Playing with Probabilities

I posted a picture on Twitter last week about my curriculum for my last Games and Game Theory class. I guess folks were surprised that it was really just a big stack of games? I’m sure that I have a syllabus somewhere but, like my students, I probably recycled it as soon as the first class was over. The whole point of the class is to find out how game theory shows up in the board games we all know and love, and these games exemplify some of those important problems. Today I want to talk about two of them in particular and how they relate to the terrible study of probability.

Mathematicians like to say that if you think you understand probability, you’re probably wrong. Actually, that might just be me, but it is certainly true that probability is notoriously counter-intuitive. Sure, a coin can only flip heads or tails. Most people, when shown a six-sided die, will come to the conclusion that a 2 is just as likely of a result as a 5. But a far fewer number will be able to explain why on a pair of six-sided dice, a 2 is absolutely not as likely a result as a 5. Even fewer are equipped to easily explain why in exact terms. Did you know that any random group of 23 people has a 50% chance that two group members will have the same birthday? Doesn’t that number seem ridiculously small? And all of this is long before we get to ideas about probability distributions and confidence intervals.

Okay fine. Let’s stop for a moment and answer a few of your questions.
1.   No, a coin cannot land on its edge. If it magically did, we wouldn’t count it anyway. In a heads-or-tails game, it’s a redo.
2.   Sure, dice are made in ways that make them inherently unfair, but these are generally ignorable, depending on the rock crusher.
3.   While the results of two six-sided dice seem like a a list of 12 outcomes, there are really 36. Et voilà!

Games that are based on two dice make these fundamental properties of probabilities more intuitive. Machi Koro and Valeria: Card Kingdoms are two incredible tableau-building games, where you purchase cards which will earn currencies when certain results are rolled on the dice each round. At the start, you only earn on a few numbers, but as you purchase more, you start to reap a serious harvest.

In Machi Koro, you are trying to build a city filled with businesses and attractions. On your turn, you roll and collect gold for every business you have showing the same number at the top. As you progress through the game, you have the option of rolling one or two dice. The businesses that trigger on 7 through 12 may be a little more glamorous, but those low numbers can keep you chugging along through the game for quite some time. At some point, every player has to make the switch, and the game suddenly changes dramatically. Machi Koro also has restaurants, which allow you to steal gold from players when certain numbers come up, and that makes this game feel pretty mean and hopeless sometimes. In the end, players need to use probability, luck, and an efficient engine to build their attractions before anyone else.

While similar in style, Valeria: Card Kingdoms has some great tweaks that makes it a very fun and engaging game. With very little inter-player conflict, everyone is free to hoard resources all they want, and they come quickly! Every card has a benefit you gain either when you roll its number, or when another player rolls it on their turn. Valeria ramps up like no game I’ve ever seen. While early turns may net you just a single gold, by the end of the game, one lucky roll of the dice can easily net you twenty or more currency. With multiple paths to victory, players are free to choose exactly what kind of citizens they want in their city, monsters they want to destroy, and domains to add to their kingdoms. This game is always a contender at my game nights!

My poor, beleaguered students had to play these two games and study the results of their choices. Would they do better in these games if they focused on a few numbers with maximum results, or would they take the broad approach and try to earn on every single possible roll of the dice? Playing around with these play styles is an excellent way for anyone to try to make the arcane study of probabilities infinitely more understandable and intuitive.

4. Are you still thinking about the birthday problem? Here’s the trick. I never said it was someone else who has the same birthday as YOU. That’s a whole different story.

UPDATE: Daily Magic Games challenged me to create a chart listing the exact probabilities for each outcome in Valeria: Card Kingdoms! So, of course…

AGT 2017 Convention Schedule

I am so excited to finally announce that I will be presenting at GenCon 50 in Indianapolis on Friday, August 18th! Growing up as a little RPG kid, I always thought GenCon was this mythical place where nerdery blossomed. People from around the world gathered to celebrate their hobby and make it better and better. Friends of mine in college flew out and came back with a brand new D&D 3rd Edition Player’s Handbook signed by the creators? It was madness. I was shocked when I was able to finally attend last year at how massive the convention really was! I just wanted to be a part of it.

Games and Game Theory 101 is a talk that I gave for the first time at PAX Dev in 2015. It’s basically my entire high school course, slammed together into a one hour introduction to game theory. We cover the seven Dilemmas and we talk about the games where they can each be found, whether on a console, computer, or tabletop. Atomic Game Theory is just a larger vehicle for that message. This talk will definitely be updated from those early days, but if you’re going to be at GenCon, you can see where it all started!

On the other hand, since I am a west coast native, my home convention has always been PAX. For those who enjoy themselves a good PAX, like I do, I have also submitted a pair of panels to PAX Dev in Seattle and the brand new PAX Unplugged in Philadelphia. These are unconfirmed as of this moment, but I am still very excited!

At PAX Dev, I’m planning to present A History of Betrayal, a delve into all sorts of games with traitor mechanics and other ways to betray your buddies. There will be a big focus on the themes of Trust and Reputation, plus the many different ways which games can force a betrayal. If that seems familiar, I have spent a few posts lately hashing out those topics in my brain! Betrayal is one of my favorite things to talk about (as Kenna will tell you, if you listen to basically any episode of our tabletop podcast Going Last!) To see the final presentation, you’ll need to make your way to PAX Dev on August 29th and 30th.

PAX Unplugged is a brand new convention focused completely on tabletop gaming, and as soon as I heard about it, I knew I needed to present some game theory! The Mechanics of Conflict is going to be introductory game theory, focused specifically on tabletop games. There’s still a good bit of time before that presentation, but my plan is to highlight a lot of the major games we’ll be seeing on the demo floor at Unplugged and break down some of their core mechanics to show how they drive the major game theory dilemmas. With the new expansion on its way, will I finally talk about Splendor? We’ll see November 17th to the 19th!

All right, I hope that’s enough ways to track down some good game theory in 2017! I hope I get to see some of you there!

Reputation and Reliability

Last episode, I talked a lot about Reputation and the problems that show up when it suddenly changes. Reputation is a huge concept in game theory and the development of strategies, and while we can intuitively understand it in social situations, it’s sometimes difficult to describe the implications. So I want to take a moment and give it some more depth, which means I need to turn to one of my favorite TV shows of all time: The West Wing.

In the third episode of the very first season, President Bartlett is faced with a tough question about military retaliation. After an attack on American troops, Bartlett is presented with a counterattack which he perceives as being too weak. He is told that this is a “proportional response,” to which he asks “What is the dis-proportional response?” The Situation Room gets tense as the military staff realize that the president is considering suddenly changing America’s reputation from a measured Tit-For-Tat to more of a Scorched Earth policy.

Reputation is all about reliability of response. In a competitive game, I can gain a reputation for fair play if I push against all players equally. If I instead beat down the weakest of my opponents into the dust before turning to the next, I may gain a reputation for ruthlessness. But as long as I gain a reliable reputation, my opponents will know what they’re getting into when we play a game together. Or maybe they’ll know not to invite me to their game night! On the other hand, when a player unexpectedly changes how they react to a situation, opponents are left startled and a little confused.

In January 2017, three professional poker players were challenged to play against Libratus, a new AI designed to win at Texas Hold-Em. In a grueling, twenty-day competition, Libratus, a 4-1 underdog, slowly took every single chip from the three poker pros. According to player Daniel McAuley, “it seemed to learn what we were doing and exploit it.” Libratus was calibrated each night after play ended, and the human players complained that they had to spend each morning figuring out the AI’s new strategy. Whether or not the AI is actually better than the humans, it surely benefited from keeping the other players confused with its constantly changing reputation.

For players who want to change their strategy often, it’s best to play a game with some randomness involved. In Lords of Waterdeep, if all of your Intrigue cards happen to hurt other players, then you are naturally going to have a strategy where you hurt other players. Or in Werewolf, your strategy changes based on which role you are randomly assigned. Either way, you don’t have to claim responsibility for your changing reputation! If you play a game that is totally based on skill, like Diplomacy, then all of this is on you.

Think about reputation the next time you sit down with your gaming group! When players act in a confusing manner, it is very possible that they are in the midst of changing their strategy in a way that you wouldn’t expect. Keep your eyes open and you can gain the advantage! And, as I mentioned in Inevitable Betrayal, pay attention to how your friends treat you when you change your own Reputation for the sake of winning the game.


9 Inevitable Betrayal

This episode is dedicated to two fantastic fans who had incredible questions, both about one of my favorite game mechanics: Betrayal! Here is a rundown on Inevitable Betrayal and the problems of Reputation.

Games with Risk Part II: Clank!

How crazy that after making an episode all about risk, I had the opportunity to play Clank! by Renegade Games. This self-styled “deck-building adventure” gives you the opportunity to compete with your fellow rogues to see who can gain the most and best treasure before the dragon returns to send you scurrying from his hoard with fangs and fire.

As players enter the castle, they take their first steps on a web of pathways leading through the castle and into the dragon’s deeps. In the deeps are a series of different artifacts, each worth a different number of victory points. Players must grab one of these and then race back towards the entrance before the dragon kills everyone.

Seems simple enough, but in order to win this game, players need to balance how deep they go in the castle, how valuable of an artifact they grab, and how quickly they can get back to the start. The game is complex enough that this balance is tricky to master! Plus, the deck you build defines how well you escape! So, things get really frustrating when the cards you need to move don’t show up.

Meanwhile, the dragon ramps up throughout the game every time a player grabs an artifact. More damage comes out the more artifacts are stolen. Which means a perfectly valid strategy is to grab the cheapest artifact you can and then run for it before damage becomes overwhelming. Since other players will need to go deeper, they’ll be forced to spend more turns potentially taking damage. In order to score any points at all, players have to at least escape out of the deep and into the castle proper, where their can be safely recovered if a dragon burns their thief to a crisp.

Is this the best strategy? Well, simply delving deep and grabbing a better artifact can’t make up for failing to escape the castle. However, spending more time in the dungeon can grant you gold coins to spend at the traditional underground market! Whether you buy a key, a crown, or a backpack, you will gain new options and very likely more victory points. There are also plenty of victory points waiting to be found by players who are willing to thoroughly explore the Deeps. Finally, once you escape, you can’t improve your deck anymore, which means you stop gaining victory points by purchasing special cards.

This game quickly becomes a Stag Hunt problem for a group of friends, when one player decides whether or not to try the Escape strategy while everyone else is engrossed in heading into the Deeps. While it is absolutely a great strategy to win the game, you may hear some groans from your friends when you try it out.

Clank! is a fantastic game with a novel approach to the deckbuilding genre. The race for artifacts is tons of fun, and the dragon mechanic builds the kind of tension that makes you hold your breath. I’ll be picking up my own copy as soon as humanly possibly.

Designing a Puzzling Experience for the Overlook Film Festival

Image: The Oregon Encyclopedia 2017

Confession time. I cried during E.T. Not because of the sadness of that poor lost alien flying back home but because that movie is terrifying. The scene where they set up the huge white tents and get set for dissection? Tiny little me just couldn’t take it. I’m no good at scary things! I close my eyes in the Haunted Mansion at Disneyland, for crying out loud. So I was the obvious choice to help design a game for Oregon’s latest festival of terror.

The Overlook Film Festival is a convention dedicated to the complete experience of horror. And so, OFF was held at the perfect venue: Timberline Lodge, famous as the setting for The Shining. Not content to simply let attendees sit around and watch movies, OFF brings in immersive projects that showcase the thrill of personal terror. So of course, there was timid little me helping develop the Immersive Horror Game.

Together with Dylan Reiff and the incredible team from Bottleneck Immersive, I helped design a four-day mystery experience, tracking the rise of a serial killer during the Festival using a clever set of puzzles and immersive moments. With some help from a bitter detective, a cheerful historian, and members of a secret society, we sent players across Timberline Lodge and Government Camp, searching for our devious little puzzles and special interactive moments.

Image: Birth.Movies.Death. 2017

Take this odd-looking cipher. Each of the main players received one fragment of a three-part piece of paper, carefully left in their hotel room. We used this mechanic as an icebreaker, so solvers would find each other during the festival. Once they put it together, they saw two major encrypted phrases. Along the top, a mixture of Morse code and the Freemason’s Cipher, which sent them to find a specific page in a specific book. But the second was entirely unclear. Was it five words? Was it five phrases with no breaks? This resisted simple decryption techniques, and players were stuck until more information came their way.

Well, the page in the book led to a phone number, which led to a person who recalls some strange code language, which eventually led to a fax machine at the Lodge with the decryption alphabet. Based on the Mary Queen of Scots cipher, this has extra characters for spaces and symbols representing “doubling the next character.” This second code had been intentionally time-locked, and gave additional story for players during the event.

Like escape rooms, games like OFF have a very different design goal than events like Puzzled Pint or DASH. Puzzles have to be shorter and created without a focus on master puzzlers. Puzzles should also be immersive, with solutions that could be easily found in the environment without having to use the internet or simply crunch data. Plus, the puzzle needed to be more about the experience than just finding the solution. Everything within the OFF Horror game was carefully crafted to lead to new ideas and new information, eventually allowing players the agency to talk to major characters become part of the story.

Overall, OFF was AMAZING. I hardly slept while I was there, since there was always something to do. And really, I can’t think of another event experience I’ve been involved in that has given me such an intense feeling of satisfaction. With tons of incredible improvisers and actors, a fantastically creative production team, devoted and detail-oriented management, and thoughtfully designed games and puzzles, I can’t wait until I get to do something like this again.

Dread and the Tragedy of the Commons

“Shaun of the Dead”

I once had a friend who, as an experiment, attempted to run a role-playing adventure that felt like a zombie-apocalypse-style horror movie. He set up a creepy soundtrack and gory movies in the background for ambiance. There was a fairly 3d representation of a house that we were trapped inside, and he had clever ideas about how to make the building fall apart over time. There were food and drinks and fun and everyone bought in to the theme…

But in the end, we called the game a failure. Horror stories are built around a growing scarcity of resources. People run out of easy solutions, like a too-convenient revolver, and are forced to survive with the worst kind of tools. Eventually, characters die as even human beings become a resource that continues to fail. D&D is not a game where resources disappear. A fighter remains just as strong whether they are fully healed or at death’s door. So there just isn’t enough tension!

Fortunately, there is a game designed to bring the tension and terror of these kind of stories to you and your gaming group. Dread, the world’s only Jenga-based roleplaying game.

The rules for Dread are simple. When you want to do something, pull a block from the tower and place it on top. If you knock over the tower, you fail and die in the worst way possible. If you knock the tower over on purpose? You die in the worst well possible, but you succeed at your final task! These simple rules allow for plenty of variations. Harder tasks may take two or even three pulls. I often add specific injuries that can require extra pulls in certain situations.

There is nothing like looking at a wobbly tower and knowing that you have to make a pull to move the story along. When death itself is on the line, what do you do? I hope you take this moment to reflect on one of the greatest Dilemmas of game theory.

The Tragedy of the Commons describes how groups of people tend to use up plentiful common goods without worrying about the consequences. Imagine a big group of friends in a room playing games together. Someone opens up a box of donut, but sets them in the neighboring room. Friends can walk into the room and eat a donut in private, but they are asked to only have two each to start. If there are more left, which seems likely, they can each have more.

I can admit it. I’m a donut eating monster. I’ll have my two, but I probably won’t ask if everyone has had two before grabbing a third. As long as I expect other people are taking care of themselves, I might even grab a fourth. So it shouldn’t be a surprise when my friend, purchaser of the aforementioned donuts, gets real mad that all the donuts are gone, declaring “I will never bring donuts again.”

The Tragedy of the Commons occurs whenever a group of people think about themselves as individuals rather than as a community. Communities are fair, attempting to find the greatest good for everyone. Individuals are looking for their own greatest good, and hoping that no Consequence steps in to shut things down. This is the problem of leaving your dishes in the sink and hoping someone else cleans them. This is the problem of bribery and pollution. It’s big.

In Dread, the Tragedy of the Commons shows up right away. As the story begins, players start pulling blocks for silly reasons. They want to check their email or search through someone’s room. The game is designed to be fun, so players act on that impulse! But eventually, their fun makes the tower wobbly. And now no one wants to act, because the consequence of continues action might be their character’s imminent demise. On the other hand, players may hold back from making pulls unless they are truly helpful to advancing the mission, leaving the tower stable and reducing the chances that all the characters die.

So how much fun should you have? Should you forsake fun for the sake of your group achieving it’s mission? I mean… I don’t know about you, but I’m all about maximum fun. And if that means I’m the class clown that gets taken out in Act One, well at least I’ll go out trying to see if I can water ski across a tightly packed zombie horde.