Rick playing chess?

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Regrettably, the mainstream press saw fit to stop at the level of goals, objectives and the roleplay element, and did not appear to find the game mechanics themselves to be newsworthy. This is understandable, given that the representational level of “Bomb London for 100 points” is probably of more interest to historians than the question of how exactly one goes about conducting such a blitz.

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For those of you who aren’t familiar with computing science, game theory or their related fields, what it means in layman’s terms is this: consider how with a simple game like Tic-Tac-Toe, pretty much everyone over the age of five has stumbled upon a strategy that will always play to a win or a draw. Well, it’s been a long time coming, but they’ve just done that with checkers.

There’s a considerable wealth of information on the Chinook website, where you can step your way through a demonstration of the proof or find your way to the article in Science.

More than anything else, I hope this kind of high-profile accomplishment encourages others to pursue studies in what is, I think, a grossly misunderstood and often ill-introduced branch of the sciences. I know that I, for one, had little idea just what I was missing until I transferred into their programme in my third year, a decision about which I have almost no regrets. Computers aren’t just tools that are meant to sit around generating heat in office cubicles, waiting to be thrown out a nearby window; their study is not limited to job training for information-age janitors, network witch-doctors and software monkeys. There’s a genuinely interesting field of scientific enquiry there to which few receive anything remotely resembling a proper introduction. I sincerely hope this is a step towards the elusive remedy.

Next stop, poker!

On a game-by-game basis, it was far from a disaster by any standard, as I won one game decisively (6 VPs on the table, 4 for Longest Road and Largest Army, and another one just to make sure) and tied for a close second in two others in the face of unfavourable dice. But I needed two wins to advance to the semis. As with most games that involve a tenuous balance of skill and chance, consistency in the face of misfortune is the mark of a skilled player. It looks like I have some ways to go.

We will speak little of Round 3, in which I did not show up, nor did the number 5, and I finished dead last with only 4 VPs. That debacle was almost entirely due to tactical and strategic miscalculation on my part, as I drew first position on the snake (placing my initial settlements first and last), grabbed a 5/9/10 and went for an expansionist wood/brick strategy, which I almost never do. Anyone who has heard me mope about Scrabble knows that I have a remarkable tendency to get overly experimental in untimely competitive situations. All three of the other players went for an ore-heavy game, and rolled the numbers to match, erecting early cities and grabbing piles of development cards while I sat on my hands with nothing of significant trade value. With no cities, no soldiers to keep the robber off my property and no 5s, my exit from contention was terrible, swift and entirely my fault.

But it happens. And while the knowledge that you played poorly is hardly a happy thought, it gives you the opportunity to shoulder the responsibility and think about how you might act differently in the future. In spite of the dice, you retain the impression that you have control over your own destiny.

However, three key elements of Settlers of Catan elevate its strategic complexity to a whole other dimension that I am only beginning to grasp. It’s non-zero-sum, it’s for four players, and it’s built on trade.

Settlers is non-zero-sum in that you can check a player, or you can block him from victory to some extent (ask Jake Troughton about the game he had elsewhere in the tournament where the other players held him at 9 VPs for well over an hour), but aside from snatching away the Longest Road or Largest Army, you can’t roll him back. Once you have points on the table, they stay on the table. And when someone coasting to victory settles on the same numbers as you, the rolls that permit you to develop confer no relative advantage. The dice may well push them over the edge, and there isn’t a damnable thing you can do about it.

And more to the point, in a four-player game, someone can hand someone else the game with a series of bad decisions, and there isn’t a thing you can do about it except sit there and watch. If the initial settlement placement pans out so one opponent is left with a disproportionate tract of uncontested land open for expansion, because the other two decided to crowd you instead, it sucks to be you and that’s that. Similarly, if another player decides to go through with an uneven trade, or break a three-way embargo, there’s little to be done apart from taking a bullet and proposing an even more ridiculous counter-offer. I’ve been on both sides of this situation. On the winning side, you try to get yourself into a position where someone else has to cooperate with you just to stay in the game.

I’m not an Xbox 360 owner, so I haven’t had a chance to poke and prod the AI behind the Settlers of Catan video game, but I’d be very interested in examining it for its shortcomings. Like the human element behind games like poker or Diplomacy, it seems to me that the trading element that fundamentally drives the course of proceedings in Settlers would be extremely difficult to formalize and refine. One of the biggest challenges when it comes to artificial intelligence is getting over the assumption that you’re playing against someone rational. Game theory was designed to fight rational fire with rational fire, which is why you end up with suboptimal equilibria like the Prisoner’s Dilemma. In Settlers, you have to account for deeply suboptimal opponents – the ones who, in the Prisoner’s Dilemma, could actually be hoodwinked into cooperating instead of defecting; the Kevin Lowes who will actually give away their Chris Prongers for less than nothing (to your divisional rivals, no less). What you do at a table of championship-level thinkers is and must be different from how you behave when someone is just there for the burgers and door prizes.

And I wouldn’t have complained about a little help from the dice.

Belated congratulations to my compadres Chris Samuel, who finished 13th with two wins and contended in the semis, and Steve Smith, who finished 19th with one win (Round 4 against me, knocking me out), and sat (but did not play) as an alternate.

Hockey anthem addendum: I have a lot of respect for Holly Cole for being one of Canada’s leading jazz ambassadors, but here’s a three-letter memo about her performance of “O Canada” at the Duck Pond in Game 2: WTF?

But first, as I have been tending to do with increasing regularity, I am going to precede the main feature with some ancillary featurettes.

I don’t write that much about hockey (proportionate to my other interests) because other, more prolific minds know a lot more about the ins and outs of the subject than I do. But I do know music, and I’m a bit of a stickler when it comes to the singing of the national anthems. I remember, with astounding clarity, that the most execrable part of watching Tampa’s home games in the Tampa-Calgary series in 2004 (aside from seeing the Lightning hoist the Cup) was Brooke Hogan’s consistently lamentable butchering of “O Canada” – and I’m sad to report that since then, Hulk’s baby girl hasn’t faded into deserved obscurity, but has instead released an album and graduated to B-list pop-stardom.

So, for all the press about how epic the Buffalo-Ottawa series will be when it comes to the action on the ice, I think it falls to somebody to mention two of the lesser-recognized reasons why it will be (and already is) so fun to watch: Doug Allen and Lyndon Slewidge. I haven’t seen every regular anthem singer currently making the rounds in the NHL, of course, but of the ones I have, these two are the very best. (And being from Calgary, where we get the excellent Heather Liscano, I do have standards.) What does the trick is their clarity, charisma, genuine quality of musicianship, and unflinching respect for what they are singing. Oh, and they stay in time. I’ve lost count of the wannabe divas who trill left and right and demonstrate nothing but a lack of education in the basics of metrical tempo (to say nothing of tone control). We’ll have none of that.

Next: Its run at the Varscona Theatre closes on Sunday, but Shadow Theatre’s production of David Belke’s Dreamland Saturday Nights is an absolute delight. I’m not as well-versed in appreciating the subtleties of the stage as I am with cinema or music, but this was my best experience with live theatre in some time. I do wonder, however, if it plays nearly as well to people who aren’t major cinephiles, as so much of its magic is referential.

And now, as promised, a bit about board games.

Last week, I went out into the wilderness with my new colleagues (pamperedness level: heated cabins), and one of them had the presence of mind to bring along the familiar diversion that we all know as Connect Four. On the last evening of our trip, when I was busy nursing a pot of cheap strawberry tea and making absolutely no progress on my cute little novel-in-progress about space colonies and married women, he challenged me to a friendly match. One friendly match quickly ignited into thirteen. We stopped when I hit ten wins. For those of you in the audience who can’t add, that’s a 10-3 record.

On paper, it looks like I demolished the poor guy; he certainly thought so, and it wasn’t until the next morning (when he beat up on someone else) that he regained some elementary semblance of confidence. To be fair, I started with six straight wins, and finished with a considerably weaker 4-3 thanks to careless errors in observation, unnecessary experimentation, and (in my opinion) noticeable improvement on the part of my opponent.

Now, I hadn’t played Connect Four in an absurdly long time: I only vaguely remember playing round after round on my Macintosh SE back in the black-and-white halcyon days of System 6, and I may have faced the occasional human opponent, though I’ve never owned a physical set myself. But the rules are simple enough that it’s not like you’re liable to forget how to play. The name of the game and the design of the board (i.e. it’s vertical, and pieces dropped in the slots tend to fall) make the mechanics about as self-evident as is possibly conceivable. That said, it would be foolish to understate its strategic complexity.

I can’t say I’ve ever considered myself any more than a casual player, and by purely casual standards, I don’t think my opponent was exceptionally bad. How, then, did I manage to be so dominant? What has really changed since the age of nine? Board game skills aren’t like fine wines: they don’t improve with age alone.

Two things come to mind: 1) serious exposure to other games of strategy, and 2) an education in the little-understood field of computing science.

The first is probably obvious. In the case of Connect Four – elegant, turn-based (but otherwise symmetrical) and fundamentally geometric – it’s easy to see how some half-decent Scrabble skills might help: looking for hotspots, settling into a rhythm of risk and reward, differentiating high-risk offensive positions from conservative and defensive ones. More pertinent would be a deterministic game like chess, where you learn to recognize certain patterns as opportunities for setting up zugzwangs and forced mates. I kind of wonder how well someone with a background in grid-based video games like Tetris Attack would fare.

There’s also the psychological element of the discipline it takes to focus on a game, exercise the patience to find the best move, intuit what your opponent is trying to do, and avoid stupid mistakes, but I don’t have that.

Less obvious to the layman is the value of a computing science education, which a lot of people out there think of as the study of computers, when in many cases it would actually be more accurate to say it is the study of problem-solving. (That’s a crude generalization as well, but still more accurate.) It’s not too hard to see how excellence at games of strategy is so often conceived as the pinnacle of whatever it is computing scientists do.

I am not saying that in a given turn in Connect Four, I’m culling a game tree in my head or performing a systematic limited depth-first search. But just as a basic level of comfort with calculus provides you with a substantially better intuitive grasp of infinities and convergences even if you don’t remember the ins and outs of solving triple integrals by substitution, I wager that an understanding of rational, computational processes provides one with an intuitive basis for pattern recognition and logical reasoning.

On top of that, it provides you with the tools to easily pursue further study. The reason I am writing this post is in part because tonight, I thought about how I might design a Connect Four AI, and I started looking at what had already been done. As a mechanically straightforward (and fully deterministic) game, it did not come as a surprise that Connect Four had already been solved. (The relevant thesis, which you can download as a 91-page PDF, is Victor Allis’s “A Knowledge-Based Approach of Connect-Four,” published in 1987. I’m not through much of it, but so far, it’s a terrific read.)

It turns out that with perfect play, the first player to move (“White” in the standard literature, as I don’t think many people with the standard Milton Bradley set care if red or yellow go first) always wins if the first move is down the centre column, just as how X can’t lose in tic-tac-toe if the first move is in the centre square. It seems intuitive, but there’s no comfort like the warm cushion of a mathematical proof.

Apart from questions of the “how did I win” variety, I think there’s another issue in play: why did I have fun? (This might not occur to those of you on another planet who play games solely for amusement and diversion and not necessarily to win, but I do, on occasion, actually have fun.)

Let’s proceed by example and analogy, shall we?

Anybody who has known me for any period of time probably has at least a cursory knowledge of where I stand when it comes to board games. There are three games in the top tier. I play Scrabble (far and away my favourite game of any sort) seriously enough to compete but not obsessively enough to truly excel; I’m fascinated by Diplomacy, but inexperienced; I adore Settlers of Catan, but I’m not nearly as good as the statement “I finished second at the University of Alberta’s POGOB! tournament in October and I’m playing in the Western Canadian championship next week” might suggest. (With games like Diplomacy and Settlers, a good reputation is a huge liability. People start ganging up on you.)

I have the deepest respect for chess, checkers and Go, but there’s such a gulf between my level of skill and what I would consider an acceptable competitive standard that I view them much like I view movies that are obviously imbued with the finest craftsmanship, but do not stir any passions on a personal level, and cannot be said to be among my favourites.

Among the other popular entertainments: I used to enjoy Risk, but I abandoned it after I found Diplomacy, and I haven’t played it since. Back when I was an only child, my family played Monopoly, but we would fight over the game and inevitably leave it unfinished; later, I discovered that we weren’t following the rules correctly anyway. I’ll play Battleship, but it’s just not the same without the “Sploosh!” and “Kaboom!” sound effects from the version in The Legend of Zelda: The Wind Waker. Then there’s the whole class of games like Cranium and Trivial Pursuit that I’m not even sure I should count: they suit social settings well, but you can’t “study” the game without feeling like you’re cheating.

I hate the Game of Life. (Not Conway’s cellular automaton, but that thinly-veiled wheel-spinning instrument of social engineering where you drive around in a little car and add pins to it when you get married, have kids, and coast towards your inconsequential demise in the thorny brambles of the American Dream.) Life sucks. No strategic depth whatsoever.

Now, let’s play Spot the Correlates. Is there anything I consistently like or dislike about board games?

If you look at the top tier – Scrabble, Diplomacy, Settlers – all three of them have an element of nondeterminism (stochastic in Scrabble, qualitative in Diplomacy, both in Settlers), but success or failure is primarily and repeatably dependent on conscious strategic decisions on the part of the player. In addition, a significant number (but not all) of these decisions are independent of who the opponent is, because they involve tactical knowledge of the game mechanics. It is possible to get progressively better as a player, but impossible to win all the time.

Connect Four initially falls into the same qualitative category as chess – although Go would be a better comparison, as it is based on placing pieces, not moving them, and there is only one type of piece. Connect Four doesn’t belong to nearly the same order of complexity, of course, but it feels like a faster-paced incarnation of the same deterministic experience. There is at least the persistent illusion of a fair fight, whereas in chess, I will almost always lose to someone who has a library of openings down pat, and almost always beat someone who can’t find his way around basic pins and skewers.

In a casual or novice-level game, you will almost never see a stalemate in chess except by accident, because the players aren’t skilled enough to set one up to avoid a loss, but they are skilled enough to finish off a familiar pattern like having a king and a rook to the opponent’s king. In expert play, draws are virtually the norm, and the result is a phenomenon called draw death: the prevalence of stalemates between players of sufficient skill exposes a serious air of futility that hangs over the game as a whole. A more familiar example of draw death is in tic-tac-toe. It doesn’t take very long for even a small child to figure out how to play every game of tic-tac-toe to a draw, at which point there is no real incentive to play anymore.

To be fair, this also happens in expert-level Diplomacy, where it is possible and not at all uncommon for the last two remaining players to entrench themselves in a stalemate line that cuts across the map, preventing each other from reaching the 18 supply centres required for victory. And a game like chess is sufficiently complex that unlike tic-tac-toe, it’s still possible to hold a championship. Draw death isn’t a reason to not play chess unless you are outstanding, in which case your name is Bobby Fischer and you remedied the problem by inventing a chess variant (Fischerandom/Chess960) where the initial placement of pieces is randomized within certain constraints.

I’m sure that against sufficiently skilled players, draw death presents a huge problem for Connect Four. But the real barrier to enjoying games of strategy is when improvement relies on the memorization of positions instead of principles; I also see it occur in Scrabble, where you need to dedicate a tremendous effort to memorizing words just to have a chance to apply strategic ideas. I like words enough that I don’t mind so much, but that obviously isn’t the case for everybody.

The elegance of Connect Four is how much complexity it manages to preserve in order to remain interesting, while its simplicity entails that it is never an exhausting game to play; it goes by so quickly that one can play round after round with little trouble. It owes at least some of its speed to a certain lack of choice, with only seven or fewer possible moves per turn. It also does not seem as susceptible to massive disparities in skill as many other games of its ilk. On the other hand, it’s entirely possible that I just don’t know the game very well yet, and that once I do, the number of players with whom I feel evenly matched (in either direction) will plummet.

And that’s why I’m behind on my novel.

The initial strategy was to ally with Austria, push out from the centre, invade France with England’s assistance and pull a sharp one-eighty eastward. The game turned out to be not quite that simple, due to the unexpected factor of Austria, Germany and Russia not consistently submitting orders. The French invasion – an uncommon opening strategy – was held back due to the uncertainty of Austria and the need to defend Venice, but still succeeded due to a feint that drew France (played by Ross) into a defensive position that forsook expansion into Iberia in Fall 1902, and the good fortune of a missed submission on his part.

With France out of the way, the three most active powers in the game, which also ended up being the last three standing – Italy, England, and Turkey – all benefited from the truancy of the competition. Without the central powers actively expanding, there was little in the way of checks and balances for the first few turns. England marched into Scandinavia and the Lowlands uncontested; Turkey, despite starting a turn late when Josh stepped in to replace a resigning participant, and was clearly in the lead by the end of 1904, but made the fatal mistake of missing a submission when he was entitled to three builds – a gaffe that, along with a failure one year later to practically knock me out of the game when he had the chance, may have compromised a Turkish victory.

Would an Italian victory have been possible in normative circumstances, where every player submitted orders on time every turn? Perhaps so, but it would hardly have come that easily. I got away with a lot of things in that game that, under balanced circumstances, would be next to impossible barring some extremely cunning negotiation tactics. A lot of bad moves on my part went unpunished: aside from leaving Naples wide open for Turkey that one turn, I conducted a risky double-cross against long-term ally England that was next to suicidal; thankfully, an Anglo-Turkish alliance never came into being.

Regardless, it does feel rewarding to pull something off so contrary to the statistical norm, handicaps and all. Right now there is an attempt to set up another Webboard game, this one on a Middle Eastern variant map. While I will not be participating in this round, I encourage you all to sign up. Diplomacy is a game that truly shines with maximal effort and participation.