Moving!

I suppose I should mention this here: I've restarted my blogging efforts, but under a new address. Please check out http://sanns-life.blogspot.com/ !

Weekly Review: "Handlebars" Music Video

I wasn't going to do back-to-back music videos, but this one really impressed me:



"Handlebars", by the Flobots. The tone is a little hip-hoppish for my taste, but it's a very poetic song and its well reinforced by the music video. The underlying message is "just because I can do something doesn't mean I should", and its satirically expressed through some very colorfully metaphors. For brownie points: the music video is actually a school project by a friend of the band. (I would have never guessed; it's quite well done.)

Focus Fire Stage 2: Playing with Fire

Now, to define a mathematical strategy for the Focus Fire game... As defined last time, there will only be two types of units in this game, and there will be nine units total per team. Since its an odd number, that means my team will be dominated by one type of unit--let's say Fire for the sake of discussion, because the exact inverse discussion would hold true if it was Ice.

Intuitively, I know all the Fire units will be most optimal attacking the same target. I also know that target should be an Ice unit (if any exist), because Fire has an attack bonus against Ice and Ice has an attack bonus against Fire. In other words, Ice opponents are both the most vulnerable and the most threatening. (This would be a little more complicated using the Paper-Rock-Scissors architecture where vulnerability and threat were divided between different units; perhaps I'll run that scenario for the next game.)

So, with the majority of the team--the Fire units--properly assigned, the only open question is: what do the minority? Do the remaining Ice units assist the Fire units so that the team maximizes its focus, or do they attack their own counterparts (enemy Fire units) so they gain their attack bonus and the team maximizes its gross damage? It's a simple binary decision, but I can't see a definite advantage to one or the other. Which has the best effectiveness? Does that depend upon team makeup at all?

Since it is only a binary decision and since it could possibly vary across teams, I'm going to make strategies for both options. Then, I'll program computer algorithms to play each option against the other across several different team permutations and see what happens. Hopefully, that should answer some questions!

Focus-Fire Stage 1: Whadda We Shoot?

As you may recall in Paper-Rock-Scissors, I made all the units attack all opponents simultameously. There's a big reason for this: the strategy of choosing which unit to attack is a major strategy in and of itself.

The Battle of Trafalgar was a naval battle between the French and the British during the Napoleonic Wars. It's significant because the British won the battle, even though the French had superior numbers. The clever British commander Admiral Lord Nelson decided to divide his fleet into two flanking forces and focus on sinking one ship instead of wounding several. This was contrary to conventional naval warfare. As a result, his ships were able to down French ships at a much quicker rate, which caused the French fleet's firepower to decrease exponentially while the British suffered only linear loses. Because of this unusual outcome, the Battle of Trafalgar is often used as a case-study for mathematical modeling military encounters.

Today, most gamers already know this strategy--if you "focus fire" your attacks on a single unit, you can decimate your opponents at an exponential rate. I wanted to incorporate this into Paper-Rock-Sciscors, but I still had the problem of which unit to attack. Should pure teams focus on attacking the units they are strongest against (agressive) or should they focus on the units that are strongest against them? Should the minorities in hybrid teams attack the same target as the majority, or should they play to their own optimal target? I didn't want to compound the experiments, so I made everyone attack everything. But now, I'm going to analyze those questions independantly.

The Game:
To simplify, let's define the RTS game to only have 2 classes--let's say, Fire and Ice. Each unit has equal effective against itself. However, Fire is twice as effective against Ice, and Ice is twice as effective against Fire. Two teams will face off, each with a combination of Fire and Ice that equals 9 total. The game will be: what is the most effective target solution for each of the nine units? Does this change as a function of team makeup, or is the best strategy universal?

Weekly Review: "Why Does My Heart Feel So Bad" Music Video

I feel a little bad putting this in because Moby is so mainstream and this is one of his more famous works. Still, I found out the other day that my self-proclaimed "techno-loving" friend didn't even know who Moby is, so maybe it this will still be new to someone.

"Why Does My Heart Feel So Bad" is one of those melancholy unresolving songs that most people would distainfully describe as "emo". Personally, though, I don't feel like it is being melancholy just for the sake of being melancholy--which I think is characteristic of emo--plus it's a very pretty song, so it doesn't phase me. The video component is also very clever--the innocent cartoon appearance masks the underlying tone, plus the character's expressions are very well done. His mouth isn't directly shown, so at times it looks like he is smiling and at other times it looks like he is frowning but you can never quit tell.

Cha-cha-changes...

A few changes in the works...

I'll be doing game-theory articles as a series of distinct stages from now on. Those stages will be:

1. Defining the problem and the associated rules


2. Estimating an effective set strategy for an antonymous player (e.g., a "bot")


3. Implementing the problem, rule set, and strategy into a model or simulation


4. Run the model/simulation and analyze the results


5. (Optional) Revise the strategy and rerun the results, if necessary

This should allow me to cover a topic better, as well as encourage me to take my time and do a good job.

Another change is how I do the labels. Labels let you automatically chain topics together. Up until now, I've been using them somewhat haphazardly, however going forward I intend to use them as a sort of archiving system. It's hard to describe write now because I don't have a lot of posts, but I think it will clear up as things go along.

I've also discovered how to schedule a post. For those of you using Blogger: it's a little tricky, because you need to log into the beta version of Blogger and enter your post in there. Once you do, though, you can schedule a "Post Date and time" under the options, and it will automatically post whenever you schedule it. I'm working on that so I can write a bunch at once and then schedule things to post in scheduled intervals.

Finally, I've been working on a new layout! Unfortunately, I don't have that layout done yet, but it is in the works! I was going to wait until it was finished before writing this, but I really don't want a reason to procrastinate on posting this. Especially since tomorrow is Wednesday, so tomorrow's post will be a review. But I already have another post game-theory post scheduled for Friday, and that will give me time to start write the following stages. Stay tuned!

Weekly Review: IrfanView Freeware

Whenever I am given a new computer, there's a few things I always do. I turn up the mouse speed and off that annoying auto-hide taskbar. I check to see what manufacturer-installed bloatware I can uninstall. I delete those annoying manufacturer-installed shortcuts on the desktop. I create a new folder entitled C:\Downloads to store all my Internet DLs. And I install IrfanView, graphics viewing program of the gods.

I was never really happy with my image viewing programs before I found IrfanView. They tended to take a while to load, consume a fair amount of disk space, only support a limited number files, and most of them were shareware so they would perpetually pester me to purchase them. Enter IrfanView. IrfanView is fast. In short, it is exactly everything that all those whiny freeware and bloatware Windows apps should be doing (IMHO). I cannot recommend it highly enough.

In game-theory related news: I've been meaning to get back on track to my original subject, but it's been tough. I was having trouble seeing how to expound on my last topic, and I had a second topic but I wasn't quite sure how to implement it. Luckily, though, I've thought of a third topic that I think will give some options to both the other two topics (as well as be interesting in and of itself). Stay tuned!

Weekly Review: Millennium Actress anime

Only the second week and already I almost dropped the ball! I was on my way to bed when I realized the date; I hadn't given the subject much thought, so I am just going to pick the last anime I've seen: Millennium Actress (a.k.a., Sennen Joyū). Millennium Actress is an animated movie directed by Satoshi Kon, whose made a name for himself through his other anime films (Perfect Blue, Tokyo Godfathers, and Paprika) and the anime series Paranoia Agent. All of these projects have received great critical appraisal with the exception of Paranoia Agent, which started off well but (IMHO) unraveled about halfway through due to a shallow underlying plot and its inability to develop character due to its own self-imposed format. But that's a tangent for another day...

MA is a story about a reculse former-actress who comes out of hiding to tell her life story for a documentary. In her retelling, she begins to "act out" her experiences for the two-man film crew, and the viewer (as well as the crew, for comedic relief) begin to see the retelling as a sort of "live" flashback. Kon compounds this effect by cleverly making her real life parallel some of the plots she's acted out in movies, though, and the two are blended together for the movie in such a way that the viewer is often left guessing as to which elements of the flashbacks are from her work and which are from her real life. It's a very similar surreal experience similar to that of Perfect Blue and Paprika. However, unlike the latter two movies, the former doesn't have the level of violence or life-threatening urgency. MA is a very peaceful (although still eventful and dramatic) watch.

I would highly recommend this one, especially to anyone who enjoys a more sophisticate tone. I can't really think of anything negative to say about it, other than perhaps that it requires undivided attention to enjoy (because of the details in the story) and that it lacks the action and violence some people expect from anime (no giant robots!).

Oh, and in case anyone was wondering: the sworeness from the paint ball experience has gone away for the most part. However, my bicep now looks someone held it up to a belt sander. It's funny sometimes how the body parts that hurt the most look fine and the parts that barely hurt look like they need a trip to the ER.

Learning to Play Paint Ball

No major post this weekend. I was out with my two young cousins in San Antonio. They took me out paint-balling on Sunday; it was an interesting experience. I had been twice before, but both times were with relatively inexperienced players using low-end guns. Yesterday, I played mostly against experienced players using mid-range guns. It was definitely an experience that I will not soon forget.


One of the things that struck me as ironic: they make a point of banning any guns that are automatic (i.e., guns that fire multiple rounds when the user presses & holds the trigger). However, manufacturers design the better paint-ball guns to have over sized, hair-sensitive triggers. As a result, users can fire several rounds-per-second even on a semi-automatic weapon just by strumming their fingers on the trigger. It's a technique referred to as "walking the trigger" in PB lingo. Here's an example:


Granted, this is a high-end gun, but I don't think the rate-of-fire drops significantly. That's why the grouping on my arm is so tight--my attacker had fired that many additional rounds at my moving body before he could react to seeing the first round hit. Meanwhile, I am shooting as fast as I can with one finger--maybe a few rounds a second--with much less range and accuracy.

Technical disadvantages aside, I still didn't perform too well. All courses had set boundaries with bunkers scattered throughout. There are two popular strategies: either push up subsequent bunkers and try to flank your opponent, or keep range and take multiple shots from a safe distance. Even with my rental gun, the idea of "wasting paint" in the backfield didn't appeal to me--I'm more of a "flank" guy, so that's what I did. The problem is, the experienced players expect a flank, so they keep a clear line of fire down both boundary lines. Most of the time, I would get pegged while trying to running along the boundary lines up to the next bunker. If I had it to do over again, I would still try to flank, but I would do so using slightly-inside routes to avoid being so predictable.

For now, though, I'm just waiting for these bruises to go away. :-P

Weekly Review: "Insomnia Olympics" Music Video

So, my original goal with this blog was to write almost exclusively articles pertaining to gaming and game development and to do so at least weekly. So far, I've done a terrible job at that--I underestimate how long it will take me to make a post, I generate extremely long posts, and my personal disparities at time management has resulted in large gaps between posts. To address this, I'm going to try to make a quasi-random review of some obscure item I've discovered. Hopefully this will encourage me to be a little more responsible in my posting as well as provide some more interesting (albeit off-topic) material to readers.

Today, I'm reviewing a music video, "Insomnia Olympics" by Blockhead. The song alone is very impressive--it's a techno blend of a horn section, piano, and a slow-but-strong drum beat that just sounds appropriate for a song with this title. But video is what makes it truely amazing. The footage is in black&white, and it features a lone man in a small room who is dealing with his insomnia--trying to read, trying to sleep, flicking playing cards around aimlessly, etc. It's very captivating.



I'm experimenting here with the embedded youtube like; I hope it works...

Disney World: Engineering Family Amusement

My family planned a vacation to Walt Disney World last week, and I was able to tag along. I'd only been to Disney World once before; I was at an age where I was old enough to know all the characters where people in costumes but not old enough to care. My goal for this trip was to get a picture taken with a Disney princess. Unfortunately, I did not achieve that goal; however, I did come to realize many of the clever details engineered into the amusement parks that I had previously overlooked.

Most people think of Disney in one of two ways: either they are some super-benevolent caring entity that can be trusted like a person, or they are an evil cold-hearted corporation that is only concerned with raising their stock price. I think of them more as a combination of those two ideas: a successful company in the market of family entertainment that is neither inherently good nor bad. They have become extremely efficient in providing family entertainment using several mediums over the years, and Disney World is their flagship enterprise. It has been optimized to maximize individuals' entertainment experience while minimizing cost. Thought has been put into practically every detail. The employees will offer assistance to any guest with a map open--even if they are otherwise preoccupied with collecting garbage or transporting merchandise. The parking lot markers have redundancy--each lane is associated with both a number and a character, but the numbers do not reset between characters so even if only one only remembers one parameter, one still has an idea where their car is. And careful detail is put into every square foot of the park: from the waiting lines to the walkways to the

The thing that amazed me the most was the actual layout of the parks. Last time I went, the Magic Kingdom (the central park) was very established, EPCOT had been around for a while but didn't have many attractions, and MGM/Hollywood Studios was still relatively new. Since then, a new park (Animal Kingdom) was constructed and both EPCOT and MGM/Hollywood Studies were improved to be more like MK.

Here's a map of Magic Kingdom:

As you can see, there is only one entrance/exit to the park (the Southern-most point) and a giant landmark (Cinderella Castle) in the middle of the park. Roads follows a basic "spoke" pattern, radiating out from the central landmark. This makes it easy to keep your orientation, as you can also orient yourself towards the castle. The parks are also divided into themed "lands". The first land connects the entrance to the central point, and it doesn't have any dedicated attractions (although it does have some roaming performers and plenty of souvenir shops). This gives visitors a majestic entrance, but encourages them to quickly spread out. Another land is devoted towards young children's' attractions to minimize traveling, but the other lands are very diverse to encourage traveling around. Any land will have at most two "major" attractions, and the park has several "major" attractions combined with various shows performed repeatedly during peak hours.

All four parks follow this basic formula. Each park and each "land" has a unique theme, but care is made so that each park has some things to interest visitors of any age or taste. The closest exception is EPCOT, which was originally constructed as more of an informational showcase than an amusement park. This has been addressed a lot, though: the park has been expanded to make Spaceship Earth closer to the center of the park and several attractions such as "Test Track" and "Soarin'" have been added to make it more appealing towards a younger crowd.

Overall, I must say I'm extremely impressed with Disney now. They've really refined their processes and now produce a quality product. I'm inclined to see if I can find a book about Disney to see in better detail some of the techniques they use; I think it would be insightful and fascinating.

Deadliest Catch Flash Game

For those of you who regularly read Penny-Arcade.com, you probably already know this. (And for those of you who don't...well, you probably should.)

Discovery has released a Flash game based around their popular series Deadliest Catch. The series is a documentary-style television show that chronicals New England lobster fishermen, and the game allows players to command their own ship and crew for one 120-hour season and try to maximize their profits.

The game is available at http://dsc.discovery.com/fansites/deadliestcatch/game/game.html

It's pretty clever marketting strategy (Season 4 starts next month), but the game itself is also fairly entertaining. Players are limited to 120 hours, 1 ship, 4 crew members, and a $250,000 budget; the trick is to discover how to maximize these parameters to get the most profit. A bigger ship can deploy more traps simultameously, but it will also move between locations slower. A more experienced crew will be able to accomplish tasks more quickly, but they will also demand a larger salary. Assigning multiple crew members to the same task will also allow them to complete it more quickly, but each crew member has a finite amount of stamina that can only be replenished by allowing them to rest.

It's fun to play around with various strategies to see if you can improve your profits. If you want my advice for a first season:

1. Buy Boat 4 with all the class B ammenities
2. Hire Charlie, Rob, Lonnie, and Dan
3. Assign everyone to bait traps and pick a location to fish about 6 hours away. Hit "Go", and the boat will start moving while the fishermen bait.
4. Pick 2 crew members (preferably 1 greenhorn and 1 deckhand) to drop traps in the new location while the other 2 rest
5. Move the boat to an adjacent location, and then drop additional traps there. If any problems arise, try to fix them while en-route so that you don't slow down your fishing.
6. Repeat steps 4-5 until you have 4 sets of traps out.
7. Move back to the location of oldests trap. Locate them and haul them on-board.
8. Repeat step 7 for all 4 sets of traps.
9. Lay out all 4 sets of traps again in new locations.

Using this strategy, I can net about $1,000,000 profit each season. I've experiemented with a few parameters, but usually the results are about the same. Right now, the high scores for the game are all above $2,000,000--I have no idea how you score that well.

A Good Anime Site

I'd like to take a moment to promote a new anime site I've been using lately: http://www.anime-planet.com/. There are a lot of anime-themed websites these days, and most of them offer the same features: a regularly-updated database of anime series, interactive forums, and reviews of some of the series. There are a three aspects about this particular site, however, that really differentiate it:

1. Recommendations
2. Dynamic profiles
3. An active community

Each anime entry has numerous "recommendations" for similar animes. This is because users can add recommendations to the database entry for other series with similar style / plot / genre / etc. For instance, several users have made recommendations for Vandread under the entry for Martian Successor Nadesico. These recommendations are tallied and then listed in order of popularity. The results are extremely helpful when trying to discover a new anime to watch because you can base your search off anime you've already enjoyed. Users can also create profiles and log which shows they've watched, what they thought about them on a 5-point scale, and add their own review. As a result, the entire site is a lot more interactive than typical sites, which has cultured an active community. The site even tracks the total run-time for each of the series and then calculates "Life Spent on Anime" for each profile. (I am currently at just over 2 weeks, FYI.) The results are even dynamically rendered into a JPG signature. Here's mine:

If you're in to anime at all, I highly recommend you check it out!

Paper-Rock-Scissors 2: The Cost of Immunity

So, last time I created a mock RTS game with three basic units and posed some questions about which compositions of units would be most effective and least effective. I've run some simulations since then based off the following rules:

1. All units will start a battle with 1.00 "health".


2. Attacks will be turn-based.


3. Each turn, every unit that started the round with positive health will deal X/100 damage to every enemy unit with positive health. X is the respective combat effectiveness against that particular unit.


4. All attacks will affect all living unit opponents simultaneously (although the exact damage to each individual opponent will vary based on effectiveness). In terms of gaming jargon, this could be considered "Area of Effect" attacks. This is to remove the complication of sequencing from the simulations.


5. If a unit receives a enough damage in a particular round to reduce its health from positive to non-positive, it will still attack during that round. This is to remove the complication of "first strike" from the simulations.


6. Once all a team's units have their health reduced to non-positive values, it will be unable to attack and deemed the losing team.


7. Once the opposing team loses, the winning team will be evaluated based on the sum of the health of all its surviving units.


8. If both teams lose the final members on the same round, the match is deemed a draw. By definition, all "mirror matches" (when two teams of identical compositions face off) will be draws.

For a team of 9 and these 3 basic units, there are 55 permutations for teams. To further simplify things, I only considered 10 teams: the "pure" teams (9 of the same unit), "combo" teams (6 of one unit and 3 of another), and a "hybrid" team (exactly 3 of each unit). That reduces the number of permutations to 10, and it provides an evenly distributed subset. Here are the results of those 10 teams fighting against each other in a table format with the total wins tallied on the right. I also took note of what I considered "decisive wins", where the winning team retained at least 20% of its units' net health (1.80). I think this is a better graphical representation of these results, though:

There's a few things to note about the results of this model. First off, the hybrid team is extremely effective--it received 7 wins, 3 draws, and 0 losses. However, it's also worth noting that each win by an extremely small margin--it only received 1 decisive win, and that was against the pure melee build (all 3 flyers were unscathed). In other words, its a very low-risk/low-gain team. Second, melee-based teams perform very poorly in general. Unlike the other classes which are at a tactical disadvantage fighting respective their weakness, melee is totally ineffective against its weakness of flying units. Even a single flying unit will ultimately destroy any number of melee units. Third, the teams built around ranged and flying units are extremely effective--they have a winning record, they have a large number of decisive wins, and the give up a low number of decisive wins to their opponents.

In retrospect, I think I made an error of judgement when I considered my combat effectiveness table to be zero-sum. Rather than adding the offensive and subtracting the defensive numbers, I think I should have averaged the fraction of offense divided by defense. In other words: melee would have a total effectivenesses of 1/1, 2/1, and 0/1; ranged would have a total effectivenesses of 1/2, 1/1, and 2/1; flying would have a total effectivenesses 1/0, 1/2, and 2/2. Obviously, these numbers will never be totally balanced because X/0 will always be infinite. I think though that if the effectiveness of melee against ranged was increased and/or the effectiveness of flyers against melee was decreased, the results would be a lot more diverse rather than having some teams blatantly more powerful than others.

In published RTS games, immunities such as melee vs flyer are very common. However, units that possess immunities are usually compromised so that melee units are not at a distinct disadvantage--e.g., the flying units will be more difficult to produce or they will have limited use in combat.

Paper-Rock-Scissors: Balancing in RTS Games

Some of my favorite games are Real-Time Strategy (RTS) games such as StarCraft, Command & Conquer, and Sacrifice. One of the reasons is because RTSs give players the opportunity to "outsmart" their opponents--particular strategies have strengths and weaknesses against others, and if one player can adapt quicker than his opponent, it gives him a definite advantage.

For example, consider the following. Let's say there's a game with three basic types of units: melee, ranged, and flying. The flying units are immune to all melee attacks, but they are weakly armored so they aren't effective against ranged attacks. The ranged units deal additional damage to the flyers, but they also take additional damage from melee attacks. And of course, the melee units have an advantage against ranged but totally ineffective against flying units. In other words, its a basic Paper-Rock-Scissors hierachy.

Let's try to quantify this system in terms of relative effectiveness. For instance, let's say a single melee fighter will have an effectiveness of 1.0 when fighting another melee unit, 2.0 when fighting against a ranged unit, and 0.0 when fighting against a flying unit. That means that one melee unit will be able to defeat a ranged unit in the same amount of time it would take two ranged units and double the time it would take a single ranged unit. No amount of time or additional melee units will be able to overcome a flying unit.

Combat Effectiveness

Unit	vs Melee	vs Ranged	vs Flying
Melee	+1/-1	+2/-1	+0/-1
Ranged	+1/-2	+1/-1	+2/-1
Flying	+1/-0	+1/-2	+2/-2

In this table, the positive number represents the offensive effectiveness and the negative number represents the defensive effectiveness (i.e, how effective the opposing unit's offense is). I chose these particular numbers to try to make each unit's total effectiveness zero-sum. But the question is, are these particular numbers good ones? The goal is to make all units uniformally balanced. Otherwise, certain strategies will be inherently more successful and players will be encouraged to use the strengths of these strategies rather than trying to adapt to his opponents' specific weaknesses.

So the question is, if someone where to create a team of 9 units and play an opponent's unknown team of 9 units, what would his best lineup be? Is there a dominant team that is much more successful than the others? Are there some lineups that are distinctly weak? If so, what could be done to this effectiveness table to make the results more diverse? I've already simulated a lot of possible scenarios, but I'll keep the results saved for my next post.

My first post

This is my first post in my personal blog. For the time being, I am posting just for the sake of creating a post, but in the future I intend to make most of my articles contain some mathematical slant on video gaming. Just so that this post isn't completely void of content, though, I'm going to link two articles that I've previously written for the (currently inactive) satirical gaming site, NotAddicted.com. NotAddicted.com would regularly publish game-related articles--mostly targetted towards MMORPGs and their associated culture--with a humorous slant.

"How to Quit WoW, IN STYLE"
http://www.notaddicted.com/forums/showthread.php?t=759

"Have you killed a Blood Elf Paladin Today?"
http://www.notaddicted.com/forums/showthread.php?t=995