Godel's Incomplete Game

Godel's Incompleteness Theorems are a pair of deep and disconcerting results in Mathematics. The main thrust of the results is any logical system will have one of two flaws: incompleteness or inconsistency. Both of these cases have disturbing implications for Math. If our construction of Math is incomplete, then there are statements we can make which are neither true nor false given our starting assumptions. If Math is inconsistent, then all statements are both true and false. The hope is that we have selected axioms such that Math is incomplete as that is the lesser of the two evils. It is worth noting that there is still a lot we can do in this case. The implication of the theorem is there is always a boundary on what we can prove, no matter how many axioms we have.

Why am I discussing a Mathematical results that is rarely used in a blog about games? If you think about it the rules of a game are like the axioms of a logical system. This means that Godel's Incompleteness Theorems apply to every game in existence! This means that there are either situations we can describe which the rules don't cover or the rules contradict themselves somewhere. Examining help forums for games, it is clear that many games suffer from one of these problems. Though this is usually chocked up to insufficient playtesting. So is Godel telling us that there is no amount of playtesting that can resolve this issue and we should just always expect such problems from our games?

Looking carefully at what incompleteness is, we see that this actually not a problem for most games. A game suffering from incompleteness just has some situation which the rules cannot decide. There is nothing that states that this situation can occur during gameplay or even that the components of the game that would cause issues even exist. The best game to explore this idea with is Magic: the Gathering. Magic being incomplete implies that there is a card or combination of cards which the rules cannot handle. This is like the double Opalescence and Humility problem before the introduction of layers. The thing about Godel is the cards that cause a rules issue might not even have been created yet. There could be a card or cards that we can write up that are perfectly valid Magic cards, but have something undecidable in the rules. So Magic escapes the Godel's problems by simply not having all possible cards existing.

This leads us to the main release valve in games for Godel's results, games are (usually) finite. Just like Magic avoids the problem by only having a tiny portion of all the infinite possible cards actually existing, other games can avoid being incomplete by bounding what can happen in game. So any game with a bounded scope can avoid the paradox of Godel's Theorems by being playtested to the point that the inevitable undecidable situation exists outside the boundary of the game.

Hence any single game can avoid rules confusion. Though there are two special cases worth thinking about more: expansions and RPGs. Expansions should be just like the base game, with enough playtesting one can push the inevitable incompleteness outsidethe scope of the game. This is usually done by adding rules to resolve situations. Under Godel's Theorem, adding new axioms does not resolve incompleteness as even with an additional axiom, there will still be some other case not covered. It is literally impossible to cover all the cases in an infinite game without contradicting yourself. We see that expansions always add rules. Sometimes they even completely rework the base rules because the new rules came in direct conflict with how new situations were handled.

This rewriting of the basic axioms is more common than one would expect. It happens with paradigm shifts in the sciences, like classical Newtonian physics to General Relativity. Or the many attempts at axiomatizing set theory in the 20th century. This has also happened in Magic with the big 6th Edition rules change. Through this we see than even expansions can avoid Godel, though they might require a complete rewrite of the rules to do so.

Tabletop RPGs are the most complex games to design. Unlike essentially all other games, they are infinite in scope. Any situation the players can imagine is possible and people are constantly pushing the limit all the time. In an environment where so many people are applying their collective creativity, it is inevitable that someone will try something that is impossible to decide with the rules. Unlike most other games, RPGs have an ultimate authority who is technically above the rules, the Game Master. It is because there is a person empowered to unilaterally resolve situations that these games function. When a situation the rules deem undecidable arises, the Game Master has the power to resolve it.

Hence, one should expect people to have game worlds run by different Game Masters function differently. One last implication of Godel's Theorems is that any undecidable statement can be determined to be either true or false and still form a consistent system. For example, see the continuum hypothesis. This means that in any RPG there will always be legitimate rules disagreements. Moreover, neither person will be wrong!

This ended up being a bit longer and more philosophical than I intended at the beginning. To sum up, Godel's Incompleteness Theorems do apply to games. Though due to their finite nature, it cannot be used as an excuse for games that needs more playtesting. The one exception are RPGs, where their unbounded nature means incompleteness will always be encountered. Luckily, there is a Game Master empowered to resolve problems as they occur.

Community in MMOs

Recently, I have been thinking about how communities form in MMOs. In truth, these are quite possibly the most important part of an MMO. Without a community, an MMO is simply a single player game where you can watch other players play the same game. With a community, you can take on far larger objective and even make friends online. The problem with communities is the game developers have no direct control over them. They can provide tools to foster their creation, but it is next to impossible to pre-create communities for a game.

I have been playing Bungie's recent title Destiny. There is a lot one can do without a community, but the highest level content requires that you find a group. The problem is Bungie greatly restricts in game communications. There are no public chat or voice channels. The closest thing would be using the Bungie forum. This seems far too much like posting an add on Craigslist. You have to get lucky in having the comparable people view your advert and you will still have to sort through a lot of crap first. There are also third party sites, like Destiny LFG, which look promising. Though it really depends on the power of their search and matching algorithms. So we will have to see.

The other method available is to send lots of messages to people in game hanging around certain spots. This is a very high variance activity. A group found me to help with the Raid on normal, and that went well. Though then a member of that group invited me to do the Raid again later and it was massive mess of cursing from a player who thought he knew more than he did. So I am not super optimistic about this tactic for finding a long term community.

My only other experience with MMO communities is EVE Online. And I started EVE after it had been running for nearly 10 years. This meant that there were many large, established communities to pick from. And all had nice websites and private voice comms. While a good part of the difference can be attributed to the difference between an established MMO and a new MMO, I think some of it comes down to the medium. It is much easier to run other programs in the background on a computer than a console. This means it is easier for communities to develop new tools to help their growth. On consoles this is much harder due to restrictions the console manufactures place on apps. This means that players have to rely more on support from both the console manufacturers and the game developers to give us tools for forming communities. In this sense, I am pessimistic for console MMO communities because no one knows the tools that we as players need better than the players. Not to mention we outnumber the developers by a huge factor meaning we have more time to develop the custom tools for our particular community instead of the one size fits all versions from the developers. I hope I am mistaken, and probably will be due to how creative players as a group are.

Alternative Methods

One topic that I have been musing about a lot recently but doesn't seem to get much discussion is that of Alts. An Alt, or alternative character, is a second or third or twentieth in game avatar, usually requiring multiple accounts. These are most common in MMOs as there are a few things that push players towards them. But it doesn't seem like developers always take into account the impact of Alt nor if they are healthy for the game.

Players start Alts for many reasons. Usually there is some limit on character abilities. Hence players need multiple characters to have full flexibility of activities in game. In games like World of Warcraft this takes the form of actual character classes which restrict your character so they are distinct from other classes. in other games like EVE it is simply more efficient to train many specialized characters than on generalist. This is mostly a function of the fact that to have multiple characters training in any game you have to pay for multiple accounts.

From the developer perspective, Having players train alts makes things easier on them. If pa player is training more than one character, they are clearly invested in the game and will probably stay for a longer period of time. In addition, the developer is making multiple subscription fees from one person instead of needing to find new subscribers. So for developers alts are useful in capturing more revenue from invested players.

Unfortunately Alts have at least 2 major downsides. First they decrease the impact of reputation. It is very easy to have an Alt for doing unscrupulous acts. Then once the penalties have built up, simply switch to another character and ignore the consequences. In games like EVE which emphasize that actions have consequences, Alts really damage this philosophy. The other downside is they decrease social interaction. There is no need to coordinate with other players if you have enough alts to run a production empire. Or why group up if you can play multiple characters at once and do group content by yourself? This seems counter to games called Massively Multiplayer Online.

One recent example of a game company thinking about alts and doing them well, in my opinion, is Bungie with Destiny. Each account gets 3 character slots, which is conveniently the number of classes in the game. So you only ever need one account to have access to all play options. In addition, individual characters do not have unique names like WOW. Instead the account has one name that is displayed no matter which character is used. This mitigates the reputation problem as the reputation is for the account instead of the character.

The other interesting feature of Bungie's implementation of Alts is they share storage space. So instead of having to do some convoluted process to get gear from your Warlock to your Titan, all you have to do is deposit the gear in the vault. Then any character on your account has access to it. So all your characters always have access to all of your best gear, so you can quickly swap to the one you want to play and go. Granted Destiny is no where near as complex as EVE, but it shows that when developers think about Alts and how players interact with them, you get a much better gaming experience.

Dissertation Files: Team Dossier

Two weeks ago I started a game of Dissertation Nemesis. My team is a little on the small side with only four members. None the less, I think it has been a very positive and valuable experience for everyone involved. So without further ado, the team:

• Fox Mulder vs. The Smoking Man (The X Files) "The Truth is out there," or at least Mulder must believe it is. The objective always seems so close. But as soon as you nail it down, all you are left with are more questions. This is a struggle with the unknown and often ill-defined nature of research. The Smoking Man and his Syndicate represent all the knowledge that you know must be out there, but always seem to fail to find. Other graduate student can be viewed as other CIA agents with one's committee as the board of directors. They are helpful but often understand less than you do.
• Sherlock Holmes vs. Professor James Moriarty This is the quintessential duel of wits. The problem is the villain sets the stage and is always ahead of the hero. The trick is seeing and anticipating the other's moves, getting better and better as one learns the patterns.
• Gambit vs. Rogue (X-Men) Gambit clearly likes Rogue and the attraction seems mutual. Unfortunately, any time he tries to pursue it past friendship, Rogue sucks the life out of him, literally.
• Shahryār vs. Scheherazade (1001 Arabian Nights) The exact opposite dynamic as Gambit and Rogue, Shahryar wants to kill Scheherazade. But her enchanting stories enchant him night after night, leaving he alive for one more day.

This team is closer to the League of Extraordinary Gentlemen instead of the avengers. The pairings have less to do with super powers than the lives or ordinary people in extraordinary situations. In addition, the pairs fall into two classes. The first is those searching for knowledge. Both Mulder and Holmes seek answers, even if there domains and approaches are different. This is a very literal interpretation of working on a dissertation. The other class of pairings are lovers at conflict. Both Gambit and Rogue and Shahryar and Scheherazade are trying to pursue romantic relationships but have major issues standing in the way. These really do capture the love-hate relationships graduate students have with their dissertation, which is often like a significant other in many ways. Personally, I like this class of pairings and am disappointed that I didn't think of them with the standard superhero and knowledge seeker archetypes.

Right now the team meets once a week for an hour. There we talk about how our week went and any other dissertation related topics. Sometimes we go into detail on someone's project. Others we just talk about our concerns, frustrations and fears relating to graduate school. This is very therapeutic as everyone has the exact same issues and needs a chance to voice them. Overall, I think everyone is very satisfied with the meetings.

At the end of each meeting, we pass out assignments for who we will check on during the week. Then everyone has one person they must ping daily to ask about how things are going and what they are up to. After the first week, we decided to require at least a paragraph response. This forces people to own what they are doing and provides more commitment. We didn't officially theme this process, but I like to think of it as field reports to my supervising officer.

As the game continues and evolves, I'll keep people posted.

Bonus Pairing: Winry vs. Edward (Fullmetal Alchemist) "Sometimes you just want to hit it with a wrench"

Skinner's gone rogue

FTL: Faster Than Light recently released a free expansion. So I booted up my copy to jump through the stars on a mission to deliver a message critical to a civil war. Many hours later, I was surprised to find myself still playing. This had me thinking about why FTL has such addictive game play. FTL is a Roguelike, a genre started by the text game Rogue. There are three key features of a Roguelike. First, everything is random. The levels, enemies, and items you get are all randomly generated. Other than you starting gear, there is no guarantee of finding any particular item or location in a play through. In FTL, there are a fixed number of stages and the power of the enemies ramps up through them, but within those minor constraints it is all random. Second, Roguelikes have perma-death. If you die, you have to start over from the beginning with a completely new random world. There is no way to revert to a saved state. Finally, Roguelikes are hard and tend to boarder on punishingly so. If you are winning more than 50% of the time, the game is too easy. Sounds like a fun game, no?

Despite how awful Roguelikes sound, they are a popular genre. Some of the popularity has to do with the creativity and adaptability these games require. But that is not what I wanted to talk about. Instead, I want to talk about the psychology of conditioning and how it relates to games, in particular operant conditioning. Loosely defined, this is providing positive or negative feedback to encourage or discourage certain behaviors. An example is Sheldon giving Penny a chocolate every time she does something he approves of when she and Lennard start dating the first time.

On the surface, this clearly relates to games. Every time you defeat an enemy or finish a quest, you are rewarded. Though often the rewards are random in games. This is where things get a bit weird. It turns out that only sometimes rewarding for a behavior reinforces the behavior better than always rewarding for it. Random rewards are one reason that gambling is so addictive.

Putting this together, we see that the difficulty and randomness of Roguelikes utilizes this random reinforcement mechanism. Instead of knowing where a certain enemy is that gives a great item, players sometimes stumble upon interesting enemies that might give a nice item. And this could happen in the next location you visit! Instead of always having the sweet taste of victory, you have to fight for it. But this makes the cases when it happens that much sweeter. Granted it is possible to have the good outcomes happen to infrequently, see the first release of Diablo III. But FTL and other successful Roguelikes condition you to want to come back for more, even though they repeatedly beat you to a pulp.

Dissertation Nemesis

nem·e·sis (noun) : an opponent or enemy that is very difficult to defeat

Right now I am struggling through my PHD thesis. Calling it my nemesis would not be an understatement. Even though I am in the home stretch, motivation to finish it has been hard to come by. I recently read Reality is Broken and starting toying with an Alternate Reality Game to find the element of fun and make this job a game. This was inspired by the part of the book talking about SuperBetter, an alternate reality game to help with injury recovery. While SuperBetter could conceivable be used to motivate thesis work, I think some variations are needed. In particular, every PHD student is working on a thesis and could use a support group. Hence, the dissertation version is more of a team game than SuperBetter.

In this game, you and your fellow dissertaters are part of some team working together for some purpose, like protecting the world. But each team member has their personal adversary, their Nemesis, that they alone can defeat. The team can and should support each other in this endeavor, but no kill stealing. Two obvious ways to theme your team would be the Justice League or the Avengers. They are working together to save humanity, but each has their own personal enemy. Thor has Loki, Captain America has HYDRA, the Incredible Hulk has his anger issues and Robert Downy Jr. Tony Stark his alcoholism.

The first step is to assemble your team. This means recruiting like Nick Furry. Your team can come from any discipline. It doesn't have to be just people in your program or sub-sub-sub-specialty of your program. In fact, it is helpful to have other perspectives and not have to worry that you are directly competing with those on your team. Recruitment is probably the hardest step. Programs tend to be very insular, especially near the end. Just remember that everyone is in the same boat as you and wants people to commiserate and support them through this. Don't get discouraged. It took Nick Furry 6 movies before he could get the entire Avengers team together.

Once you have assembled your team, everyone needs to pick their in game identity and Nemesis. Your group doesn't need to have as tight themeing as the Justice League or Avengers. Mixing DC and Marvel is perfectly fine. Or a mash-up like the League of Extraordinary Gentlemen does for classic literature or Fables for faerie tales.

Picking your nemesis is as important as who you are. This dichotomy represents the major focus of your energies. While some characters, like Sherlock Holmes and Moriarty, are easy to pair, others are much harder. Batman has so many great opponents in his rouges' gallery that you can really fine tune you Nemesis to how your thesis feels to you. Maybe it is the Riddler if your thesis is an enigma to solve. Or perhaps the Joker because your dissertation is just wonton destruction and chaos. Or Ra's al Ghul if you keep having to rewrite the same portion of your thesis over and over again. I would just recommend against Captain Ahab chasing the white whale as that doesn't end well.

Once you have your team and nemesis, you need a base of operations. The Avengers have the S.H.E.I.L.D. helicarrier and the Justice League their satellite. This is your teams safe area. It is a place you can go and talk shop without reservations. It could be a lounge in your department, some meeting room on campus or even your groups' favorite coffee house. Any place you can all gather and talk about the dissertation writing process comfortably will do. In addition, also schedule a weekly meeting there. During this meeting your team should discuss how they are faring against their nemesis. Is the battle going well? Do they need some help? What are people worried about that is coming up? This way the team can support each other and help those that are struggling.

Contact with your team should not be limited to just the weekly meetings. Members of your group should be in contact daily. This does not mean talking to everyone every day. If you know someone predicted a hard week or had a hard previous week, check in to see how they are doing. Conversely if you are struggling, don't be afraid to reach out, that is what your team is for. This can be as simple as and e-mail, Facebook Post or text. Or if someone needs something bigger people can meet up for lunch or coffee to help formulate strategies.

Outside of the normal meetings and check-ins, having group writing sessions is extremely valuable. Having everyone gather to write for a few hours is a great commitment device. In this scenario, all your nemesis have banded together to create a super team to challenge your own. Only a concerted, joint effort can push them back. This is a great way to start the game or re-set people's writing if their schedules have gotten screwed up.

Finally, you need goals and achievements. Goals are things that you have set out to do and achievements are things that other people bestow upon you. Both are important to the process. Goals enable you to focus your efforts. Achievements show you hidden strengths and provide positive reinforcement.

Clearly, your ultimate goal is the defeat of your Nemesis finishing your dissertation. This should be broken into smaller pieces so that every day you can complete a goal. Goals should vary in length and difficulty with some of them being quite a stretch. Short term goals can be like writing a page of text or finishing a subsection. Stretch goals are things that you would like to see in your dissertation that aren't key to its completion. Keep a running list of these and update your team on your progress at the meetings. This provides both a way to track progress and a commitment device for accomplishing your goals.

Achievements aren't things you can work for but can give others. They should be recognitions of a job well done or acknowledgments of a strength the person is overlooking. Obvious achievements would be congratulations for finishing a chapter or surviving giving a presentation on your work. Smaller ones could be about regaining momentum after a speed bump or making a really cool graphic for your thesis. Even things like recognition for a very cool turn of phrase in the text or handling a tough adviser meeting are achievement worthy.

Everyone should make an effort to hand out achievements to other people and publicize them. Group meetings are a good place for them as everyone is there. But even during a daily check in they can be awarded if you think the person has done something achievement worthy which they might have overlooked. So if you see Batman working for 8 hours straight, especially if he has never done this before, telling the group that he is a Diligent Detective would be in order.

Doing a dissertation is a unique experience, which can be very isolating. The alternate reality game outlined above is an attempt to create a framework where dissertaters can socialize around their work. Its goal is to provide a support network of like minded individuals so you can push each other over the hump and finish your thesis. I am not sure it is complete in its current form, but should provide a good starting point. Hopefully, I'll assemble a team and be able to post updates to the rules as we play.

PnP Wiz-War - Part 4: Finishing touches

In addition to the base game, I also printed out the community expansion. This adds many more cards to play with and lots more tokens to cut out. As of now I have not integrated any of the community expansion cards into my deck. Most of them are on the complex end and many of the basic support cards are missing to make a usable expansion. In particular, number cards (27.5% of the normal deck) and Pick Lock (3%) are not included in the file. I used Ilya's source files to add the community expansion symbol to some number cards and pick lock cards, which will let me tweak the deck. I will probably just select my favorite cards from the community expansion and balance them with numbers, Pick Locks and some other simple cards from the original game after some plays.

For the tokens I followed my previous method. First I pasted one set of each token to a big sheet of matte board.

So Many Tokens...

Once affixed, I sprayed with my ink fixative and allowed it to dry overnight. Then I scored the tokens and cut the outline of each strip and attached the back label, except for the creatures. These I fully cut out because I wanted the creature names to be on the same edge on both sides. With the original game, I could rotate 1/2 the labels before printing in the source files. Unfortunately, I don't have the source files for the full community expansion, which meant I had to do it the old fashioned way. Once the backs were attached, I sprayed them with my ink fixative. Then sliced them apart.

Community Expansion Tokens

This completed all the game components. In addition to the pieces, one also needs the rules. At the time of this post, there isn't a super good version of the rules to print and use. The core rules can be found on at Wiz-War.com along with a good card FAQ. Sadly the formatting on that site sucks. The first few pages of Kwanchai's Wiz War Redesign have the rules from the website formatted nicely. Unfortunately, there have been a few player made updates to clarify the rules. In particular, the distinction between Line of Sight and Line of Movement, which is present on Ilya's redesign, but not in the core rules. So in addition to the core rules, I strongly recommend having Ilya's Quick Reference on hand. It doesn't have the complete rules, but enough to get you started and fill in some of the clarifications to the core rules. I had mine laminated.

Quick Reference & Rules

I also found some great storage options for my copy. At my local hobby store, there was a square box which was perfect dimensions to hold all the boards & warps. I also purchased one of the small plastic dividers for all the different tokens. For the cards, I used one of my Magic: the Gathering boxing I had lying around. This is the complete set.

Completed Set!

One last thing, you will need a 4 sided die to play the game. Every reference in Wiz-War to a die is to a 4 sided die. This can be found at any gaming store.