The Splendor Solution

Have you played Splendor? If not, you really should. It’s a great game where you play a gem merchant, collecting gem resources to buy better and better mines and shops to sell your wares. Purchasing these mines and shops give you permanent gem resources, allowing you to buy better mines and shops and so on. The game is fantastic because of the huge ramp that becomes available to you during play. At the start, you strive for the most basic mines. By the end, you could buy those on a whim, but you’re on the lookout for better and better storefronts. The game ends when someone hits fifteen victory points, so its important for players to build a gem engine, gathering points as quickly as possible. When you do? It’s a very satisfying experience.

In theory, that’s how the game is supposed to work. The Splendor problem is that this isn’t the key to victory.

One day, I decided to play in a Splendor tournament in Portland. As I recall, the winner would earn some promo goods, but I admit that I lost focus on the prize very quickly. This was the day I learned about the Splendor problem.

Splendor is a game that has a flow in mind. The cards at the bottom have a low cost, but low victory point value. So you grab gems to acquire them, which takes a couple turns. Once you have enough of those, they help you grab the second level of cards. These help you take the third level, and you can finally grab the Lords at the top. The Lords require you to own certain colors of gem cards, so players are careful about what they acquire during the game. This flow is built into the setup of the game, the rule book, and the playmat. Sadly, it’s all wrong.

During the tournament, three of us played with the flow. The fourth player had been taught the real strategy. As soon as I saw it implemented, I recognized that the flow was wrong. Building a gem engine wasn’t the key to victory. Instead, players should use highly targeted efficiency. Skip level one cards entirely. Find a level two card that only requires one gem type. Reserve that card, granting you a wild Gold token. Take only that gem resource. Eventually, acquire that card. Do it again. Then move to level 3. Have fifteen victory points before anyone else hits six.

Why does it work? Beyond being ruthlessly efficient, this strategy also requires you to take most of a single gem type. Since other players need a wide variety of gems, they will find themselves starved for that gem type. This turns a vaguely competitive game into a different one, where efficient players are now controlling the resource market. It’s mean. I tried it once, instantly won, and gave up on the tournament.

The Splendor solution brings back the fun of the game and, I hope, the original intent.

The new expansion Cities of Splendor adds four variants to the game. Instead of Lords at the top, there are Cities. These either require a TON of gem cards to get, or a massive pile of victory points. Plus, now the game doesn’t exactly end at a victory point total. The game ends on the round when someone gets a City, and only players with a City are in the running to win the game.

When you add Cities into the mix, the game becomes a race to build a City as fast as you can. In this case, having a lot of gem resource cards is a huge advantage. Now, players have a realistic chance at victory no matter which strategy they employ.

I am, of course, very interested to see how this expansion plays out in reality. In my demo, players seemed very excited to play with the flow of the game. But it still may be possible for that alternative strategy to win out with certain Cities. We’ll see! Plus, with three other variations I haven’t even discovered yet, I think this expansion is actually going to put Splendor back on my play list for a while! That might be the most welcome change of all.

Cracking the Emoticode

Last week was the culmination of mountains of research and development as my team and I launched the Emoticode, a three-day livestream on Twitch promoting the release of Activision’s Call of Duty: WWII. Over the course of those three days and eight hundred-thousand views, thousands of players competed to crack a series of forty-five ciphers, with solvers gaining a beta invite to the game. In the end, my devious ciphers stood up to the onslaught for almost fifty hours, and they would indeed have been doomed without me watching for the perfect moment to drop just the right hints.

At a baseline, each of the ciphers had to stand up to random brute-force attacks by hundreds of guessers for at least an hour. Meanwhile, they still needed to be solvable by fans who had potentially never cracked a cipher in their lives. Best of all, the cipher would be transmitted only by a series of blinking emotes in the Emoticode typewriter with no direction or guidance unless a hint was needed. A wide web of impenetrable difficulty until a solver can find the single, clever way to break through.

This is the kind of challenge I enjoy the most.

It turned out that the solution to this challenge was scaffolding. You probably remember this from your math classes—you studied addition, then learned that multiplication was just like adding, but faster! Your skills leveled up over time. When we build a proper scaffold, we allow players to build their skills. Which is why you should play Lords of Waterdeep before you take a crack at Agricola. But back to codes…

Our first ciphers were the simplest. Starting from a few hints, players needed to translate the Emotes into letters and numbers. In this alphabet, you might get emotes that translate to ?A??IN? and have to come up with the right solution. Since you know most of the letters, those ?s would have to be C, G, K, P, or Q. G is a good guess for the last letter, and soon we’re at !solve PACKING and victory. Of course, it wasn’t quite that easy, and it instantly got harder.

Before too long, we moved into simple substitution, like the Caesar or Atbash ciphers. Not much harder, but then we’d do some transposition, like a Rail Fence or Columnar Substitution. And then? We’d start doing both at the same time. I’d throw in Braille or Morse Code to keep things fresh, and then dig into some Binary or Hexadecimal digits. By the end of the Emoticode, our top solvers knew every single one of these types of ciphering systems, plus Vigenere, Playfair, and One-Time Pads. It was incredible to see these brand new solvers have a series of tricks they could bring out to try against my ciphers! On the other hand, if I’d started with a Rail Fence Hexadecimal Atbash puzzle, absolutely none of this would have ever occurred.

Scaffolding is something I learned as a teacher, but you often see it in board games as well. The extremely new Apocrypha has a pre-wrapped deck that you are meant to play without shuffling at all! A video guide helps lead you through the scenario. Once you play those early missions, additional rules and features can be tacked on to make things difficult in fun ways, not just through complexity and obfuscation. One of my favorite games in the world, Race for the Galaxy, fails to do this, and I have the worst time convincing new players to take a chance on the game.

By the end of the Emoticode experience, I’d written forty-five ciphers and spent almost that many hours moderating Twitch and Discord servers filled with people trying to solve my devious codes. A group of solvers banded together and are now looking for more puzzles and codes to solve as a new team! For a guy who teaches Cryptography, this was the perfect outcome. Along with my immediate twenty straight hours of sleep.

(And no, this was not a trial to get into the NSA. As I kept getting asked on Twitch every ten minutes.)

Robo Rally: Rebooted

Robo Rally 2016 from Avalon Hill

Yesterday was a serious reminder that all the games I played back in college are getting a revamp. First, the announcement from Fantasy Flight Games about the impending Fourth Edition of Twilight Imperium. Second, and much more fun for me, was the opportunity to play the recently updated Robo Rally.

Where to even start? Robo Rally is the chaotic programming game where players try to race their little robots around the factory to reach checkpoints before anyone else. It’s a huge, fun, ridiculous mess and we played it all the time. Were there problems? Absolutely. And instead of telling you what they were, I’ll leave it up to superhuman designer Richard Garfield.

“…when I play games with which I have finished the design I feel bad whenever I see a flaw. Generally when I force myself to play I enjoy myself, but that is my nature. When it came to RoboRally I really had trouble with the flaws, in part because it is one of my earliest designs and I care deeply about it. [My wife] suggested I redesign it using my 25 odd additional years of design experience. The more I thought about it the more I liked that idea so I began to think about a RoboRally reboot.”

As someone with game design aspirations of my own, this really resonated with me. Who wants to look back on something they know they did wrong, simply to look at what they did wrong? Self-forgiveness isn’t easy. Years of teaching, begging students to edit their work and learn from their mistakes taught me that this isn’t easy. So I admire Garfield’s efforts here to look back and fix a well-loved game that could honestly use a fix.

Robo Rally uses a series of programming cards to move around the board. Each turn, you draw nine cards and plan out a series of five register moves. When each player is done, everyone flips over their first register card, performing them in order. Sometimes, that means you step into another robot’s way unintentionally, and it pushes you into an unplanned spot. Other times, the board zips you around on a conveyor or crushes you in cannery row. Even in a perfect world, players can mismanage their program and end up in a totally weird place. Then it’s time to flip over the second card, and chaos gets magnified.

Twonky’s brand new player board!

Of course, in the old version, everyone drew from the same deck. Which meant it was possible to draw nine left turns. Knowing this was not fun, Garfield redesigned the game so all players had their own deck.

Fans of deckbuilders will instantly recognize how this affects game probabilities. Since every deck has the same set of cards, hands of nine become more predictable. Sure, I may not always get a Move 3, but I can be all-but-certain that my hand will contain forward motion. In the old game, that wasn’t quite a safe bet.

Individual decks also allowed Garfield to update the damage system. In the old game, players might have one of their registers lock, meaning that the card they had in that particular register phase could stay there for turns and turns on end. Otherwise, damage just reduced the number of cards you could draw, making it even more likely that your turns would be entirely out of your control. The counter was to Shut Down, removing all damage by skipping your turn. Skipping a turn is, unfortunately, not fun.

However, in the time since then, we’ve seen plenty of deckbuilders introduce a variation on Curse or Waste cards. These useless filler cards just waste a bit of your time and make this turn a little tougher. Garfield used this idea to add Spam cards rather than damage. These feel like something a robot would hate, and allows for variations like Virus Spam or Trojan Horses, making what would otherwise be a simple damage counter into an interesting series of choices.

Reading the rundown of what Richard Garfield changed in Robo Rally is an opportunity to watch a master at work. I absolutely recommend that you check it out, and if you were a fan of the old game, try out the new one and see how it plays! It feels streamlined, simplified, and actually plays like the programatic robot combat racing game I’d always hoped to play.

An Overwatch Game Changer

Folks, I was so good for so long. I didn’t buy Overwatch because I know myself. As soon as I picked it up, I knew I’d dive in and battle my way up into the competitive levels. I can’t help it—I don’t want to help it! I love playing FPS games, and once I get started the only thing that gets me to stop is the eternal knowledge that rent is coming due.

Ugh, reality.

So I waited until the school year was over and decided to devote a portion of my summer to learning this ridiculous and wonderful game. Immediately, I found myself in a situation like this one.

This picture shows the inside of a spawn area. Spawn zones are protected by yellow forcefields which keep the enemy from stepping inside. The blue team is attempting to get outside of the front door, but the red team has it barricaded. When the blue players die, they respawn nearby. When the red players die, they have a long hike to get back to the battle. Even so, a few capable players can keep the entire enemy team locked up for the five minutes it takes to win.

Ready for a wild opinion? This situation is bad for the game and should be fixed. Maybe with something like this:

First off, let’s agree that this situation, one where more than half of the match is over and one team can’t get out of their spawn, is a broken game. Sure, that team might escape and maybe they’ll even make it to the objective and turn this into a real match. But right now, this game is super lame, and there’s no indication that it’s going to end.

What happens to players when a game is broken? They give up. If they aren’t playing with friends, they drop out of the game, because they’d rather start a new one that’s more fair. This broken game is totally demoralizing to the losing team. So we’ll plan to fix the game as soon as this occurs (This introduces a new problem, but let’s hold on to it for a minute). Let’s say that game is Broken when one team is trapped in their base for more than two minutes, the match is half over, and one player from the trapped team has left the game.

You know what kind of game I do like? Games with Betrayers. So let’s make things interesting. As soon as one player leaves, we do this.

What happens next? The stronger team immediately becomes weaker but they don’t yet know how. Overwatch is a game about team balance, so suddenly losing a healer or a tank can severely change things. Even losing a major damage dealer allows the other team a huge opportunity. While the strong team is trying to figure things out and possibly take down one of their former teammates, the trapped team has a new chance to break out and make the game a little bit more fair.

Will this put the game back to normal? No, but we already assumed the match was broken and our goal was to make it more interesting for players. It gives some hope back to the trapped team and keeps the trapping team on their toes. Of course, it also adds a new problem. Teams with hope don’t have players who get frustrated and drop out—they have hope! If no one leaves, what happens then? We could trigger this mode before a player drops, but then it’s 7 vs 5 instead of 6 vs 6! Can this problem ever truly be solved?

Let’s call this a work in progress… I’ve got some more Overwatch to play right now!

The Puzzle Keyring

Back in January, I started designing a set of puzzle reference cards that I could take with me to events like Puzzled Pint or DASH. Strangely, I received an email at the same time from the folks at Kickstarter telling me about an initiative called Make100. They figured that since I’d spent so much time looking at Kickstarter campaigns on Going Last and backing them, that maybe I’d like to take a crack at creation. I freaked out, came up with a plan, and somehow made it work.

The early version wasn’t fantastic, I admit. I’d decided to make this educational and try to teach people how to solve puzzles. After years of playing, running, and making puzzles, I knew this was a difficult task. It’s like learning proofs in Geometry—there’s a moment where it clicks, but all the moments before that can be filled with frustration.

How do you know what code to break? How do you know what the author intended you to do? What’s the best order? These ideas are difficult to get across to new puzzlers because they really need to be experienced before they can be understood. I know, cheap answer. My Geometry students weren’t happy either.

Eventually, I came up with a new design, which had a little section set aside asking about the puzzle you were trying to solve. After looking at a puzzle, there are usually concepts and keywords that jump out at you and give a little bit of direction… but only if you know what to look for. This little sideways border says “HEY, if you see these keywords, consider reading this card!” Then, the front of the card provides further context. On the back is the solution method.

As a teacher, I don’t often have the experience of making things like this. I know plenty of game designers and developers who build prototypes and musicians who make and produce their own albums and merchandise, but I haven’t been that kind of person. Let me tell you, it feels pretty fantastic.

If you want to see a copy of the Puzzle Keyring, feel free to track me down at conventions later this year! I’ll be hauling this little project of mind across the country to show it off to everyone I know. Plus, with project creation under my belt, I’ll probably also have a game prototype or two to try out as well!

Let’s make more stuff! I’m not sure if I can stop!

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!