Required Reading: Game Theory in the Age of Chaos

Before you get started on this article, let me ask you two questions. Do you like game theory? Do you dislike what the current administration is doing to this country? Great. Get this book. With that out of the way, let’s get to a heartfelt blog post.


PAX Dev is an incredible opportunity for game designers and developers of all stripes to come together in a convention filled with great panels and workshops that really help build up our industry into the best thing it can be. I’d tell you more about it, but I can’t. It’s a black-box convention, which means that anything presented or discussed there is off-limits to the press or to the outside world. This safety measure is a huge benefit to making changes in the world of gaming. So while I can’t talk about much of what happened beyond my own presentations, I can mention one major event that took place during the closing panel of PAX Dev 2017. Mike Selinker led an incredible lineup of people in discussing the impact game creators can make in the world around us. I stood up and talked about how helping students learn about game theory and solve conflicts was something that felt more meaningful every day. I felt lucky to be part of it, both as a presenter and as a witness to that massive event.

With that in mind, Mike continued to write essays which attempted to explain the events of the day with his background in games and tactics in full force. His essays dug deep, explaining the antics of the current administration in terms that every game player could understand. Mike studied the politics behind the wall, nuclear standoffs, and reckless trade policies, each with in-depth research and analysis. Far too soon, Mike had more than enough material to publish the essays as single collection—a clear intersection between game theory and the political landscape we see every day. Each essay feels like a clarion call that breaks down the seeming chaos and attempts to find the underlying strategy and order.

As a game theorist, I’ve been keenly interested in these essays, so I’d tell you to grab a copy of Game Theory in the Age of Chaos for Mike’s words alone. However, each of these essays also includes a short section of my own, which helps to illuminate the game theory with a second voice. I’ve run through and explained important basics like utility theory and the volunteer’s dilemma, but also larger topics like veto power, armor theory, and the gambler’s fallacy. My hope is that you walk away from this book with not only a clearer understanding of the current administration, but also a great primer on some of the most important ideas in game theory. Both of these things feel more important every single day.

Sure, we’d love to just apply game theory to our favorite games, but the field was crafted specifically to explain situations in politics and economics. Mike has done heroic work binding the two together, and for a short time, you can get your own copy for one cent, as long as you donate $25 to the Democratic Party. It’s hard to imagine a better analysis and guide through the chaos that has become our everyday political lives.

Like Mike says, “It’s better than screaming all the time.”

The Symmetries of Asymmetric Play

A few years ago, I met up with a group of friends to playtest a groundbreaking new game. Everyone sat at the edge of our seats as we cut out cardstock tiles and reviewed the rules, because this was going to be the start of a new craze—the asymmetric game. Each of us would be playing the same game, but we’d have different goals and abilities as we battled for victory. Truth is, none of us really knew what that meant.

“So it’s like playing Tag, and one of us is It but the rest are all trying to run away?”

“What about Magic? Is it like you’re playing Big Green Monsters and I’m playing Blue-White Control?”

“Or maybe it’s like playing World of Warcraft or something? We’re all different classes but we all hit the same buttons to do things?”

“What exactly are we playing here?”


Since then, I’ve started to come up with some answers to these early questions. I’ve played a few, and generally an asymmetric game comes in one of a few categories. From games like World of Warcraft (cooperative games with similar goals but differing styles) to Tag (competitive gaming with very different goals and styles), asymmetry presents in a few different ways.

“May the odds be ever in your favor”

That playtest with the tiles in the basement? That was my first introduction to Vast: The Crystal Caverns, the new asymmetric hotness that was preparing to take over the gaming world. In Vast, each player gets their own role, pieces, player board, and their very own rulebook. That’s how crazy this game needed to be to make asymmetry work.

Here’s the brief rundown. The Knight is trying to kill the Dragon, who just wants to rise from its slumber and escape the Cave. The Goblins want to trap and kill the Knight, while the Cave wants to trap everyone inside for eternity. Then there’s the Thief who just wants to grab a bunch of treasure. At any moment, one player is closer to their own goal and needs to be reigned in by a team-up of the other players. This leads to a lot of temporary alliances as everyone jockeys for position and final victory.

Vast delved into asymmetry by also making the mechanics extremely different for each role. This makes each play a wildly different experience, but it also means that each time you play, you basically have to relearn the intricacies of the game from a new perspective. The Knight has to explore to gain items that increases their stats, but the Cave is choosing how to build the board in order to lay traps for the other players. For new players, this is very frustrating.

The team behind Vast is also working on two other games, Vast: The Mysterious Manor and Root. I’ve only played an early prototype of TMM, which continues the theme of its predecessor (playing the Manor is amazing), but Root has branched out into another path. Players in Root all have similar abilities, though different goals. Well, at the very least, each player is using a different kind of game mechanic and engine, but the specific details of battling around the map are very similar. This has the effect of making it easier to learn and play, but also muddies up the distinctions between player roles. I’m excited to try it out more to determine which game hits my table more often!

“It’s a race!”

When players aren’t directly competing, it becomes a little bit easier to give people wildly different gameplay. I was a little shocked at how much I enjoyed playing the new game Villainous, a game licensed right from Disney. In this game, each player has their own board as they take on the role of a famous Disney villain and attempt to play out their own evil plan. As the cunning Jafar, I searched for the Magic Lamp in the Cave of Wonders, using it to summon Genie, and then Hypnotized that magical being for my own nefarious goals back in my Palace. At the same time, the Queen of Hearts was trying to turn a bunch of Card Guards into Wickets for a wild game of croquet over on her own evil board.

As we battled our own tales, we sometimes had the option of adding some drama to our opponents’ stories. Each player had a Fate deck full of heroes and other acts of goodness which would make it that much harder for a Villain to succeed. The Villains would have to stop their plan to deal with this Fate in order to get back into the swing of evil.

What I enjoyed about this design was that even though each player had their own rulebook, they were trying to do things we, as Disney fans, already understood. The mechanism might be strange, but my goal was exactly the one I remembered from the movies. This led to an experience that was remarkably successful for a game that seemed to be built out of such disparate parts.

“With our powers combined…”

My favorite subset of asymmetric play is the one where everyone needs to hold up their end for the team to succeed. For example, I was obsessed for a long time with an MMO called Puzzle Pirates. As we sailed around on tiny little shipping runs, there were four different puzzles that kept a ship moving. My goal was always to be the best at the sailing game on the entire server. Did someone want me to do carpentry instead? Or bilge? Instant mutiny. I wasn’t bad at navigation, but sailing was the dream. And the better I sailed, the faster our ship soared across the sea.

A bad sailor set your ship adrift. But so did someone bad at bilging or carpentry. If your crew wasn’t the best at something, you’d put multiple players on the same task. And then, to make me feel incredible, individual results were posted every few minutes, just to keep us invested on being amazing.

That feeling is harder to apply to a board game, but easily the top of the pack is the fantastic Spirit Island. In this “Reverse-4X” game, you play one of the island’s spirits, fighting back against the colonialist invaders and sending them back into the sea. Each spirit plays in a totally different way, with some focused on creating Fear, some manipulating the beasts and native Dahan, and others simply burning those invaders to the ground. As the game progresses, each Spirit is capable of more and more, which makes it very important for each player to be on top of their game. The invaders are tough, and routing them is going to take a concerted effort.

In some cases, the game makes it impossible for certain spirits to affect certain spaces on the board. Without beasts to manifest from, Sharp Fangs Behind the Leaves is locked out of the more developed locations. A Spread of Rampant Green has the most impact in Marshes and Wetlands. Ocean’s Hungry Grasp is a coastal spirit, able to destroy invaders along the shoreline, but has little power to affect the interior. With wildly different spirit abilities, weaknesses, and a pile of invader scenarios and difficulties, Spirit Island is a true test of cooperation.


When it comes down to it, the weirdest thing about asymmetric games is that they’re the ones we’re really used to in the real world. We’re used to playing with different abilities, coming from different backgrounds, and with massively different goals in mind. We grew up with them. They resonate with the stories we tell. The strange idea is actually the one that says we’re all the same and all trying to get to the same place. Asymmetry is normal. It just took board games a while to catch up.

The Wedding Puzzle

Do you ever wish that strange and mysterious events would just… occur? As a lifelong fan of adventure stories, I certainly do. With that kind of heroic inspiration in mind, my wife Angela and I made an irrevocable decision. Exactly one year ago, in the warm, glowing moments directly after our space-themed wedding ceremony, we orchestrated a devious puzzle hunt for our completely surprised attendees. Because that’s how the Malena-Webbers plan their wedding.

Step 1: Honesty

Both of us love puzzles and games, and we wanted to make sure our entire day was infused with these ideas. We solved a puzzle during the ceremony and had board games available during the reception. Games are important to us both and as we started playing them together, we realized that we didn’t have as much fun when a game forced us to be dishonest. Even holding onto a secret was troubling. So as we planned out the game, we wanted to make sure that we wouldn’t have to lie to anyone for any reason—or force anyone else to lie! Honesty would be our credo. Which meant I had a lot of secret preparations and work to do.

I began writing the puzzles in December. They needed to be crafted for an audience of our friends, which includes both puzzle-masters and puzzle-phobes. So we wanted big, fun reveals and the ability to opt in or out as any guest saw fit. Multiple iterations later, we had our plan. We filmed an introductory video and I frantically built props that could be set throughout the wedding without any guests knowing or finding them in advance! I ended up setting many of the props around the room myself and decided “I can do this myself!” was as close as I’d get to crossing that honesty line, even to the members of our wedding party. It was a struggle. But we came, we saw, we… let’s just say it went pretty well.

Step 2: Learning Experiences

On April 1st, 2017, we walked back down the aisle after exchanging rings and vows to (of course) thunderous applause. We found a quiet hallway and hid, knowing that the puzzle was about to begin! Our guests found their tables, each with a perfect theme like Lord of the Rings, Dungeons and Dragons, or Tabletop Games. You know, the stuff we like.

After a few moments, our two Astronaut MCs took the stage and played our introduction: We’d already lost our rings! It was up to our gathered friends to find them. There might be some kind of note on the back of the placemats…

In this puzzle step, each placemat had a large letter written on the back. When kept in order, the set at each table formed a word, with one or two extra letters, but the word was for the theme at another table! So the Oregon table might have GOLLUM+RT, which meant they needed to team up with the Lord of the Rings table! As the tables formed into three groups, those extra letters would form a series of three words, revealing the next instruction.

We heard the ruckus begin as we hid, waiting for the climactic moment when they’d complete the puzzle. Time dragged on and eventually I had to peek. The crowd was stumped! I sat back, panicking and hoping for an update from a worried Astronaut. Eventually, we learned that one table had mixed up their letters and formed a word I hadn’t even considered! As confusion reigned, all of the placemats were removed from the tables and placed out in the floor for further public debate.

They got it eventually, but I certainly learned the value of being prepared for the unexpected.

This puzzle solved to RINGING PRESENT INTERIOR, and the guests quickly moved on to the next stage.

Step 3: The Hero Moment

A table had been set up in advance for wedding cards and gifts, including three that I’d planted there that morning. Two made silly sounds when shaken, but one had a bell that rang loudly! The guests looked at each other before tearing open the paper, ripping into the box, and finding a very special Rubik’s Cube covered in stickers.

Has there ever been a moment in your life when you wished that your particular set of skills might make the difference between life and death? Or the difference between your friends getting their rings back or not? I wanted to give one player that miraculous moment on a big stage, while at the same time hoping that anyone in the room could solve a Rubik’s Cube!

Thankfully, we’ve got the right kind of friends. When the Cube was solved, it read THE SECRET CODE BEHIND THE CONSTELLATIONS. The guests looked around and saw the beautiful constellation paintings that had been painted by the incredible  Susan Webber and set around the room throughout the day and quickly wondered what was on the other side.

Step 4: Finding Joy in Challenges

The guests peered behind the paintings and didn’t see anything. Then they noticed that there was paper attached to the back of each painting, hiding the canvas beneath.

With quick sideways glances to make sure that decoration destruction was allowed in this puzzle, they eventually ripped through the paper and saw cards tacked to the inside.

These cards were collected, brought up to the mainstage, and assembled on the floor for everyone to see. Though the writing made it a little tough, they eventually found the final instruction—WHAT DID THAT HOBBITS ASK WHEN HE TRICKSED ME?

Our guests then went up to the Astronaut MCs who had been taunting them throughout the day and asked “What have I got in my pocket?” They said, “I don’t know what YOU have in YOUR pocket, but we have rings in ours!”

And like that, the rings were found. Marriage saved.

Step 5: It’s a Wonderful Life

In the year since we ran this puzzle, Angela and I have picked up and moved to a new city, found new jobs and new opportunities, and brought new friends into our lives. It has often been stressful and challenging, but we’ve made sure to spend time playing games, solving puzzles, and trying to maintain this constant sense of wonderment in our marriage and our lives. I think we both love the joy that comes from navigating a challenge and bringing it to successful and satisfying conclusion! All these puzzles and games and all the friends we’ve been fortunate enough to share these events with made our lives better and helped make our wedding the most wonderful day I’ve ever had.

To my dearest wife, Happy Anniversary! Here’s to many more games to come!

(The first anniversary is the Puzzle-Based Blog Post Anniversary, right?)

Disrupting The Spacecrime Continuum

Back in December, Renegade Games launched a solo campaign for one of my favorite games, Clank! In! Space! In this preset story, our hero is a thief who must repeatedly break in to the massive battleship of Lord Eradikus, stealing his most treasured objects while making alliances and finding secrets along the way. Each mission of this deckbuilding adventure has specific goals, pushing players to draft a certain style of card or gather a certain kind of treasure. At mission’s end, players are ranked based on their performance, allowing them to replay the mission later on in hopes of beating that goal.

As someone who has played a good amount of Clank!, this solo app has given me an interesting insight into the game. When the game is played in its regular multiplayer mode, the game becomes more difficult as the players progress. If players are slow to purchase cards and move through the maze, the game reacts in kind, doling out damage at a slower and safer rate. If players move quickly, the game likewise ramps up to a higher difficulty. This sliding scale of difficulty gives players a self-guided buffer to their own efficiency. Let’s break this down into a decision tree based on player speed.

Rather than being about maximizing my own efficiency, Clank! is really a game where I need to be aware of my opponents and just keep up. If they start making some big moves, I need to do the same thing. If I fall behind, I am suddenly in danger of losing. But as long as I play at the same level as my opponents, the game is pretty fair.

Solo play throws this logic out the window. Suddenly, I’m playing against an app without mercy. Even worse, I lose my tells—there aren’t any other players to judge my own deck against! What we really need to do is determine the app’s game mechanism in order to determine how best to beat that algorithm.

Dr. Whiskers is also pretty mean to our hero!

Each turn, I am allowed to purchase cards from the market. Either I can buy the reserve cards, like Boldly Go and FAZR, or I can buy any of the six available premium cards in the marketplace. These premium cards are replaced at the end of the turn, and if any of the replacements have the Eradikus symbol on them, Lord Eradikus attacks and potentially damages the players. If players don’t buy cards, they don’t get hurt as often. The app, however, deletes one or two cards at the end of every turn, which means Eradikus could deal damage to you on a very regular basis. This is especially true because you are the only target of that enemy damage!

The only counter to this constant barrage of damage is to take fewer turns. Which makes it ever more important that the solo player drafts cards allowing them to move around the board as quickly as possible. This requires the player to build an efficient deck.

Yes, I keep using the word efficient, but what does that mean? In any deckbuilder, it means that a deck maximizes every turn. Sometimes, an efficient turn is the one where you play through so many cards that you gain an endless wealth of options. Other times, an efficient turn is simply drawing and playing the five best cards in your deck. In each of these instances, your starting cards are the least worthwhile cards in your deck! Strive for methods to banish these from your deck as soon as humanly possible.

If streamlining your deck isn’t an option, look for cards that allow you to move through the maze. Multiple boot icons, small scale teleportation, and the ability to move through guard stations each grant you more efficient turns on the board. Sure, you may take damage as you move through enemies, but the game stalls when you can’t move. Stalling is always bad. In the same way, purchasing Keys from the Market give you new routes through the maze that you wouldn’t otherwise be able to take.

Clank! In! Space! is a fantastic game, and the solo app is a wonderful way to test out your strategies and see if you can maximize your own efficiency. Good luck, fellow thieves! Lord Eradikus is indeed a powerful foe…

Momentum and the Markovian Game

This is the Markovian expansion to Photosynthesis I’m looking for!

After writing last week about random paths and probability, Dave Chalker mentioned on Twitter that this idea reminded him of Markov Chains. In fact, a random path is one of the simplest examples of a Markovian system: given the present state of the system, knowledge of the past is unnecessary to predicting the future. In a random path, each of the past turns aggregate together to describe my current status. However, once I know where I am, I no longer need to remember where I was in each of those past moments! In a sense, this path has achieved a state of “memorylessness.” It didn’t take long to develop the question that would apply this observation to games.

Can games be Markovian? If so, what does that look like?

Let’s parse that out a bit. In a game theoretic way, I describe games as a series of atomic decisions, and a strategy as making choices to achieve a particular goal. To say that a game is Markovian would mean that I can theoretically erase my memory after each turn—I should be able to look at the game board and determine the optimal play without knowing the choices I made in previous turns.

For example, say someone asks me to take over for them in a game of Candyland. I glance at the board to find out the current state of the game. I’m on a blue space, and I’m in third place. Do I need to look back through the discard pile to evaluate what to do on my turn? Absolutely not. I just draw a card and move my piece a little farther down the track towards Candyland.

On the other hand, we’ve got Texas Hold’em. In a single hand of Poker, I have to continually judge everything that has happened up to the moment I take my turn. Do I think that someone’s bet signifies that they’ve made their hand? Or does probability lead me to believe they’re bluffing? What new cards have come out, giving me new information and new chances of making my own hand?

Yes, the letter “P” does not appear in the word “Momentum.” No, I don’t get it either.

Clearly, there is some kind of spectrum here, so let’s quickly go back to school and talk about momentum. Just to cover some introductory physics, we state that momentum is a quantity of motion, determined by the product of mass and velocity. We also know that velocity is a result of an object being accelerated by an initial force. When we try to translate that idea in terms of games, we could say that a gain in momentum is the result of a successful strategy being played out over multiple turns.

So, can you gain momentum in Candyland? Absolutely not. But in Poker? In Football? Sportscasters often talk about momentum when playing highly competitive games. Whether we’re talking about some kind of charismatic supremacy or simply expert-level play, it’s easy to see when someone starts to take control of a game by gaining momentum, which is a likely sign that we’re looking at a Markovian game.

What about one of my favorite games, Betrayal at House on the Hill? Where does it fall on this Markovian spectrum? After many playthroughs, it feels like a player could gain momentum. They can constantly catch a break, randomly drawing more omens and items than other players while they fail checks and take damage. However, that momentum is merely the result of random chance, not conscious choice. Instead, if we consider that any player at any moment could swap out with a new player without any change at all in strategy or efficiency, we could easily call Betrayal a Markovian game.

What about a game like Dominion? One of the rules of Deckbuilders is that I’m not allowed to look through my deck at any moment, which means that if I arrive mid-game, I can’t know what cards I should buy to keep the deck moving at top efficiency. Deckbuilders are all about building momentum while dealing with imperfect information. Which is tons of fun, but totally not Markovian.

At this point, I just want a test to find out if a game meets these Markovian criteria. So here we go. Let’s make a declarative statement!**

A Markovian Game fulfills both of the following equivalent definitions:
1. Having knowledge of past turns does not increase the optimization of future turns.
2. Momentum cannot be gained during the game, except by random chance.

So what about some of my absolute favorite games? How do they fare against the criteria?

Party Games: I was surprised to apply this idea and find out that not all party games fit this mold! Of course, games like Cards Against Humanity are Markovian, until you start playing with a judge’s preferences in mind. But Codenames is totally not Markovian. Either you’re engaged in the game, hearing all the past clues from both teams as part of your future decision making progress or you’re bad at the game.

The Builders: I already mentioned that deckbuilders aren’t Markovian, but a tableau-builder like Machi Koro absolutely meets these requirements. There’s nothing hidden in Machi Koro. I can look at the cards I’ve previously chosen as well as everyone else’s when I make my next decision. Even a more complex game like Valeria Card Kingdoms doesn’t have a “memory” beyond the state you can see at the start of your turn.

Role-Playing Games: I am clearly a non-Markovian roleplayer. I like to build the kind of story that comes from a table of totally engaged players who are listening to each other and acting as part of a community. But I’ve also sat at tables with players who are on their phone from the moment their turn is over until they start again. They ask the same question almost every time: Who’s still up? The player reads the current state of the game and is usually able to make an effective attack routine because it’s easy to build a D&D character who does the same thing every turn! I shoot the strongest looking person with two arrows. In this sense, there’s even a Markovian playstyle! It isn’t my preferred playstyle, but does it necessarily make the game less effective? I’m not sure I can say.

The Questionables: What about Vast? I love that game, but it is a complex game potentially involving constantly changing deals and alliances. Those are huge giveaways that a game isn’t Markovian at all. If I have to remember how your betrayal when I make my future plans… I guess that means we can cross off every single game with a secret betrayer mechanic from our list.

The Strategies: I am sad to say that Hearts doesn’t make this list. You have to do to much strategizing! Since that is against our definition, I’ll also add every other game where a strategy takes time… you know, since that’s basically exactly how we came up with our description of momentum.


Okay, let’s wrap this monster post up. Why do I care about Markovian games? I’m working up a hypothesis that Markovian Games are easier for new gamers. This might be the key to fixing my holiday game nights forever.

Dear readers, let’s get some data together! Pick some of your favorite games and determine whether or not they meet the Markovian criteria posted above. Then use your experience and think about whether or not those games are good for brand new players. Finally, send me your results at richard@atomicgametheory.com. We need a ton of data from a bunch of different people before even approaching statistical professionalism, so let’s get cracking!

**For the sake of completion, we are treading perilously close to some serious mathematics with the idea of Markovian Decision Processes in Stochastic Games. However, the definitions used are so disjointed from the games we’re talking about that, yeah, I’m just making up a new criteria.

Predicting The Random Path

As I’ve probably mentioned before, randomness and probability are highly unintuitive ideas. Not that we can’t understand what they are, but that their natures make it difficult to predict what will happen in specific situations. One great example of probability comes from an idea we call the random path. Imagine a person walking down the street. Before taking a step, they have to spin around until they are facing in a random direction. This erratic motion could lead to a completely chaotic mess with interesting applications to study, but this experiment also has some problems. Motion creates momentum, so our walker might tend towards one direction over another. They might also spin for the same amount of time each step, always turning precisely 270 degrees.

Instead, let’s look at the simplest version of this example: the one dimensional path. We’ll start by setting a meeple on the zero step of a physical number line. For each step, we’ll flip a coin and roll 1d10. If the coin shows heads, we’ll move to the left a number of spaces equal to the d10 roll. If the coin shows tails, we’ll move to the right.

Let’s also attempt to answer the following two questions:
a. Can we predict where the meeple will be after 10 turns?
b. How long does the number line need to be for a 10 turn walk?


So, like any good statistician, I first tried it out. I completed a series of ten experiments and recorded my results. My results varied from 12 on the right to 31 on the left. Seven of my random paths ended on the left, while only three went right. I hadn’t expected any significantly larger numbers, but I was certainly hoping!

I could have instead looked at this mathematically right from the start. D&D players are very aware that the average result of a ten-sided die is 5.5. I could just consider an average roll every turn. We might also expect that in ten coin flips, we might get heads and tails each five times. In that case, our theoretical average result would be to end up right where we started at zero.

My results are clearly not average, because I never returned a zero! My results weren’t far off, but I need more data to see what’s about to happen. I sent a request out on Twitter and within minutes (Thanks @LtHummus!), I had 1000 additional results and the ability to create as many more as I wanted. What I ended up confirming was one of the most important theories of statistics: given enough results, the experimental mean matches the theoretical. This doesn’t mean I can tell precisely where an individual path will end, but it does give us some place to start.


The second task is significantly more interesting. It feels more likely that we’ll get a result like zero, but the big question is how far does our number line need to stretch. We can see that a result of 100 to the left or right is entirely possible, but it isn’t very likely—in fact, the odds are 1 in 5,120,000,000,000 that the meeple ends up at one of the two extremes! So, how many numbers do we need in our line?

Take a look at this data all grouped up. Our experiment forms a simple bell curve! This kind of data is the easiest to analyze. We can see the most of the results are clustered around zero. To talk more mathematically about this clustering, we need to know the standard deviation of our data. The standard deviation measures how grouped our data happens to be. If the standard deviation is small, the data is clumped around the mean. With a large standard deviation, the data is more spread out.

Lucky for us, we’ve got a solid bell curve. In a problem like ours, statisticians know that 68% of all results will lie within one standard deviation of the mean. So 68% of all paths will end somewhere between 20 to the left and 20 to the right. To get 99.7% of all paths in our number line, we only need to get out to 61 on each end! Anything beyond that would be a pretty rare outlier. Even in the 1000 data points I took, none of them fall outside this range.

Overall, our experiment is impossible to predict. Given the random nature of each path, there are just too many possible permutations to consider. However, we can certainly say that it is very likely that the result will end between 61 to the left and right, and we definitely wouldn’t be surprised if it was much closer to zero. Going deeper requires some tougher statistics that we’ll save for another day.


Why in the world am I talking about randomness like this? Because patterns exist in everything. We can look at self-similarity in chaos theory and fractals, but let’s think about where randomness shows up in games. When someone dislikes a game because it is “too random,” often it’s because the final outcome is too hard to predict. A chosen action may not propel someone in the direction they were hoping.

Games involving chance make it clear that specific outcomes are not completely within a player’s control. Clank! isn’t too different from the random path problem. Looking into whether a player will be able to move the right number of spaces involves analyzing their deck and doing a very similar kind of calculation. In this case, rather than rolling 1d10, we’re considering how many cards in the deck have a movement icon.

Cards in Clank! may have icons for Purchasing, Movement, or Fighting enemies. The success and consequences of a player’s actions depend on what happens to be on the cards they draw that turn. They may have an average of one movement a turn, but may instead end up with turns having no movement or other turns with three moves when only one is needed. What we can see from problems like the random path is that if I have 19 cards in my deck and only 4 have a movement icon, the probability that I draw 3 or 4 of them in one turn is very unlikely—but can I get 2? Is that too extreme? All of that leads to the tension that helps make Clank! such an incredible game!

Other games involving randomness include dice games like Zombie Dice and Las Vegas, but also resource gathering games like Catan or Valeria: Card Kingdoms. In each of these games, looking at all the possibilities and paring them down to the realistic probabilities is the key to defeating their internal randomness.

Illimat: Preparing for Harvest

Photo by Autumn de Wilde

Illimat is a wonderful new board game, developed as a collaboration between prolific game designer Keith Baker and prolific musicians The Decemberists. Years back, the band members shot a series of promo photos with an arcane looking game board, provoking a sense of deep mystery amongst their fans. The object, known as the Illimat, was covered with strange sigils and odd patterns, and generally looked unlike any other game. Eventually, these two Portland-based creators met and decided to build a set of rules to turn this mysterious object into a playable game—and Illimat was born.

As someone who demoed Illimat many times at different conventions, I grew used to repeating a few quotes about the game. “It feels like something you’d find in your grandmother’s attic.” Which is both an intriguing phrase and absolutely true! Illimat is based on classic cardgames called Cassino and Scopa, giving it a feel very different from most modern board games.

The Children love to steal your Illimat cards.
Art by Carson Ellis

In most games we play these days, designers fight to avoid wasted turns—no one should have a turn where they don’t change the state of their hand or the game, right? Some deckbuilders have unfortunate turns when you don’t buy anything, but these are far and away atypical moments in the game. On the other hand, the Illimat endgame can feel a lot like a round of Hearts. If most of the hearts were thrown out in the middle of the round, the end has little value for any player. Likewise, if a player realizes they cannot take any of the remaining tricks, they may as well play with their cards face-up. In Illimat, the last few turns can be filled with throwaways that have no impact on the final score.

During my demos and subsequent plays of Illimat, I found that this endgame feature, built directly from the classic games I grew up playing, often frustrated new players. With that in mind, I wanted to delve a little bit into the mechanics of Illimat and see exactly where to find the point-grabbing action. Some of this analysis is from my personal experience, so may differ from your experience based on playstyles.

Every time a player takes a turn in Illimat, they may take one of three actions: Sow, Harvest, or Stockpile. Each of these requires a single card in hand to be played into one of the four quadrants, or fields, on the board. In a two or three-player game, there are four suits of thirteen cards each, while a four-player game adds a fifth suit. The most used action is Harvest, which is playing one card from your hand to Harvest a card with the same number value from a Field. Both cards are then added to your Harvest pile. When Harvesting more than one card, all of those cards are added to your Harvest pile.

Harvesting is absolutely an opportunistic action that is not always available to a player, which means it pays to be efficient. The more often I can grab two or more cards in a single action, the better off I am. At the end of the game, the player who has Harvested the most cards gains four points—by far the largest source of points in the game. In most games I’ve seen, the winning player has Harvested from 16 to 24 cards.

Whenever a field is completely cleared, a quick check is made to see if it should be reseeded with three new cards from the deck. Reseeding adds more options to the board, while simultaneously reducing the number of turns left in the game. Reseeding can happen anywhere from an unlikely zero to an equally unlikely seven times.

In my experience, for a two-player game, each player has sixteen turns. Reseeding will likely occur either three or four times. A three-player game is much faster with each player taking ten turns. Due to the fast game, reseeding will likely occur either four or five times. Finally, while a four-player game adds a new suit, players will still only get nine turns. Reseeding is more frequent, and will likely occur five or six times.

In an average game, it feels unlikely that you can drastically ramp up your Harvesting efficiency beyond an average of 2.0 cards per turn. More than that would take an impressive streak of good luck! Depending on how often you can Harvest and how efficient you are, you can likely Harvest the following number of cards:

There is a very interesting thing to notice on this table, which is the moment when Harvest efficiently become a better source of cards than Harvesting constantly. Finding powerful ways to Harvest multiple cards per round clearly leaves you with extra turns when you don’t need to Harvest at all—including those final rounds!

Here’s the moral of this particular story: Illimat is a game about Harvesting efficiently at opportune moments, not slowly ramping up to a powerful Harvest-filled endgame. This efficiency will leave us with turns that feel wasted, not because we aren’t playing well, but because the game doesn’t require us to have great opportunities every single turn. We can create those moments by Stockpiling (an action requiring a post all on it’s own!) but us simple farmers need to be ready to capitalize at any moment.

I love playing Illimat and I have been very fortunate to be part of the playtest process for a long, long time. Beyond the incredible art by Carson Ellis and the fantastic theme and mystery given by The Decemberists, the gameplay created here by Keith Baker will keep me embroiled in the complicated act of farming for years to come.