When Stories Collide

With a full decade of teaching under my belt, I thought I had a handle on saying things out loud. I’ve tried to capture students by bringing the strange history of mathematicians to liven up even the driest of lessons. For the last few years, I’ve been presenting game theory ideas to packed houses at conventions across the country, and I’ve even performed with Gosh Darn Fiasco at even more. I mean, I’ve sat down at tables for years playing RPGs with total strangers and bringing to life weird and fantastical stories for hours at a time. I thought I had this.

I was not prepared to stand up and tell a story all about myself for Story Collider.

I really thought I was. I’d scripted out the entire ten minute story. I’d faithfully memorized the text and really annoyed my fellow teachers by closing my door and reciting between classes. But when it came down to it, I just wasn’t ready for the emotion that would come from talking about my own personal stories. By being open and honest about a pretty ridiculous time in my life, I felt a real sense of warmth and worth. The other speakers were also smart and charming and wonderful. Being part of Story Collider was an incredible experience, which was certainly helped by the fact that I made it all about game theory.


It’s difficult for me to think back to a time when my world did not revolve around the topics of mathematics and education. I’ve been a teacher for twelve years, so by this point, I feel like I confidently state that I have heard every single stereotypical story about math experiences. I’ve worked in schools specifically to help kids who have troubles in math. I’ve spoken to their parents. And their friends. And my friends. And complete strangers, because as I have learned, there are few things that unite us as a people quite as much the dislike of mathematics, either algebra or geometry, depending on the person. 

To break down the story, it’s often a deep and abiding love and/or hatred for a specific textbook or a lesson or a teacher, with a few variations. I’ve made bingo cards just for the first conversation I have with anyone after they learn that I am a math teacher. Surprise, everyone wins.

I’m here to say that, after years watching stories about school where the math teacher is a villain, I get it. We taught you the bad math. Please don’t tell anyone I called it the bad math. We’re trained to teach a very binary kind of math which must be taught in a specific sequence and is always right or wrong. It’s easy to teach and assign homework and test and grade. But it is hardly the math of our everyday lives.

For example, though I didn’t know it at the time, I had my first real mathematical breakthrough in middle school.

I grew up on the mean streets of Portland, Oregon. But then we packed up and moved to the suburbs. And then again out to the country.

So imagine this ten year old future math teacher, showing up in a new school and trying really hard to make a good first impression like he’s a cool kid from the city. Turns out, my first day was also school picture day and I doubt I had ever looked more pathetic. I have since, sure, but this may have been the first time I truly felt pathetic. My dad had passed away at the start of the summer, and I was trapped in this new terrible school without any friends at all. I was like a little sadness sponge, and if you pushed or squeezed me too much, a torrent of tears would just burst out. Which was often tested by my new classmates while playing football at recess.

And that was the start of my year as The Crying Kid. Every school seems to have one, and once upon a time, it was me.

Things got better over time, but then, in seventh grade, I found myself at a middle school dance. Even now, I feel a little ripple in my stomach just thinking about it. But these were the moments that could supposedly help a weird kid make friends, or at least that’s what my mom kept telling me as she pushed me out the door of our Jeep Cherokee.

I have no idea how to dance, so I find myself wandering the school. I enter a long, empty hallway, getting about halfway down when I see a familiar face come around the corner. She smiles, waves, and says “Hello.”

Here’s where my math brain kicked in for the first time. A basic social interaction.

Most likely, she was simply expecting me to respond in a normal way. You know, like a human. And yet, I wondered, what if she wasn’t talking to me? Sure, we were the only two people in the hallway, but consider this. Earlier, the hallway had zero people. Then there was just me. Now there were two people. Clearly, it was just as likely that a third person had stepped into the hall behind me because that’s how math works.

Does this guy even have a Fields Medal?

As the most famous mathematician in the world once said, “Life finds a way.” And yeah, it’s a little weird that the most famous mathematician in the world is Jeff Goldblum in Jurassic Park.

Anyway, there I was, trapped in the middle of the hallway faced with a decision about whether to respond to a polite Hello with a Hello of my own. Perchance a Hi.

Very quickly, I built up a mental construct which could weigh the consequences of my possible choices in order to determine the best possible outcome. Also, like a human.

Overall, the best outcome is what you’d expect. Two young people being cautiously friendly. But if she was actually talking to someone else, then I was very eager to avoid the most embarrassing option which would be to give an enthusiastic HEYYYY…

So, if she were talking to someone else, my best outcome would be to assume that and stay quiet.

Taking a situation like this and applying a construct called a utility matrix to gauge decisions is a branch of mathematics called Game Theory. I love game theory! It was designed as a way to understand economics, but it can really be applied to any kind of conflict. By simulating an opposed set of actions, we can develop strategies that lead all players, or at least all friendly players, to their greatest reward.

One possible outcome of this hallway encounter was a happy, normal, human conversation. A solid outcome for a tortuous middle school dance. The second possibility is the one I feared the most; as I replied with hello, two people would start to laugh at me for thinking anyone might ever want to talk to me. I would live my life in shame, and my only friends would be the animals on our farm. We’d wander the forest together, solving forest crimes, whatever those might be.

The third outcome is the one I expected, where I’d be silent, and those two people would go be happy together. I would be ignored, but safe.

Of course what actually happened was the fourth option. Instead of replying, I turned around to see who she could actually be talking to, assuming that it wasn’t me. In that moment, I heard a noise that is clearly weighing on me almost three decades later. She said “Awwww. I was saying hi to you!”

The good news is that this meant that my mother was right and this dance might be some kind of transition from being the Crying Kid to maybe more like who I was going to be as a person.

Years later, I began studying Game Theory, and realized just how many of my personal interactions could have been simulated and analyzed.

One major game theory interaction is called Chicken. Traditionally, it’s Rebel Without A Cause, racing cars towards the edge of the cliff, each racer unwilling to be the chicken and swerve away first. However, if neither swerves away, they both die. And yet, the winning strategy is to continue towards the edge of the cliff! That’s wild to me. But since I’m not legally allowed to discuss my sordid cliff racing histories, let’s talk about my college roommates and our general disdain for common chores.

I don’t want to do my dishes, so I stack them by the sink. So does everyone else. We all know that the dish supply is limited, and we’ll soon be forced to eat our greasy delivery pizza right from the cardboard box. Eventually, Kim is going to call a house meeting and lay down some new rules, and I’m forced to nod and say sure, sure, I’ll do the dishes as long as everyone else around here pulls their weight too, and then Ryan is going to get those big wild eyes and demand an apology because he did the dishes last week and he will be damned before he does the dishes twice in a row, and soon enough everyone is way too mad to play Smash Brothers like we do every single night, or did before the dishes ruined our lives.

So I did some of the dishes. And then Ryan did some of the dishes. And then, we Smashed.

Anyway, that story is also the Cuban Missile Crisis.

Being able to relate a huge, global conflict to my college kitchen is what makes Game Theory so powerful. It’s about conflict, and humanity happens to be really, really good at conflict.

For example, I was once locked into an important conflict about llamas. We had a pair of them growing up, for important high-elevation backpacking reasons, but a fun moment happened right before my Senior Prom. My mom wanted me to take a picture standing in my tux, right next to Hobie the Wonder Llama. At the time, as one might imagine, I was not very excited about this particular photo shoot. I was worried that every single human in the world would laugh at me, and began to consider choosing my teenage dignity over my mom’s desires. On the other hand, my mom wanted us to work together to make something potentially amazing. But, she could have been wrong.

This is actually Mister Goodbar, but Hobie was always my favorite Wonder Llama.

So to break it down, I was worried that a large group experiment would fall through, and I was considering the option of backing out. This is a problem we call Stag Hunt. We can all play a fun game together, but if I take my ball and go home, at least I still have my ball while the rest of you have nothing.

Fortunately for me, when my mom has a plan, I try to cooperate. So now I have one of the greatest prom photos ever taken in a pasture in Oregon.

Looking back, I can’t help but wonder what would have happened if young me had been taught about game theory. What if I’d been taught to weigh the rewards and consequences of my choices and actually learn how to think in the moments before I act? It could have been transformative. Instead, I got an A in Pre-Algebra.

Let’s be honest, I got an A in every math class.

The best I can do these days is to help spread this knowledge to others because I want to make math relevant to our lives. And someday, I want to throw away those bingo cards as our experiences with math truly become something fun and personal and truly worth sharing in a positive way. It certainly isn’t just us weird kids and sadness sponges who need to think about conflict and choices.

Speaking of weird kids, my mom was right. The girl in the hallway and I did become friends. We ended up being dance partners and worked on the high school newspaper together, and she’s doing quite well today. I might even send her a copy of this story, after I complete a thorough analysis of the possible benefits and consequences, just like a real human.

Rise of Tribes and the Tragedy of the Commons

You know that feeling when you sit down to a play a game without really knowing what to expect, and then are immediately blown away by the cleverness of the mechanics, the scope of gameplay, and the overall experience you have that brings joy to your little tabletop gaming heart? I hope so. It feels pretty good and you each deserve that moment. To give you an example, you might want to check out Rise of Tribes by Brad Brooks and published by Breaking Games. I was introduced to both the game and designer at a local board game prototyping event, and I haven’t been able to shut my mouth about it since. Seriously, you should already be driving to your FLGS to pick up a copy.

Rise of Tribes is all about bringing your people to greatness. To begin, each player chooses one of the Tribes, and in the advanced game, picks one of that tribe’s two Leaders. You lay out a series of hexes representing Lakes, Forests, and Mountains, where your tribe members might gain Food, Wood, and Stone. You get two actions per turn, choosing to Grow your tribe, Move around the board, Gather new resources, or Lead your way to new opportunities. From there, you race against the other players to construct villages, research new technologies, and achieve goals for your tribe to do what every civilization in history has ever wanted to do—collect Fifteen Victory Points.

Okay, so you may think this sounds a lot like Twilight Imperium or Sid Meier’s Civilization or a host of other games with similar themes. What sets Rise of Tribes apart for me is a dedication to two particular mechanics. One makes the game infinitely more fun than any other area control game I’ve played, and the other is an intriguing twist on the Tragedy of the Commons.

Let’s start with fun! Have I mentioned how much I dislike Risk? It’s a game we all need to play, but the idea of moving huge units around and rolling dice in a very random way… you’ve heard the arguments before, I’m sure. It isn’t fun for me. In fact, I don’t really enjoy games where combat is a necessary path to victory, because I don’t think zero-sum games are a ton of fun for everyone throughout the game. If your gain comes from my loss, I’d rather play Scrabble. Scythe was a great example of a game where some battle was needed, but very quickly, players stopped gaining points for fighting! Two victories, and you could tell your military to take a nap.

In Rise of Tribes, players can be on the same hex space as much as they want. As they peacefully coexist in the same space, both players can utilize that hex just as if they were the only ones there. They couldn’t choose to attack each other, even if they wanted to, without a good reason. Which in this case is defined by population.

Each hex has a population limit of five tribe members. Which means that on this board, the Red and Blue players coexist in all spaces just fine, but someone messed up in the circled Forest space. Here, the population has hit a critical level and Mother Nature needs to step in.

Do we roll dice? Draw cards? Play Rock, Paper, Scissors? Slap Jack? Nay. Instead, every tribe loses one of their members in that hex, and that process continues until only one tribe remains. In this case, since the two sides are even, all six tribe members are lost. Welcome to the brutal truth that combat is bad for both sides. More importantly, combat itself is never worth Victory Points. It may help a tribe achieve its Goals, but combat for its own sake is never something that helps you progress.

By simplifying combat and making it such a huge penalty for both sides, players shy away from it unless they must battle to complete a goal. Even then, since all goals are public information, every player can see the battle coming and decide how they plan to respond.

I love the flow of combat, but what draws me to Rise of Tribes is an ingenious way to choose your actions each round.

Place your die to the left, push the action dice, remove the last one. This strategic planning mechanism is just so satisfying!

At the start of the game, you set three dice to specific faces above each potential action in the game—a Sun, then a Moon, and finally a Blank face. At the start of your turn, you roll the remaining two dice and consider your options. For your first action, you choose one of your dice and place it to the left side of the action’s dice. Then, you push them all to the right, putting your dice into the left-hand space, and removing the far right one from the action. Finally, you see how lucky your action is going to be. If the board shows two Suns, you get the best possible outcome. If it shows two Moons, you get the worst. Anything else is the normal action.

This means that on a lucky day, you grow your tribe by twice as many members than on an unlucky day. Your tribe can move farther and gather more, as long as that sun keeps shining down. It’s a beautiful, thematic mechanism that gives the game a healthy dose of intrigue and strategy.

As the game progresses, you soon begin to realize that your turns are affected by the players who have gone before. If everyone before me left Suns on an action, then no matter what I place, I’ll have a good day! Well, hold on. Doesn’t that mean that even if I place a Moon there, it won’t hurt me? And then the next player has to deal with my leftover Moon? What if they roll two Moons? How should I play best to help myself?

Welcome to the Tragedy of the Commons! You made it. Congratulations.

The Tragedy of the Commons is a game theory simulation of a common good and the problems that come when players are able to abuse that good. Imagine that you live in an apartment complex, and one mysterious tenant keeps filling up the shared dumpster with a ruined couch every single week. It’s funny the first time and nothing happens. But the next week, another tenant joins in. Soon enough, there are seven couches in the trash! Now, there’s no space for anyone else to put in their trash, and the garbage company is getting frustrated and responds by increasing their rates in your building.

What kind of responses happen when you, as the law-abiding tenant that you are, suddenly lose access to a common good through the actions of others? Do you bring a mob to the parking garage and lay in wait, preparing an ambush of suddenly screaming, angry tenants when that couch-ruiner walks in? Do you simply accept that bad things happen and pay the increased bill? Or maybe you decide that nothing matters at all, and you can join in the couch chaos too!

There’s a glorious moment in Rise of Tribes when everyone has been dropping Suns down on Gather so everyone can have a mountain of resources the entire game, and then, with a sudden grin, one player plops down a Moon. They’ve decided to throw a couch in the dumpster. Do you put down a Moon as well, sentencing the Gather action to unlucky doom and gloom for turns and turns to come? Do you fight back and try to salvage the situation with another Sun? Shrug your shoulders and drop a Blank? This might be my new favorite simulation of the Tragedy of the Commons!

Rise of Tribes is a fun, fantastic, civilization building game that plays in a relatively quick 30–60 minutes. With plenty of varied Leader abilities, a bunch of different options available in terms of Goals and Technologies, and a string of unique Events that shake things up completely, this is absolutely a game that’s going to show up at my game nights for a long time to come.

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.