## Fallout 4 - Come As You Are

While building up my settlements in Fallout 4, I noticed that there was a "Powered Speaker" and wondered what I could do with it.   Between the "Interval Switch", "Delayed On Switch" and the "Delayed Off Switch", I figured I had enough tools to make some some music in my Coastal Cottage.  To start, I decided on remaking one of the first songs I learned on guitar: Nirvana's Come As You Are.

Despite my best efforts, it's still not quite perfect.  It seems like the timing on the switches isn't as exact as I needed it to be for this wiring system, and it seems like some switches will occasionally stay on despite having no power.   I found that the most reliable method was to alternate between two offset interval switches with a slight overlap to form a loop, and use a chain of delays to space out the individual notes.

Resource-wise, I found myself needing tons of copper and ceramic.  The most time consuming part was setting up the delays and notes via terminal.  Below is the diagram I created as a reference so I could set several things at once.

I hope this will inspire some discussion on how to create music in Fallout 4.  If you put one together or have an idea on how to streamline the process, please share in the comments!

## RFC: Are geometric constructions still relevant?

Dear friends, fellow math teachers, game developers and artists.

I've got this little dilemma I'm wondering if you could help me with. You see, part of my geometry curriculum deals with compass and straightedge constructions. My colleagues have suggested that this is a topic we, not exactly skip, but... I dunno what the appropriate word here is... trim?  They argue that it's largely irrelevant for our students, is overly difficult, and represents a minimal component of the SOL test. And I don't think they're wrong. I haven't used a compass and straightedge since I left high school either.

However, something about these constructions strikes as beautiful. Part of me thinks that's enough reason to include them, but it also got me thinking about more practical applications of them.   Where did use them?  I used them making video games.  Video games build worlds out of "lines" and "spheres".  Beautiful worlds.

My question is this, do my 3D artist friends feel the same way?  Do you remember your compass and straightedge constructions?  Do you use them, or some derivation thereof, in your everyday work?  Are you glad to have learned them?  Or are the elementary constructions made so trivial in modern 3D modeling software that you don't even think about them?

## The Future of AI: 13 year old Ukrainian boy Looking for Guild?

I recently finished reading Michio Kaku's The Future of the Mind and found it very thought provoking.  A combination of cutting-edge advances in psychology, artificial intelligence and physics, mixed together with numerous pop-culture references made for a very informative and inspiring read.  Many of the ideas presented seemed very reminiscent of the narratives in The Mind's I, but with a greater emphasis on the practicality of technological advances.  While I would no doubt recommend it to an interested reader, I don't exactly intend for this post to turn into a book review.  This is more of a personal reflection on some of my thoughts while reading it.

## Defining Consciousness: Kaku vs Jaynes

My first point of intrigue begins with Kaku's definition of consciousness, which he calls the "space-time theory of consciousness":

Consciousness is the process of creating a model of the world using multiple feedback loops in various parameters (e.g., in temperature, space time, and relation to others), in order to accomplish a goal (e.g. find mates, food, shelter).

Consciousness is a notoriously difficult phenomenon to define, as this is as good of a definition as any in the context of the discussion. What's interesting about this definition is that it begins with a very broad base and scales upward.  Under Kaku's definition, even a thermostat has consciousness -- although to the lowest possible degree.  In fact, he defines several levels of consciousness and units of measurement within those levels.  Our thermostat is at the lowest end of the scale, Level 0, as it has only a single feedback loop (temperature).  Level 0 also includes other systems with limited mobility but more feedback variables such as plants.  Level 1 consciousness adds spacial awareness reasoning, while Level 2 adds social behaviour.  Level 3 finally includes human consciousness:

Human consciousness is a specific form of consciousness that creates a model of the world and then simulates it in time, by evaluating the past to simulate the future. This requires mediating and evaluating man feedback loops in order to make a decision to achieve a goal.

This definition is much closer to conventional usage of the word "consciousness".  However, for me this definition seemed exceptionally similar to a very specific definition I'd seen before.  This contains all the essential components of Julian Jaynes' definition in The Origin of Consciousness!

Jaynes argued that the four defining characteristics of consciousness are an analog “I”, (2) a metaphor “me”, (3) inner narrative, and (4) introspective mind-space.  The "analog 'I'" is similar to what Kaku describes as the brain's "CEO" -- the centralized sense of self that makes decisions about possible courses of action.  Jaynes' "introspective mind-space" is analogous to the "model of the world" in Kaku's definition -- our comprehensive understanding of the environment around us.  The "metaphor 'me'" is the representation of oneself within that world model that provides the "feedback loop" about the costs and benefits of hypothetical actions.  Finally, what Jaynes' describes as "inner narrative" serves as the simulation in Kaku's model.

This final point is the primary difference between the two models.  One of the possible shortcomings of Jaynes' definition is that the notion of an "inner narrative" is too dependent on language.  However, Kaku avoids this confusion by using the term "simulation".  Jaynes' hypothesis was that language provided humanity with the mental constructs needed to simulate the future in a mental model.  I think the differences in language are understandable given the respective contexts.  Jaynes was attempting to establish a theory of how consciousness developed, while Kaku was attempting to summarize the model of consciousness that has emerged through brain imaging technology.

While I must admit some disappointment that Jaynes was not mentioned by name, it's partly understandable.  Jaynes' theory is still highly controversial and not yet widely accepted in the scientific community.  With Kaku's emphasis on scientific advances, it might have been inappropriate for this book.  Nevertheless, I'd be interested to hear Kaku's thoughts on Jaynes' theory after having written this book.  Jaynes didn't have the luxuries of modern neuroscience at his disposal, but that only makes the predictions of the theory more fascinating.

## Artificial Intelligence (or the illusion thereof)

While I continued to read on, I happened to come across a news story proclaiming that Turing Test had been passed.  Now, there's a couple caveats to this claim.  For one, this is not the first time a computer has successfully duped people into thinking it was human.  Programs like ELIZA and ALICE have paved the way for more sophisticated chatterbots over the years.  What makes this new bot, Eugene, so interesting is the way in which it confused the judges.

There's plenty of room for debate about the technical merits of Eugene's programming.  However, I do think Eugene's success is a marvel of social engineering.  By introducing itself as a "13-year old Ukrainian boy", the bot effectively lowers the standard for acceptable conversation.  The bot is (1) pretending to be a child and (2) pretending to be a non-native speaker.  Childhood naivety excuses a lack of knowledge about the world, while the secondary language excuses a lack of grammar.   Together, these two conditions provide a cover for the most common shortcomings of chatterbots.

With Kaku's new definition of consciousness in mind, I started to think more about the Turing Test and what it was really measuring.  Here we have a "Level 0" consciousness pretending to be a "Level 3" consciousness by exploiting the social behaviors typical of a "Level 2" consciousness.  I think it would be a far stretch to label Eugene as a "Level 3" consciousness, but does his social manipulation ability sufficiently demonstrate "Level 2" consciousness? I'm not really sure.

Before we can even answer that, Kaku's model of consciousness poses an even more fundamental question.  Is it possible to obtain "Level (n)" consciousness without obtaining "Level (n-1)"?

If yes, then maybe these levels aren't really levels at all.  Maybe one's "consciousness" isn't a scalar value, but a vector rating of each type of consciousness.  A a human would score reasonably high in all four categories. Eugene is scoring high on Level 0, moderate on Level 2, and poor on Levels 1 and 3.

If no, then maybe the flaw in the A.I. development is that we're attempting to develop social skills before spacial skills.  This is partly due to the structure of the Turing Test.  Perhaps, like the Jaynesian definition of consciousness, we're focused a bit too much on the language.  Maybe it's time to replace the Turing Test with something a little more robust that takes multiple levels of consciousness into consideration.

## The MMORPG-Turing Test

Lately I've been playing a bit of Wildstar.  Like many popular MMORPGs, one of the significant problems facing the newly launched title is rampant botting.   As games of this genre have grown in popularity, the virtual in-game currency becomes a commodity with real-world value.  The time-consuming process behind the collection of in-game currency, or gold farming, provides ample motivation for sellers to automate the process using a computer program.  Developers like Carbine are in a constant arms race to keep these bots out of the game to preserve the game experience for human players.

Most of these bots are incredibly simple.  Many of them simply play back a pre-recorded set of keystrokes to the application.  More sophisticated bots might read, and potentially alter, the game programs memory to perform more complicated actions.  Often times these bots double as an advertising platform for the gold seller, and spam the in-game communication channels with the sellers website.  It's also quite common for the websites to contain key-loggers, as hijacking an existing player's account is far more profitable than botting itself.

While I'm annoyed by bots as much as the next player, I must admit some level of intrigue with the phenomena.  The MMORPG environment is essentially a Turing Test at an epic scale.  Not only is the player-base of the game is on the constant look out for bot-like behavior, but also the developers implement algorithms for detecting bots.  A successful AI would not only need to deceive humans, but also deceive other programs.  It makes me wonder how sophisticated a program would need to be so that the bot would be indistinguishable from a human player.   The odds are probably stacked against such a program.

Having played games of this type for quite some time, I've played with gamers who are non-native speaker or children and I've also seen my share of bots.  While the "13 year old Ukrainian boy" ploy might work in a text-based chat, I think it would be much more difficult to pull off in an online game.  It's difficult to articulate, but human players just move differently.  They react to changes in the environment in a way that is fluid and dynamic.  On the surface, they display a certain degree of unpredictability while also revealing high-level patterns.  Human players also show goal oriented behavior, but the goal of the player may not necessarily align with the goal of the game. It's these type of qualities  that I would expect to see from a "Level 1" consciousness.

Furthermore, online games have a complex social structure.  Players have friends, guilds, and random acquaintances.  Humans tend to interact differently depending on the nature of this relation.  In contrast, a typical chatterbot treats everyone it interacts with the same.  While some groups of players have very lax standards for who they play with, other groups hold very high standards for player ability and/or sociability.  Eugene would have a very difficult time getting into an end-game raiding guild.  If a bot could successfully infiltrate such a group, without their knowledge, it might qualify as a "Level 2" consciousness.

When we get to "Level 3" consciousness, that's where things get tricky.  The bot would not only need to understand the game world well enough to simulate the future, but it would also need to be able to communicate those predictions to the social group.  It is, after all, a cooperative game and that communication is necessary to predict the behavior of other players.  The bot also needs to be careful not to predict the future too well.  It's entirely possible for a bot to exhibit super-human behavior and consequently give itself away.

With those conditions for the various levels of consciousness, MMORPGs also enforce a form of natural selection on bots.  Behave too predictably?  Banned by bot detection algorithms.  Fail to fool human players?  Blacklisted by the community.  Wildstar also potentially offers an additional survival resource in the form of C.R.E.D.D., which could require the bot to make sufficient in-game funds to continue its subscription (and consequently, its survival).

Now, I'm not encouraging programmers to start making Wildstar bots.  It's against the Terms of Service and I really don't want to have to deal with anymore than are already there.  However, I do think that an MMORPG-like environment offers a far more robust test of artificial intelligence than a simple text-based chat if we're looking at consciousness using Kaku's definition.   Perhaps in the future, a game where players and bots can play side-by-side will exist for this purpose.

## Conclusion

When I first started reading Kaku's Future of the Mind, I felt like his definition of consciousness was merely a summary of the existing literature.  As I continued reading, the depth of his definition seemed to continually grow on me.  In the end, I think that it might actually offer some testable hypotheses for furthering AI development.  I still think Kaku needs to read Jaynes' work if he hasn't already, but I also think he's demonstrated that there's room for improvement in that definition.   Kaku certainly managed to stimulate my curiosity, and I call that a successful book.

## Meta-Pokemon

In a previous post, I mentioned my fascination with Twitch Plays Pokemon (TPP). The reason behind this stems from the many layers of metagaming that take place in TPP. As I discussed in my previous post, the most basic definition of metagaming is "using resources outside the game to improve the outcome within the game". However, there's another definition of metagaming that has grown in usage thanks to Hofsteadter: "a game about a game". This reflexive definition of metagaming is where the complexity of TPP begins to shine. Let's take a stroll through some various types of metagaming taking place in TPP.

## Outside resources

At the base level, we have players making use of a variety of outside resources to improve their performance inside the game. For Pokemon, the most useful resources might include maps, beastiaries, and Pokemon-type matchups. In TPP, many players also bring with them their own previous experiences with the game.

Pokemon itself is a metagame. Within the world of the game, the Pokemon League is its own game within the game. A Pokemon player is playing the role of a character who is taking part in game tournament. What makes TPP so interesting is that that it adds a game outside the game. Players in TPP can cooperate or compete for control of the game character. In effect, TPP is a meta-metagame: a game about a game about a game. Players in TPP are controlling the actions of a game character participating in a game tournament. It's Pokemon-ception!

## Gaming the population

Another use of metagaming is to take knowledge of the trends in player behaviors and utilize that information to improve the outcome within the game. In TPP, players would use social media sites such as Reddit to encourage the spread of certain strategies. Knowledge of social patterns in the general population TPP players enables a few players to guide the strategy of the collective in a desirable directions. Memes like "up over down" bring structure to an otherwise chaotic system and quickly become the dominant strategy.

## Gaming the rules

One of my favorite pastimes in theory-crafting, which is itself a form of metagaming. Here, we take the rules of the game and look at possible strategies like a game. The method TPP used in the final boss fight is a perfect example of this. The boss is programmed to select a move type that the player's pokemon is weak against and one of these moves deals no damage. By using a pokemon that is weak against this particular move, the boss is locked into a strategy that will never do any damage! Not only do the TPP players turn the rules of the game against it, but they also needed to organize the population to pull it off!

## Gaming the population

Another use of metagaming is to take knowledge of the trends in player behaviors and utilize that information to improve the outcome within the game. In TPP, players would use social media sites such as Reddit to encourage the spread of certain strategies. Knowledge of social patterns in the general population TPP players enables a few players to guide the strategy of the collective in a desirable directions. Memes like "up over down" bring structure to an otherwise chaotic system and quickly become the dominant strategy.

## Rule modification games

One of the defining characteristics of a game are the rules. The rules of Pokemon are well defined by the game's code, but the rules of TPP are malleable. We can choose between "chaos" and "democracy". Under chaos, every player input gets sent to the game. Under democracy, players vote on the next action to send. When we look at the selection of rules in terms of a game where we try to maximize viewers/participates, we get another type of metagaming.

## The Nintendo Power Generation

I've been feeling a bit nostalgic about some old video games lately.  This is thanks in part to some recent articles on Kotaku about struggling to fit video games into adult life, the joy of discovering JRPGs, and the fascinating phenomenon of Twitch Plays Pokemon. I'll get into Twitch Plays Pokemon in more detail later,  but for now I wanted to start with something a little closer to home.  Although I played Pokemon while growing up, I tend to associate the game-play with that of Dragon Warrior.  This probably says something about my age, which is an interesting on its own, but the connection I'm going to focus on here is "metagaming".

I'm fortunate to have grown up with video games from an early age.  My parents owned an Intellivision, and I would often beg them to play BurgerTime.   I was really young at this point and there weren't many other games on the Intellivision that I could enjoy without being able to read.   When the Nintendo Entertainment System came out, this opened the floodgates of exciting new games.  The NES quickly became a family bonding experience.  Between Super Mario Bros., Duck Hunt, Track and Field, and The Legend of Zelda, there was something for everyone in the house!

This is the earliest example that I can recall of metagaming.  Metagaming, in its simplest terms, is the use of resources outside of a game to improve the outcome within the game.  In the case of Dragon Warrior, the "Explorer's Handbook" contained a variety of information about the game that otherwise might have only been discovered through trial and error.  It included maps of the entire game and information about the strengths and weaknesses of the foes within each area.  The maps in particular were exceptionally useful for two reasons.  First, visibility within the dungeons was limited to a small area provided by use of a torch item.  Using a map made it possible to make it through the dungeon without using a torch, and also making sure to collect all of the important treasures.  Secondly, the overworld map was divided into areas with radically different monsters.  Wandering into an area at too low of a level would mean certain death.  I probably wouldn't have even been able to complete the game if it wasn't for the "Explorer's Handbook".

The metagaming didn't end with Dragon Warrior.  In fact, it was only the beginning.  The monthly subscription soon turned into an addiction that almost paralleled the video games themselves ("almost" being the operative word).   I must have read through the Nintendo Power Final Fantasy Strategy Guide at least a dozen times before even playing the game.  I was always reading up on the latest releases during the week, and would rent the game that interested me most over a weekend for a marathon gaming session.  It got to the point where the store I rented from was asking me about what up-coming titles they should order!

Over time, my passion for metagaming started to influence my choice of games.  Games like Marble Madness and Bubble Bobble that were once my favorites, started to lose their appeal.  My reflexes on titles like these had actually improved with extensive practice, but there was always a brick wall where those reflexes weren't fast enough.  Even if I knew what was coming, lacking of coordination required to pull it off became a point of frustration.    I gradually started to lean towards games where having an outside knowledge was an advantage.  JRPGs like Dragon Warrior and Final Fantasy started to become my favorite genre.   That's not to say I shied away from "twitch" games.  I just focused on "twitch" games where strategy and knowledge could influence the outcome.   I was particularly fond of fighting games like Street Fighter II, since knowing the move-set of each character was a distinct advantage in arcades where my quarter was on the line.

I've come to accept that I enjoy metagaming, sometimes as much as playing the game itself.  However, there are places where it's not always acceptable.  Metagaming is also often used as a negative term in pen and paper role playing games like Dungeons and Dragons where it breaks the sense of immersion when a player uses knowledge that his/her character would not know.  I'm definitely one of those players that devours the entire rule-book before creating a D&D character to ensure that I'm developing it in an optimal way.  I can't help it.  For me, learning about the game is an integral part of the gaming experience.  I don't necessarily do it out of a desire to win.  I just enjoy the process of researching the rules, developing a theory about how best to play, and then putting it into practice to see if it works.  There's a real science to gaming for those who are willing to look for it.

The reason I wanted to share this story is that I've been in a number of conversations with individuals in older generations who have a negative opinion on video games.  "Kids these days just play video games all the time and don't understand what it's like in the real world," they often say.  I wanted to present a different perspective here.  For the metagamers of the world, the line between the game and real world is fuzzy.   There's a generation of gamers who've learned important real world knowledge and skills to help them improve their game-play.  For members of my age cohort, Nintendo Power provided an outlet for us to grow and excel as individuals.  I, for one, am glad to have been able to experience the joy of metagaming and will continue to metagame my way to the future.

## GW2: Scepter Guide for New Mesmers

When I first played the original Guild Wars beta, over 7 years ago, the mesmer came with a disclaimer on the character creator stating that the profession required advanced tactics and may not be suitable for new players. I was hooked on the mesmer from there on. In Guild Wars 2, this iconic class has undergone a substancial overhaul and is much more self-sufficient than in the original. However, the GW2 mesmer still has a somewhat steeper learning curve relative to some other professions. I posted a version of the following on the official forums during BWE3 to help new players more effectively use the mesmer's starting weapon: the scepter. My hope is that this guide will help make the first 10 levels of the game as painless as possible, at which point you can really start to customize the mesmer to your preferred playstyle.

Every new character in GW2 starts in a story mode instance based on the selected race. If this is your first time playing GW2, you should use this opportunity to check out the game options, display settings and key bindings before heading off towards the opening quest objective. Soon enough you'll encounter your first enemy or "mob". You only have one attack unlocked, Ether Bolt, so use it. The basic auto-attack on the scepter has a 3 step chain. On every third attack, it creates a clone that looks like you and attacks your mob but doesn't really do any damage. Now that you have a clone, let's use F1 or F2 to shatter him for some extra damage. If the mob is attacking your clone or not attacking at all, hit F1 for Mind Wrack which deals direct damage to the mob. If the mob is attacking you or an ally, use F2 for Cry of Frustration which causes a condition called confusion that causes damage when that mob uses a skill. Try both of them out and get a feel for how much damage they do with a single clone. When you unlock your second skill, Illusionary Counter, you can use it to block an attack and generate a clone or tap it twice to blind your foe instead. Test out both of your shatters with two clones and see how they've improved. If you find yourself taking too much damage, use skill #6 to heal yourself. You may even unlock your third weapon skill which is a hard hitting channelled attack that applies several stacks of confusion.

Eventually you'll get to an epic cinematic and huge boss mob. Look out for red circles or big attack animations and dodge out of the way. If you happen to get hit, don't panic -- you're not dead yet. Start to use the #1 attack in the downed state on one of the low level mobs in the area. You can also use the #2 skill to create a decoy, the #3 skill to summon a phantasm to lay some extra hurt your target, or the #4 skill to heal yourself if you're close to bleeding out. Keep it up until you score a kill and rally. Go back to working on the boss mob until you finish it off and save the day!

After killing the boss, you get another nice cut scene and a quest reward. This includes a bag, some XP, some coin, and your choice of two off-hand weapons. I’d highly recommend choosing the focus from the first quest reward. Not only is Temporal Curtain great for travelling, but it’s also great for snaring melee attackers so you avoid getting hit and acts as a light field. The Illusionary Warden gives you some AoE damage -- which the scepter is lacking, provides defense against projectiles and doubles as a whirl finisher. This means that once you've unlocked both of the focus skills you can do your own skill combos! Start with using Illusionary Warden on a mob then place a Temporal Curtain on top of him. The resulting combo shoots Cleansing Bolts in different directions and remove conditions from allies that they hit. While testing this out, you may observe that the Illusionary Warden is a stationary phantasm, and won’t move until you use a shatter skill. I’d also recommend that you have at least one clone up before summoning the Warden so he doesn’t get killed right away.

Against melee attackers, you want to open with the scepter auto attack and use Temporal Curtain to cripple them. Your goal is to get at least two clones up before the mob gets close to you. When the mob starts to get close, use Confusion Images. While channeling, use Cry of Frustration. Depending on how many clones you had up, the mob should have 8-9 stacks of confusion. and should be just about to swing at you. Use Illusionary Counter to block the attack, and watch the mob take massive confusion damage while you get away scratch free! If that didn’t kill it, go back to auto-attacking, use the dodge roll to avoid the next two attacks, then use Mind Wrack when you get enough clones.

In dynamic events with lots of people, don’t be stingy with your shatters. The odds of you getting 3 illusions up in such a situation are pretty slim unless you're fighting a champion, so don't hestitate to do a single illusion shatter if that's all you can get off before the mob dies. If possible, try to summon your Warden on a target in the middle of a group with high health, let him do his attack once, then shatter him. He’s going to die when your target dies anyways, so you may as well get the most out of it.

Once you've reached level 5, you'll unlock your first utility skill. There's a lot of really great skills to choose from here, but the one I would recommend picking up first is Blink. This is a ground targeted skill that teleports you to the selected location while breaking stuns. The reason I suggest this skill first is that it will help you get around the map a little bit faster when out of combat, while also helping you keep your distance from melee mobs. Look for skill challenges on the map, marked with the blue chevron, and complete them to unlock some other utility skills of your choice. My personal favorites on the 1st tier are Null Field and Signet of Domination. If you're unsure of how a particular skill works, you can always use the PvP menu to go to the Mists and test it out on the target dummies there.

Eventually you'll start to encounter some ranged attackers. Against these mobs you can open with Confusing Images and Illusionary Counter since they’ll generally start attacking right away. Since you get a clone on counter, this will give you a distraction to summon an Illusionary Warden on them and block their projectiles. Once you get a few more skill points, you can combine confusion with the Feedback utility skill to quickly take down ranged attackers.

I’d recommend sticking with scepter/focus until at least level 7 when you unlock weapon swapping. Weapon swapping really opens up a lot of play-style options for the mesmer. It’s much easier to survive as sword mesmer when you can weapon swap to a staff for Phase Retreat after blowing your defensive cool-downs. Likewise, the greatsword benefits from a weapon swap once enemies get close. You may want to keep the scepter/focus on a weapon swap until you unlock all the skills on your weapon of choice. These are just my opinions of course, so if there’s a weapon combination you really want to play with go right ahead! Regardless of what you choose, you should always keep a focus in your bag so that you can switch to it when you're not in combat for the swiftness buff.

I just hope that these tips help some newcomers who might be turned off by the scepter after hearing horror stories from the first two BWEs. The scepter was vastly improved in BWE3 and I expect it to be even more polished by release. Overall, I think that using the scepter/focus will help you learn how to effectively utilize the core mesmer mechanics. There’s a lot to learn about playing a mesmer, but the class has a nice rhythm once you get used to it. Stick it out for a while and you might be pleasantly surprised!

## Guild Wars 2: Mesmer Sharper Images Analysis

This weekend marks the 3rd Beta World Event for Guild Wars 2. I wrote a little bit about my general experiences in the first BWE, but this time I'm focusing on a very specific area of the game. In the first BWE, I was just playing the game and having fun with it. In the second BWE, I started to do a lot more "testing". In particular, one of the things I was testing was the "Sharper Images" trait.

Sharper Images (SI) is a Dueling trait that causes critical hits from Illusions to inflict bleeding for 5 seconds. This trait was bugged in the first BW1 and didn't work at all. In the second BWE1, it worked as described but a second phantasm trait called "Phantasmal Haste" was bugged resulting in some crazy damage output. This means that I didn't get a very good perspective on how these two traits would work together, but that's okay because I can do the math! In addition to seeing how the phantasm related traits would interact together, I also wanted to find out which stats to gear for in order to maximize my damage. In order to do this, we first need some information about how damage is calculated in GW2. Assuming a level 80 character:

• Pandara_RA! at Team Legacy worked out the following formula for the base damage of an attack: $Base Damage = \frac{(Power) \cdot (Weapon Damage) \cdot (Skill Coefficient)}{Target Armor}$
• The chance of getting a critical attack is determined by the Precision above the base: $CritRate= \frac{4 + (Precision - Base)/21}{100}$
• When an attack criticals, it hits for 50% more damage plus any bonus to critical damage (Prowess). With this, we can find out the average damage of an attack using: $Direct Damage = (Base Damage) \cdot (1+(Crit Rate) \cdot (0.5+\frac{Prowess}{100}))$
• The last piece of information we need is the bleeding damage, which is dependent on condition damage (Malice). According to the GW2 wiki this is determined by $\frac{damage}{second} = 40+0.05 \cdot (Malice)$. The bleed duration of 5 seconds can be improved through stats, but only pulses once per second. This means that we can round the duration down to find the number of pulses and find the total bleed damage: $\frac{damage}{second} \cdot \lfloor duration \rfloor$

To get a rough estimate of Phantasm DPS, I put these formulas together with some various equipment set-ups and trait choices. You can download this spreadsheet here. To make things simplier, I focused entirely on "Illusionary Duelist" with SI because I knew it hits 8 times every 10 seconds. I also had to make several assumptions about how certain traits would stack, and all of this is subject to change when the game is released anyway. Despite these shortcomings, I found several interesting results:

• Without any bonus condition damage, SI can add about 10%-20% damage depending on the target's armor (best against higher armor foes) when used in conjunction with Phantasmal Fury. This puts it on par with most damage traits at the adept level.
• With a skill coefficient of about 0.5 (a total guess BTW), the direct damage builds and condition damage builds I tried seem to even out in terms of potential damage. A lower skill coefficient tends to favor condition damage and a higher one favors direct damage.
• Chaotic Transference bonus seems lack-luster relative to the heavy investment.
• Phantasmal Strength and Empowered Illusions complement each other well in a power Build, but the investment for Phantasmal Strength doesn't seem worth it in a condition damage build.
• Phantasmal Haste tends to work better with a condition damage build than a power build. You don't need to hit hard with SI, you just need to hit often.
• Investing 20 points into Domination can have a big effect on condition damage builds because it extends bleeds for an extra tick. This makes Lyssa's Runes a potentially interesting choice with SI because of the +10% condition duration, allowing you to spend 10 of those points from Domination elsewhere with minimal DPS loss.
• The Rampager jewelry seems to be a better choice than Rabid for a condition damage build with SI. There's no point to having strong bleeds if you aren't applying them frequently enough.

There's still a lot more analysis to be done here and some empirical data to collect in BWE3 to verify these findings, but the results look promising. As it stands, you can make SI work in either a direct damage phantasm build or condition damage build with the appropriate gear. Small tweaks to the skill coefficient can keep the two builds competitive if necessary. This fits with Arena.Net's philosophy of having multiple play-styles be equally viable.

I'd encourage you to try out the spreadsheet with other gear and build combinations that I didn't try. If you're feeling adventurous, you might even extend it to include skills other than iDuelist or other traits I may have overlooked. If you find out any more information about how phantasm damage is calculated I'd love to hear about it in the comments!

Happy theory-crafting!

## Update: BWE3

I did a little testing during BWE3, regarding the attack rates and skill coefficients of the different phantasms. This information should help give an idea of how much each phantasm benefits from stacking Power vs stacking crit/condition damage for Sharper Images. Please note that my recharge times were approximated, and Sanek over at GW2Guru came up with somewhat different numbers. I'm including both my attack rates and his for comparison:

 illusion Hits Recharge Attack Rate (hits/sec) Sanek's Recharge Sanek's Rate (Hit/sec) Approx. Skill Coef. DPS Coef. (Mine) DPS Coef. (Sanek) iDuelist 8 10 0.8 7.5 1.066666667 0.228956229 0.183164983 0.244219978 iSwordsman 1 3 0.333333333 5.5 0.181818182 0.734006734 0.244668911 0.13345577 iWarlock 1 5 0.2 6 0.166666667 0.080808081 0.016161616 0.013468013 iBerserker 1 5 0.2 6 0.166666667 0.281144781 0.056228956 0.046857464 iMage 1 5 0.2 6.7 0.149253731 0.397306397 0.079461279 0.059299462 iDefender 1 3 0.333333333 4.5 0.222222222 0.131313131 0.043771044 0.029180696 iDisenchanter 1 3 0.333333333 4.5 0.222222222 0.131313131 0.043771044 0.029180696 iWarden 12 10 1.2 14 0.857142857 0.033670034 0.04040404 0.028860029 swordClone 3 3 1 staffClone 1 1 1 scepterClone 2 3 0.666666667 gsClone 3 2 1.5

Knowing that the skill coefficient for iDuelist is only 0.23, stacking for condition damage seems to be the best method to maximize damage over time with Sharper Images given a high enough crit rate to apply it consistently. As a general rule of thumb, if your crit rate is less than 50% then you should be gearing for power and if your crit rate is greater than 50% then you should be gearing for condition damage.

A few other interesting things to note:

• iSwordsman has one of the best skill coefficients of any phantasm. If you're not using Sharper Images and have Power oriented spec, you may want to try out the off-hand sword.
• iWarlock's DPS is pretty pitiful without conditions. I'm not sure what the bonus per condition is, but I'd recommend having two staff clones up with iWarlock since they have a much faster attack rate. Edit: 10% bonus per condition
• iWarden has quick attack rate and is has an AoE attack, but remember that this Phantasm is stationary. You're very unlikely to get all 12 hits against a real player.
• iBerserker has slow recharge AoE attack that moves down a line. It might be possible to hit an opponent twice with this if they're running in the same direction, but I can't be sure about it.
• The Greatsword clones have the fastest attack rate of any illusion according to my tests. It seems kind of odd that the best clone for Sharper Images would be on a weapon with no innate condition damage.
• iMage has a high skill coefficient but low attack rate. At first glance, this looks like it would be better for a power build than condition build, but you should remember that he also applies Confusion on attack.
• iMage and iDisenchanter have bouncing attacks that hit three targets: 1 enemy and 2 allies. I couldn't seem to get it to hit the same enemy twice, but this is something to check for on release.
• Keep in mind that my original spreadsheet assumes that you leave your Phantasms out all the time. As of BWE3, this is no longer the optimal play-style. If you decide to go with a Power build, you'll probably get the best burst damage by using Mind Wrack right after your phanstasm's first attack cylce. Likewise, Cry of Frustration can now dish out some major hurt if you're built for condition damage.

## Guild Wars 2 Beta World Event 4/27-4/29: "Over & Under"

At long last, I finally got my chance to play Guild Wars 2! An ambitious title to say the least, GW2 is leaps and bounds ahead of its predecessor. I clocked in as much time as I could over the beta weekend, and am now going through withdrawal so I thought I'd take this opportunity to share my experiences. I had hoped to record some video over the weekend, but the performance impact was a little more than I expected. A choppy YouTube video would hardly do this game justice, so you'll just have to settle for a written account.

As a mesmer primary in the original Guild Wars, it should be no surprise that I gravitated towards this class in GW2. I had my concerns about how this class would carry over, but any doubts that I had are now gone. The GW2 mesmer uses completely different game mechanics than the GW1 Mesmer, but it still captures the essential feeling of the class. I played the mesmer class through the end of the BWE personal story line at level 18, and spend the rest of my time playing PvP with various classes.

Coming from GW1, I had a lot of preconceived notions as to what GW2 would be like. It makes sense to organize these into the parts I overestimated and parts I underestimated. These are not necessarily pros and cons, but simply differences between how I thought GW2 would work and how it actually worked. Keep in mind that the game is still a work in progress, and I'm trying to give an honest opinion so that it can be made even better in the future.

Since I spent the most time playing a mesmer, that's probably the best place for me to start. From the very beginning of the game, it became clear that I had overestimated the shatter skills and underestimated the phantasm skills. Don't get me wrong, a Mind Wrack with both traits is definitely a force to be reckoned with, but it's just that I thought that the Mind Wrack traits and a high level of Guile would be essential to any mesmer build. It turned out that this wasn't the case and there were other viable ways of playing the class. In fact, the phantasms were so awesome that I was usually hesitant to shred them. The three illusion limit also meant that I had to be careful about when I used my clones to not overwrite my phantasms. Since the illusions are locked on to a single target, this added an additional incentive to shred them before the target dies. All of these considerations made the shatter skills something that required careful timing and not just another skill to spam.

As far as the mesmer weapons are concerned, I think I overestimated the scepter and underestimated the staff. The scepter was great at pumping out clones, but I ended up relying on phantasms for most of my damage and it was hard to keep up confusion in PvP. On the other hand, I found myself enjoying the staff a lot more than I expected. The idea of random conditions and boons was something of a turn off for me when I first read the skill descriptions, but the way that it worked was that offensive buffs/debuffs were tied to offensive skills and the defensive buffs/debuffs were tied to defensive skills. Even though the results were random, they were still something that was useful in the situation.

Slightly related to the points above, I think I overestimated the confusion condition and underestimated poison. I think that part of this was that I was trying to compare confusion with hexes like Empathy and Backfire in GW1, where a whole stack of hexes becomes problematic to remove. A whole stack of confusion in GW2 still only counts as one condition, making it relatively easy to remove -- if it was even worth removing at all. On the other hand, I somehow missed the memo about poison reducing healing by 33%. This healing reduction coupled with a sometimes deceptively long duration made poison into one of the more threatening conditions for me. I distinctly remember this one thief that I fought where I had to keep spamming my healing skill until my condition removal was up again to avoid dying from poison long after I had killed him. By the time I was able to remove it, he had respawned and was back for more while I was still at 25% health -- ouch.

One of the other things that caught me off guard was that I overestimated Vitality and underestimated Toughness. In GW1, gearing for PvP was quite simple: stack as much health as you can. GW1 had a large number of armor ignoring damage sources and having enough health to survive a large damage spike was essential to surviving long enough for the healers to react. In GW2, there are no "healers". I found that rather than dealing with a single large damage spike, sustained damage was much more of a threat. This made it more practical for me to focus on improving damage mitigation rather than just stacking health. Of course, this might also be a function of beta players not using voice chat to coordinate spikes.

In terms of the PvP modes, I think I overestimated "Structured PvP" and underestimated "World vs World". I spent a lot of time playing Random Arenas in GW1 and it seemed like the "Structured PvP" was going to be right up my alley. I enjoyed the Structured PvP in GW2, but I think that was mainly because it gave me a chance to play with a fully leveled and unlocked character. The problem I had with Structured PvP it was that it felt too much like an FPS match to me. Win or lose, you were queued for the next match on the same server, fighting the same opponents with the same team over and over until someone leaves. Despite the best efforts of the game to auto-balance the teams, they were often off by one player which makes a big difference with smaller numbers. Nothing like fighting a 2 on 1 battle to ruin the fun. I also spotted a couple of "leechers" in the beta, which I thought was kind of odd. Its not like it was worth farming Glory in the beta, so I'm assuming that they just went AFK and forgot about it. However, "World vs. World" was a completely epic experience. Despite the fact that none of us really knew what we were doing, the sheer number of people on the battlefield was a sight to behold. In comparison to World of Warcraft, World vs World seemed like Alterac Valley on steroids with added benefits outside of the battleground. The only downside to World vs World that I saw was that the repair costs could rack up quickly if you were careless.

All in all, I think Guild Wars 2 met and then exceeded my expectations in a lot of areas. If I were to make a comparison, it felt like Guild Wars 2 was like the MMO equivalent of an Elder Scrolls game. The starting "tutorial zones" seemed less like a tutorial and more like a story "hook" -- my favorite of which being the Charr. The dynamic event system made questing feel less like a grind and more like a sandbox. There's a main story if you want to follow it, or you can just go explore the world and do whatever you like.

I also felt like I had a great amount of freedom in how to play my class. The build I finally settled on with my mesmer in PvP was this one. The Illusionary Warlock and Illusionary Duelist combination packed some serious damage while the Chaos traits and crippling clones made me pretty difficult to kill. Chaos Storm and Null Field allowed me to skill combo by myself for extra conditions. The Portal skill was simply amazing in Conquest mode for feigning retreat from a node, only to return later with reinforcements. The only downside of this build was that I had to be careful when swapping the scepter so that I didn't overwrite my phantasms with clones -- I would just use the two pistol skills and the channeled confusion skill then immediately swap back to the staff. In PvE I replaced the pistol with a focus and Portal with Blink to get around faster, since the burst damage wasn't as important.

Another hidden surprise was the crafting system. I didn't get much time to play with it, but it seemed to be a nice balance between the "discovery" system of Final Fantasy XI and the "recipe list" system of World of Warcraft. You combine random materials to learn new recipes, but once you learn they are added to the recipe list. As an added bonus, it seemed to accelerate the crafting process when I was creating items in bulk! It's the little details like that which made me feel GW2 was respecting the time I spent playing.

Are you a long time Guild Wars player that participated in the GW2 Beta? What did you underestimate or overestimate about the sequel?

## Final Fantasy XIII-2 Clock Paradox and Hamiltonian Digraphs

I'm a long time fan of the Final Fantasy series, going back FF1 on the NES. In fact, I often cite FF4 (FF2 US) as my favorite game of all time. I enjoyed it so much that it inspired me to learn how to program! One of my earliest Java applets was based on a Final Fantasy game and now, 15 years later, I'm at it again.
I had a blast playing FF13, so when I heard about its sequel I had to pick it up. The game is fun and all, but I've become slightly obsessed with a particular minigame: The Clock Paradox.

The rules of the game are simple. You are presented with a "clock" with some number of buttons around it. Each of these buttons is labeled with a number. Stepping on any of the buttons deactivates that button and moves the two hands of the clock to positions that are the distance away from that button specified by the labeled number. After activating your first button, you can only activate the buttons which are pointed at by the hands of the clock. Your goal is to deactivate all of the buttons on the clock. If both hands of the clock point to deactivated buttons and active buttons still remain, then you lose and must start over.
See this minigame in action in the video below:

You may not know this about me, but I'm not a real big fan of manual "guess and check". I would rather spend several hours building a model of the clock problem and implementing a depth first search to find the solution, than spend the 5 minutes of game time trying different combinations until I find one that works. Yes, I'm completely serious. Here it is.
I think that the reason why I'm drawn to this problem is that it bears a close relation to one of the Millennial Problems: P vs NP. In particular, the Clock Paradox is a special case of the Hamiltonian Path Problem on a directed graph (or digraph). We can turn the Clock Paradox into a digraph with the following construction: create a starting vertex, draw arcs to each position on the clock and place a vertex, and finally draw two arcs from each positions following the potential clock hands from that position. The Hamiltonian path is a sequence of arcs that will visit each vertex exactly one. If such a path exists, then the Clock Paradox is solvable.

This little minigame raises several serious mathematical questions:

• What percentage of the possible Clock Paradoxes are solvable?
• Is there a faster method of solving the Clock Paradox? Can it be done in polynomial time, or is it strictly exponential?
• Is there any practical advise topology can offer to help players solve these puzzles?
• Is there anything these puzzles can teach us about the general Hamiltonian Path Problem?

I don't claim to know the answers, but I would offer the following advise: see if you can identify a node with only one way in or out. If you can, then you know that you'll need to start or end. If all else fails, you can always cheat by plugging it into my sim!
That's all I have for today. Maybe there will be some rigged chocobo races in the future... kupo.

## Unraveling Complex Systems: MvC3, Metagaming and Genetic Algorithms

Last year, I wrote an article about Street Fighter and Game Theory for Mathematics Awareness month. This year, the theme is “Unraveling Complex Systems” and I thought I would take the opportunity to expand on the mathematics of fighting games. Lately I've been playing a lot of Marvel vs Capcom 3, and in this article I'm going to attempt to show how the online community in MvC3 is a complex system. This article is intended for casual video gamers, but the mathematically curious might enjoy playing with included sample code. The sample code has been written in Scheme using Racket, formerly known as Dr. Scheme.

# Marvel vs Capcom 3 and Rock, Paper, Scissors

In my last article, I made the case that fighting games in general can be thought of as a game of “Rock, Paper, Scissors”. In Marvel vs. Capcom 3, there are several different levels of “Rock, Paper, Scissors” going on within a single match. In addition to the “High, Low, Overhead” game discussed in my previous article, we also have games like “Attack, Block, Throw” and “Jump-in, Anti-Air, Projectile”. You can even see something of a “Rock, Paper, Scissors” game going on between different characters. What makes MvC3 different from other games in the fighting genre is that you have a roster of three characters playing simultaneously. This makes between individual character differences less important in the larger scheme of things, but what is more important is the strategy behind those three characters.

In MvC3, there are three basic strategies: “rush-down”, “keep-away”, and “turtle”. The “rush-down” strategy is simple, get up close to the opponent and attempt to dish out as much damage as possible. Some characters lend themselves to this strategy more than others, with a few notable ones being Wesker and Wolverine. The idea behind “keep-away” is to control the distance between you and your opponent using ranged attacks and projectiles. Some characters with a good keep-away game include Storm and Sentinel. The last strategy is “turtling”, which is playing a defensive game while waiting for an opportunity to punish a mistake from the opponent. Characters like Haggar and Hulk can make short work of an opponent once the right opportunity arises. While “turtling” can be highly effective against “rush-down” tactics, it tends to not do well against “keep-away” tactics. Thus, “rush-down” beats “keep-away”, “keep-away” beats “turtle”, and “turtle” beats “rush-down” – completing our game of “Rock, Paper, Scissors”. The pay-off matrix for this model might look something like this:

 Rush-Down Keep-Away Turtle Rush-Down (0,0) (10,0) (0,10) Keep-Away (0,10) (0,0) (10,0) Turtle (10,0) (0,10) (0,0)

Consider a match-up between characters like Wolverine and Storm. Wolverine's set of moves might complement a rush-down approach while Storm's set of moves complement a keep-away strategy. The player playing Storm would likely attempt to “keep-away” from Wolverine as long as possible, chipping away at his health via block damage. Essentially, Wolverine has forced into a “turtle” position while the distance between the two is large because he doesn't have the tools to attack from afar. Wolverine's “rush-down” game doesn't start until he closes the distance between them. Once Wolverine is in close, it's going to be hard for Storm to shake him. Storm would need to switch into a “turtle” strategy until she can find an opening between the oncoming attacks to create some distance again.

Keep in mind that these are strategies, and not dispositions of particular character. While some characters in MvC3 may lend themselves to a certain strategy over others, you have three characters to choose from and all of them can be played in any of these three styles to some extent. A individual character's weaknesses can be compensated for with the appropriate assists. For example, the Wolverine player might choose a partner like Magneto with a beam-assist to help with his ranged game and the Storm player might choose a defensive assist like Haggar to help counter rush-down tactics.

In a given game of MvC3, it's important to be able to change strategies on the fly. You might start the match with a “rush-down” approach, change to “keep-away” when the opponent starts “turtling”, then go back to a “rush-down” to finish off the match. Abstractly, we can look at MvC3 as a mixed strategy by assigning a probability to each of these three play styles. For example, lets consider two players in a hypothetical match. Player 1 chooses a rush-down heavy team mixed with a little turtling -- lets say 80% rush down, 0% keep away, and 20% turtling. Player 2 chooses a well balanced team, but leaning slightly towards the keep-away game – 30% rush-down, 40% keep-away, and 30% turtling. We can multiply these strategies with our pay-off matrix to find the expected outcome. In this case, the average pay-off is 3.8 for player 1 and 3.2 for player 2. Over the long run, we might expect player 1 to win roughly 54% of the time. By specializing in one strategy at the expense of others, player 1 has gained a slight advantage over player 2. However, player 1's strategy could also be foiled by a player that has chosen to focus on “turtling”. Consider a third player with a strategy of 0% rush-down, 40% keep-away, and 60% turtle. This player would have a 5.6 to 3.2 advantage over player 1, but be at a slight disadvantage to player two by a rate of 3 to 3.6.

# Metagaming

In the example above, we've seen how it's possible to adjust strategies to gain an advantage over a particular opponent. In the event that you know nothing about your opponent's strategy, your best bet (from a mathematical standpoint) is to play each strategy with equal probability. However, the pay-off from this particular strategy is that you'll break even – win 1/3 of the matches, lose 1/3 of the matches and tie 1/3 of the matches. In order to win with any consistency, it is necessary to predict which strategy your opponent will play. This is where metagaming comes in.

Metagaming is the art of stepping outside of the game and using information external to the game rules to optimize the potential pay-off. In MvC3, we might examine the frequency with which each character is played and keep track of trends in player strategy. If the majority of the population is predominantly playing one strategy, then it's possible build a counter-strategy that will result in a favorable outcome. For example, Sentinel tends to emerge as a high-frequency character in MvC3 online matches. Sentinel's strong keep-away game (high beam, low beam, rinse & repeat) tends to shutdown a large number of beginning players. In order to win against Sentinel, it's necessary to be able to close that distance and rush him down. A character like Wesker might be particularly well suited for this role.

The metagame of MvC3 is constantly changing. As new strategies become dominant, new counter strategies emerge. On occasion, one of these new counter strategies will become dominant and new counter strategies will will start to develop. Each individual player is an autonomous agent. That player makes his/her own decisions about how to play. However, this player is not alone and may face a diverse range of opponents, each with their own individual strategies. Depending on what types of opponents a player faces, that player can learn from those matches and adapt a new strategy when appropriate.

From a mathematical standpoint, the metagame in MvC3 is essentially a “complex system”. We have a network of independent players connected together by matches played online. The game itself is highly structured with a fixed set of rules, but when we look at the system as a whole it can exhibit a variety of unexpected behaviors. To look at this system from a mathematical viewpoint, we might take a modeling approach. We set up a simple model of the system, add some players and connections between them, then let the model run and see what kinds of properties emerge.

# Genetic Algorithms

One way that we might model this system is by using a genetic algorithm. A genetic algorithm is a programming paradigm based on evolution by natural selection. Natural selection dictates that the organisms that are best fitted for survival in a population are the ones that live to reproduce and pass their genes on to a new generation. In the context of this particular system, our environment is a population of players with varying strategies. Instead of genes, we have strategies employed by those players. If a player's strategy works relatively well against the population, that player will likely continue to use it. If a strategy doesn't work, it's back to training for a new one.

With this basic genetic algorithm, let's see what happens when we start with a small group of 5 players each playing a perfectly balanced game (1/3, 1/3, 1/3). After each play-off, the top 4 players keep their existing strategies and the loser goes back to the drawing board and chooses a new strategy at random. As we look at the changes in strategy over time, we can see that the top 4 players stay the same, generation after generation. We say that (1/3, 1/3, 1/3) is an “evolutionarily stable strategy”. As long as the majority of the population plays this strategy, no new strategy can take over the population. In gaming, this is not really a desirable thing to happen. The game isn't fun when every plays the same thing, and players generally refer to this as a “stale metagame”. It really shouldn't be that surprising that the system behaves like this, considering that (1/3, 1/3, 1/3) is the mathematically optimal strategy for this particular payoff matrix.

One of the interesting things about complex systems, is that you often see a high sensitivity to initial conditions. If we make a small change to the initial strategies in the previous example, say (.34, .33, .33) instead of (1/3, 1/3, 1/3), this increases the likeliness of a new strategy to infiltrate that elusive top four. There's an element of randomness as to when the new strategy will succeed, it could happen after the first generation or after the hundredth. Once it does, it starts to change the environment which allows other new strategies to succeed as well. In some sample runs of this population, only one or two of the original strategies were left after 10,000 generations – but there's a great deal of variance between trials. Playing a well balanced game is often a key feature of the new strategies, but might start to see a slight shift from “rush-down” to “turtle” emerging over time, countering the initial population's slight bias toward this strategy.

When MvC3 first came out, the metagame was largely dominated by a single character: Sentinel. Upon observing this, Capcom issued a patch reducing Sentinel's health. Some players criticized Capcom for this move, because it didn't change the gameplay mechanics that were being abused, but from our example here we can see how a small change can have large effects on the metagame. Overall, I think this was a pretty smart move by Capcom – it was just enough change to make the metagame interesting again.

The previous two examples have dealt with small populations that are mostly uniform to start with. In the real world of MvC3 online play, there are thousands of players with dramatically different strategies to start with. To attempt to model the MvC3 metagame, we need to look at larger player pools with a greater diversity of play-styles. To get a feel for this, let's look at a population of 20 random strategies, and replace the bottom 5 players with new strategies each round. With these changes, we see much more variance in the top players.

From one sample run with these conditions:

• The top strategy after the first generation was (0.54, 0.27, 0.19).
• The top strategy after 10 generations was (0.13, 0.81, 0.06).
• The top strategy after 100 generations was (0.69, 0.06, 0.24).
• The top strategy after 1,000 generations was (0.04, 0.81, 0.15).

There are many interesting observations to be made about the behavior of this model. First, we see that the metagame is much more dynamic when we start with random conditions instead of a uniform population. Balanced strategies tend to do well overall, but many of the top strategies are not necessarily balanced. Remember, its not the strategy alone that determines success, but the combination of the strategy and population. The fact that the top strategies after 10 and 1,000 generations are both “keep-away” heavy is a result of the population being “turtle” heavy during those particular generations. As the population changes, so do the winning strategies change. This ebb and flow from one strategy to another is what keeps the metagame interesting.

# Conclusions

I think there's a couple of important lessons to be learned here for people who are new to the fighting game genre. The first lesson is the importance of a balanced game. If everyone is playing a balanced game, then the only way to be successful to play a balanced game. The second lesson is to not underestimate “gimmick builds” – strategies that focus on maximizing a particular play style at the expense of other. When there is a tendency for the general population to play a certain way, the right counter strategy can be highly effective. The third lesson is to learn from your mistakes. If your team strategy isn't working, don't be afraid to mix it up. You might find a new strategy works better against the general population.

As a footnote, I'd like to point out that this model is a very simplified version of what goes on in MvC3 games. For an example of what some “real” MvC3 games look like, I'd recommend having a look at Andre vs Marn's First to Ten. As you watch, see if you can identify when each player is playing which strategy. Does the rush-down/keep-away/turtle model fit with actual fights? How does changing out Akuma for Sentinel change Marn's strategy? Is this change predicted by our model?

# Further Investigations

I've intentionally been a little vague with the definition of complex system, in part because most definitions are high level descriptions of behavior. Am I correct in the assertion that MvC3 single player is not a complex system, but the MvC3 multiplayer “metagame” is a complex system?

One of the things I find interesting about MvC is the assist system. In this system, its technically possible for a player to employ two different strategies simultaneously. How can we change our model to account for this?

One common practice for genetic algorithms is to mix the genes of successful players to create new players, rather than just randomly selecting a new strategy as done in this example. Typically this is done by using a “crossover”, which selects randomly selects genes from two parents. How does this change the results of the genetic algorithm?

Another way of looking at the players is to actually model each player as a program. This technique is often called genetic programming. What kind of programs do you think would be most successful?