Infinity: Mangling the Math

This is the story of a premature panic, and a cautionary tale about how you should take the time to understand even accurate information. It starts almost a week ago…

One of our playtesters — John — is a programmer at an absurdly prominent software company. One day he sends me an email, telling me he’s written an Infinity combat simulator in C#.

Input Attack and Defense for two characters, and the program will roll the dice for attack, keep track of Wounds and Wound penalties, and simulate the fight. Then it does this 100,000 times. After, it gives you victory percentage, average length of combat, and damage per round.

My response was precisely this:

That is, seriously, so cool. And now, a Japanese emoticon: 

b ^.^ d

This aid is a tremendous boon to playtesting. It means I can skip all the mundane PvP combats, and concentrate on specific scenarios that test parts of the rules other than “Wham! Wham!” But, there was a problem.

The next day, John sent me the first table of results (using Attack/Defense figures I suggested). The very first result listed the length of combat for that A/D combination…

203 rounds.



At that point, my brain shut down and panic set in. 200 rounds? How the hell can a combat between two identical characters with equal Attack and Defense last 200 rounds? That’s a huge hole! That’s a wreck-the-game’s-playability hole. And how did I miss it?

So, John sent in another batch of results, and I looked those over. Then he called up and we spent his lunch hour talking over the various rules changes and how those might effect the game. At this point, I was still in panic mode.

The next day, I decided to try a more comprehensive test. I came up with three scenarios, all involving average characters, in a fist fight, a gun fight, and a knife fight. In the back of my mind, though, was the panic:

200 rounds? That’s insane! How did I miss that? How the hell do I fix that without wrecking the core mechanic of the entire system?

So, I wrote out the unarmed combat bout, which has evenly matched characters. And I went back to the results file, and this is what I found:

                Adam       Bob
Attack:         15         15
Defense:        20         20
Win %:          49.89%     50.11%
Avg DPR:        0.045      0.045
Average # of rounds: 202.7314

Do you see the error I made? I misread the table. In my mind, this was 20 Attack, 20 Defense for each character. Instead, it was 15 Attack and 20 Defense. As soon as I understood that, my panic faded away and I began to really analyze the data: what does this mean, in concrete terms?

15 Attack vs. 20 Defense represents two absurdly well-armored people with pretty weak weapons. In other words, a duel between two Abrams tanks, armed only with Nerf dart guns.

Of course such a combat is going to take forever. It should. It’s two guys who only hurt each other 1 out of 10 rounds (and then only for 1-4 Wounds). And, instead of using a better weapon, switching to a different attack, changing tactics, using Combat Interactions, calling for reinforcements, fleeing, or anything else, they just continue wailing away at each other.

The length of the combat matches the stupidity of the participants. It is, as I’d suggested in the call, a corner case.

But what about more reasonable situations? Let’s take the sample three I suggested.

Common situation: Two average people with minimal training in a gun fight, knife fight, and fist fight.

Average people, pistols:

Dex 8 (+2), End 8 (+2). Dodge 1 +2 = 3, firearms 1 +2 = 3. Pistol DR 14 (.38 Revolver).

Attack: 17
Defense: 11

How long does the combat last?

                Adam       Bob
Attack:         26         26
Defense:        20         20
Win %:          49.94%     50.06%
Avg DPR:        3.7        3.7
Average # of rounds: 3.32583

Combat lasts 4 Rounds. That seems pretty reasonable, and logical (given how much damage .38 pistols do).

Average people, knife fight:

Dex 8 (+2), Str 8 (+2), End 8 (+2). Melee weapons 1 +2 = 3. Knife (Str+1), DR = 9 (8 +1).

Attack: 12
Defense: 11

                Adam       Bob
Attack:         21         21
Defense:        20         20
Win %:          49.83%     50.17%
Avg DPR:        1.1        1.1
Average # of rounds: 10.31562

A little longer, but pretty reasonable, especially for two equally matched combatants. Those kinds of fights are the long-running, epic duels of the cinema. Bond and the fencing master in Die Another Day, as an example, or the several duels in Disney’s The Three Musketeers.

Average people, fist fight:

Dex 8 (+2), Str 8 (+2), End 8 (+2). Unarmed combat 1 +2 = 3. Fists DR 8.

Attack: 11
Defense: 11

                Adam       Bob
Attack:         20         20
Defense:        20         20
Win %:          50.20%     49.80 %
Avg DPR:        0.76       0.75
Average # of rounds: 14.44288

14 rounds is a little long, but not unreasonable (especially for two barely trained fighters wailing away). And that’s the worst-case scenario for typical combats.

That is, 14, 10, and 4 are not the “average” length of combats. They’re the upper limit on combat length for 1 on 1 fights. Every other combat that isn’t “Abrams with nerf guns” will be shorter. And 14 rounds is pretty good.

After I realized this, the panic subsided and I could look at the numbers and analyze the entire situation. My conclusions:

  1. Don’t jump to conclusions. Even accurate data can be misread. Take the time to understand the data, before you act on it.
  2. The system holds up well. At 20 Wounds, combat lasts a reasonable amount of time. More, the length of combat is directly related to perceptible and logical differences. For example, fists don’t do as much damage as knives, so those combats last longer. That’s how it should be.
  3. The system covers a hole that comes up in many systems: no matter the skills, weapons, or Attributes of the characters involved, any attack can miss, hit for no damage, or do a varying amount of damage. More, which of the three happens is directly related to how well you did. A better attack does more damage than a worse attack.
  4. 20 Wounds for everyone was absolutely the right decision. The reason 17 Attack vs. 11 Defense is exactly the same as 26 Attack vs 20 Defense is because of this. With 20 Wounds for everybody, the odds and mechanics can scale indefinitely. 15 Attack vs 10 Defense is exactly the same as 55 Attack vs. 50 Defense, and 105 Attack vs. 100 Defense. The system is playable at low levels, high levels, and insanely high levels without needing patches or odd rules. That’s a tremendous strength.
  5. As a designer, I actually have a good grasp on the odds of the system. Part of what caused the panic was a completely unforeseen result. Once I understood the real math (see #1), I realized that the above round lengths for pistol fights, knife fights, and fist fights were all roughly what I would have predicted. The realization reassured me that I wasn’t as incompetent as I’d thought.
  6. With two combatants, and allowing only for attacks and passive defenses, there are 4 variables: Attack(a), Attack(b), Defense(a), and Defense(b). If you were to create a matrix of where each of these 4 variables were independently varied, to map out the probabilities and round length, it’d be a 4-dimensional probability map. Yeah, RPG’s are complicated.

Now that the panic’s passed, and I can look at the numbers straight, I’m reassured. It looks solid enough to take to testing.

Big thanks to John for doing some brutal (virtual) playtesting, and for serving as a sounding board. (Also, people should note that John’s data was (AFAICT) utterly accurate. The error was one of interpretation, not computation.)

Post written under the influence of: AC/DC, Survivor, Simon & Garfunkel, Sheena Easton, Falco, Kid Rock, Run-D.M.C., Fastball, Bush, Falco, Styx, Puff Daddy, & Delerium. (Individual tracks, in that order.)

Cinematic Indulgences: What’s the Deal With Dredd?

“Talky” isn’t his strong suit.

The Walking Dead is, I argued, talky. And whiny. Exemplified by Dale and the interminable argument about whether to spare a self-admitted rapist and would-be murderer, who’s part of a gang of murderers, thieves, and rapists.

I don’t want to discuss the argument itself — mostly because it’s so stupid (hint: you shoot murdering rapists!) — but the talkiness. It’s a symbol not only of pretentiousness, but of artlessness.

Part of a review of Dredd from another blog (content warning: Right-Wing blog):

[A]re these guys completely unfamiliar with filmmaking for the past 20 years? Don’t they know that we’re supposed to have faked-up conflict between the characters?

[…] Why, this Dredd and Anderson sort of confront their job (and later, their dangerous predicament) with something that almost looks like trained professional detachment.

You can’t have a movie about characters with trained professional detachment. You need them SHOUTING THINGS AT EACH OTHER and SCREAMING HOW MUCH THEY HATE THE BAD GUYS […]

Yup. Drama requires conflict, and conflict (in too many shows) involves people arguing. Interminably. In self-serious tones. About Deep Serious Issues.

Dramatic art, that is fiction (as opposed to painting), deals with themes: the subject beneath the action. A conversation is never just a conversation, it’s always about something else. Themes have to be presented with subtlety, they’re about subtext, not text.

(Example: The story “Hills Like White Elephants” by Ernest Hemingway is entirely about subtext. Everything that happens seems to be banal and boring, until you get the subtext.)

But pretentious art is all about the text. Your main goal is for people to KNOW you’re all Deep and Serious and Insightful, so the audience has to Get It. And the only way to ensure they Get It is to hit them over the head with your Serious and Important Message.

It’s artless. It’s ham-handed. It’s crude and obvious and an embarrassment to good fiction. And much of the talking in The Walking Dead is ham-handed and obvious. Which is boring and tedious, especially when stretched to ten or fifteen minutes.

Dredd isn’t a perfect movie, but it’s actually a damn good action movie (if graphically violent). And it treats its audience with some respect. All of the moments of thematic resonance are implicit, not explicit.

Thus, it sneaks in a lot of insightful moments that make the characters more human, and hence more interesting. By not striving for Importance, it has the room to be insightful.

[Ob. Gaming Reference: Are you kidding me? This is Dredd. It has psionics, cyberware, and guns that fire phosphorous rounds. Spec-Fic is always on topic for a gaming blog.]

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Cinematic Indulgences: Missing the Point of Your Own Premise

The Devil Wears Prada
Devilish fashion.

So, let’s talk The Devil Wears Prada.

(No, I’m not kidding. Yes, I actually like the movie. I also like Saw, the JJ Abrams Star Trek, The Replacements, Mary Poppins, and most Pixar movies. Deal, alright?)

In Prada, a fresh-faced college journalism graduate, Andrea Sachs (played by Anne Hathaway), tries to get jobs at a number of news magazines, and fails. Finally she is hired as a personal assistant (“1st Assistant”) by the notoriously demanding Miranda Priestly, played by Meryl Streep, the editor of the landmark fashion industry magazine Runway. Sachs is told that if she works for Priestly for a year, she can get a job at any media organization in the country.

Sachs know nothing of fashion, and has mild contempt for the industry. She considers it beneath her, but choses to work at Runway because she want to succeed at magazine writing. “A million girls would die to work there” (as several people note), but Sachs only deigns to work there.

So, the stakes: Work for Priestly for a year, in an industry you have contempt for, in return for which you can get hired at any news organization in the country and begin to report on “real news”.

The obstacles: Miranda Priestly is the ultimate “drop them into the deep end” boss. She has exacting standards and is utterly, maybe insanely, demanding. Working for her is a brutal bootcamp. (Which is why people are willing to hire assistants who survive. “If you can make it there, you can make it anywhere.”)

[Ob. gaming reference: Stories, and games, are all about high stakes and obstacles to those stakes. Characters — and by extension players — have to earn success, or the game’s no fun. See here for more.]

The stakes and the obstacles provide the fodder for perfect dramatic conflict. So what went wrong?

Spoilers below! Ye be warned.

For one, the filmmakers chumped out. (Fine, the chump-out was in the original novel.)

What do I mean? Writers force characters to make tough choices: Do I tell my boss about my coworker embezzling funds, or do I stay loyal to my friend (and become complicit in his thievery)?

Characters need to make tough choices, it’s where they reveal who they really are. (And not in interminable talky sequences, unlike Harry Potter and The Deathly Hallows.) Writers chump out when they take the burden of choice off their character’s shoulders, when convenient things happen that just magically make the problem go away.

(Dexter is particularly bad about this. How many times has Dexter been close to being unmasked, only to have someone else step in and clean up his problem? All the way back to Doakes, at least.)

Sachs excels at her job. She achieves the impossible. At a critical juncture, Priestly demands the unpublished 7th Harry Potter manuscript for her daughters, and expects Sachs to get it while at the same time running about town to get a steak from a restaurant that won’t be open for another hour. And Sachs gets it. Has it bound. And makes sure it’s on the train with the two little girls.

Sachs does the impossible.

At another point Sachs is unexpectedly asked to assist Priestly at a party, by memorizing the faces and bios of dozens of guests. The other assistant Emily, a girl who’s been continuously abusive of Sachs, had weeks to prepare. Sachs had hours. Yet, at the party, Sachs comes through in a clinch and the other girl chokes.

As a result, Priestly decides to take Sachs to Paris for the annual fashion shows, because Sachs is the best candidate for the job. This is the (sorta) tough choice: go to Paris, because it’s what the job requires, or quit, forfeiting all the effort put into an impossibly tough job, allowing Emily to go in your place.

This is, in actuality, a silly little conundrum. It’s based solely around guilt. “Oh noes, I’m really good at an impossibly tough job, and this other girl is mediocre! How can I let myself succeed? Oh noes!”

Yet the writers don’t have the balls to allow Sachs to make the choice. Emily gets hit by a car, breaks her leg, and can’t physically attend the shows and parties in France. Sachs is relieved of the burden of having to choose.

But its worse than that. Despite the fact that Sachs had no choice to make, the writers try to play it off like she did. At the climax of the movie, Sachs has a moral crisis because Priestly protects herself from being fired, via politicking and, in the process, prevents one of her underlings (Nigel) from being hired by another company.

Oh, it’s so terrible! Oh, it’s so bad!

Sachs says “I could never do what you did to Nigel.”

Priestly responds, “You already did, to Emily.”

Bwuh? No, she didn’t. Emily broke her leg. Sachs didn’t stab her in the back, Emily was in the hospital. She couldn’t do the job, Sachs was just stepping in.

I wish Sachs had been forced to make the tough choice, but you writers chumped the hell out. You took the decision off her shoulders, and as a result she has is not complicit in the situation. Yet both Priestly and Sachs act like she was. Achiever’s guilt.

It’s maddening. It completely robs the climax of any real emotional or moral insight and impact. Sachs feels guilty, because of an accident she had nothing to do with, and as a result leaves Priestly without an assistant in the middle of Paris Fashion Week. That’s not a bold statement of personal empowerment, it’s a foolish little decision, made by a silly, stupid little girl. (Which Sachs isn’t.)

This movie could have been great. It could have been a compelling story of how one person survived an impossible situation, thrived, and as a result succeeded in her industry.

I’m not a feminist, but I believe that both men and women both have the strength to endure and succeed. The more painful the circumstances they endure, the more incredible and praiseworthy their success. And movies which illustrate this have the potential to be meaningful, because they illustrate deep truth:

People must sacrifice to succeed.

This is a truth as old as humanity. And Sachs sacrificed and succeeded.

And what does she get from it? Her narcissistic friends constantly guilt trip her about not spending time with them, because she’s doing a tough job for one year. Sachs gives them $1900 Marc Jacobs purses and $1100 Bang and Olufsen phones as gifts, and still they complain. Sachs misses her boyfriend’s birthday party, because of another Priestly demand, and her boyfriend guilt trips her, like she’s doing a bad thing by ensuring her future. And Sachs guilt trips herself, about the Emily situation.

And at the end of the movie she comes crawling back to the boyfriend, saying she’s wrong. By then Sachs has excelled in the job, earning the respect of everyone around her (Gisele Bündchen complimenting her on her fashion sense), including her insanely demanding, impossible-to-please boss. So why are we, as an audience meant to think that’s a bad thing?

Why does she have to apologize for excelling? Excellence is never something one should apologize for.

Yet a strong, capable, confident woman, who did the impossible, is forced by the script to apologize to the weak, effeminate boyfriend for being successful. This is chick lit, written by a wealthy East Coast liberal woman, trading in the ugliest stereotypes of women.

And you know what? Sachs wasn’t wrong. At the end of the movie, she’s interviewing for a news magazine, the dream job she came to New York to find, and she gets it. Because of Miranda Priestly.

The editor says he called Priestly, who said “Of all the assistants she’d had, you were the biggest disappointment, and if I don’t hire you, I’m an idiot. You must have done something right.”

Sachs sacrificed, and succeeded because of that sacrifice. She isn’t a silly little girl, as much as the script tries to portray her as one.

Life is tough. Success takes hard work. This is a truth the movie could have illustrated vividly. But the writers missed the point of their own premise.

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Cinematic Indulgences: What’s the Deal With The Walking Dead?

Atlanta, after.

I wanted to love this series. I love zombie flicks, and have for almost 30 years. But no matter how much I’ve wanted to love The Walking Dead, something’s always felt off.

I finally figured out what it is: the show is pretentious. That’s its Achilles Heel.

My short definition of pretension is: the affectation of intellectual, moral, or artistic profundity. Pretension is more concerned with trying to impress others than striving to do your best (which may eventually impress others without you worrying over it).

The Walking Dead isn’t content with being a really good zombie story with solid characterization. It has to Be Important Art, like it was Shakespeare or something.

People — justly — complained about the second season being all talky. Well, all that talk mostly sprang from an effort to make it Deep and Meaningful — Dramatic characters standing around discussing Dramatic and Important issues. But the material just didn’t support that level of self-seriousness.

Frankly, that kind of insight only comes from a deep understanding of human nature, wisdom so deeply ingrained it’s just part of the writer or showrunner, so it comes out in their material without them even trying. If you’re not a deep person, if your thinking is limited to cliches and ideological cant, then you’re not going to produce anything deep and meaningful.

And trying to force meaning into cliche causes pretentiousness. Desperately aware that you’re not that insightful, you try and fake it. You lie to yourself, till you almost believe it, then you attack those who speak the truth: you’ve made a competent zombie flick, but it’s no Richard III.

Why can’t people be satisfied with making the best goddamn <whatever> they can? The best goddamn pop song. The best goddamn zombie flick. The best goddamn roleplaying game.

Why? Because that’s not good enough. You’re not an Important Artiste, making a Grand and Serious Statement. And you desperately need to be Important.

The urge to be Important and Honored has ruined more good pop culture than Uwe Boll.

Pretentiousness is always based in contempt for the art form or genre, because (deep down) you think you’re not Important enough by being a pop lyricist, a zombie filmmaker, or a game designer. You want to be better than that, Be Taken Seriously, to impress other people, to be Someone Important, so you try and force the art form to be something different.

You stick in heavy-handed allegories. You trot out well-worn cliches as meaningful insights. You create cardboard-thin characters who exist only to illustrate some political point.

Which makes for shitty art. And that’s exactly what’s hampered a series that flirts with legendary greatness, as a zombie flick.

I say this as a person who’s paid for all 3 Walking Dead seasons on iTunes, and watched each one multiple times (7 times for the first season). I’ve seen the series, and its pretensions are what dooms it to mediocrity.

If it embraced the material, and focused on being a great zombie flick, then dramatic and moving moments would organically arise. Ironically, by trying to be Important, it makes itself mediocre.

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[pt. 5]

Understanding your own system is a key step of game design. Not just how you intend it to be played, but how real people “in-the-wild” actually play it. Too much complexity makes it difficult to understand, and thus difficult to precisely craft your mechanics.

As an indirect medium, you either have to keep the game simple enough that you can predict what can be done (eliminate every single option but A or B and you can be pretty confident that players will choose A or B about 60% of the time), build on existing mechanics with known effects (as with much of the OSR), or you need to be willing to invest in sufficient playtesting to explore and understand the complexities of your system.

The complexity and indirection of RPG’s are why playtesting is so important, and especially playtesting with a variety of players, and without personal intervention from the designer. It isn’t just to troubleshoot rulebook design, nor is it solely for balance purposes.

Emergent play comes from the players and GM’s interacting with the material, and it is shaped by the gestalt (agglomerated influence) of your rules. This is tricky to predict, and hard to control. In most cases, you just have to release it and see how people play it.

The emergent gamestyle will never exactly match the designer’s expectations. As GM’s, we can’t even predict what five close friends of ours will do in a module, much less could we predict what five thousand complete strangers will do with our game.

This is a good thing. So long as the designer did a competent job, the people playing the game will find their own fun. (If they don’t, or can’t, that means the designer dropped the ball.)

Find out what people liked about your game, where their fun lies, and enhance it. Don’t obsess that they’re using your deeply personal game of personal, deep horror to play out “werewolves-as-Daredevil” scenarios. Embrace the unexpected.

It can easily be argued that game design will never be the craft that directing a movie or writing as novel can be. Again, to assay an analogy, it’s more like beadwork: game designers build beads, but it’s up to the players and GM’s to create necklaces (or bracelets or pillow cushions or whatever they like) from them. We can’t build the necklaces, but we can built the best damn beads in existence.

Designers can’t control the game experience the way a director can. They still have an influence, even if it’s vague and imprecise. They can still work as hard as they can to provide the best and most useful raw materials for others to find their fun.

D&D 3e and Play Style

[pt. 4]

Many factors can add more effective complexity to a game, outside of the mechanics themselves. D&D 3e is an instructive example.

The game itself changed several mechanics from classic D&D/AD&D. These changes, however well intentioned, made predicting play patterns difficult. When rules change, player behavior changes.

Some notable changes, which would have larger than expected affects on play, were Feats, Prestige Classes, and the flexible multi-classing. These were neat toys for players, a virtue overlooked or downplayed by many 3e critics, but they did have concrete drawbacks.

WoTC splatbooks and the d20 boom all added their own complexities, as the amount of available material (including optional rules, replacement Core Classes, new Core Classes, and additional Feats and Prestige Classes) increased linearly, but, if included, the complexity increased exponentially.

(The sheer quantity of material allowed for unpredictable synergies between disparate rules. Thorough playtesting was just not possible.)

This was manageable in play, for DM’s. (Don’t allow what you don’t want.) But it made predicting play patterns nearly impossible, for everyone.

The size of the customer base played a role as well. Many people played 3e (and continue to this day, especially if one includes Pathfinder). A larger customer base means more players of divergent backgrounds, each of whom has their own idiosyncratic approach. More players is more complexity (as a common approach can’t be assumed).

Short term play patterns were, to a limited extent, somewhat predictable for most players, as the assumed play style of earlier editions was inherited. Absent the mechanical assumptions that gave rise to the style, things were bound to change. (At least, in a community as diverse, active, and distributed as 3e’s was.)

As players and GM’s learned the game, behaviors changed. Games come alive during play, and the same group with the same rules set will play the same game slightly differently a year from now. (Assuming regular play.) With 3e, the long-term patterns of play were very different than the short-term play (as the final form of the game was new, even to its designers, and players adjusted behavior as they mastered the system).

Examples: Great hostility towards save-or-die effects, as a result of the low Saves of fighters and other classes vs. high level Spells. Removal of inherent breaks to high level spells, leading to the “quadratic wizard, linear fighter” debates (or, at least granting them a new intensity). Mastery of Druid and Cleric options leading to “CoDZilla” complaints (most acute with the 3.5 revision). These attitudes emerged over time.

Simplicity is a virtue (when not taken to a fault), and the difficulty of predicting player responses is one reason why. Rules affect play, and in unexpected and unpredictable ways.

Infinity: Volley Attack

Volley Attack

The Volley Attack is a maneuver common to cinema and real life. It represents a multitude of characters all attacking the same target at once, combining their attacks to deal more damage than any could by themselves. (And, though it’s called a Volley, it applies to any situation in which multiple attackers are assaulting a single target, not just arrow fire.)

Volley Attacks are a special use of the Coordination Challenge rules. Because it deals with both Skill and Combat Challenges, it is slightly more complicated than regular Coordination, though the basic rule is unchanged.

Characters using weapons generate Attack Totals (including their Damage Rating), while characters using skills generate Skill Totals. Related skills include any skills the gamemaster agrees are relevant. (A maneuver, for example, might cause the target to turn, exposing a weak spot.)

The base Total in a Volley Attack is whichever Attack Total is highest. Every other Combat or Skill Total that beats a CR 0 adds a +1 to this base Total. These are added together to get the final Attack Total.

The final Attack Total is compared to the Defense Rating of the target, with the Result Rating read as Damage. (See “Combat”.)

Example: A group of characters breaking into a lab are attacked by a security robot. After a couple of futile rounds of attack, it becomes clear that individually, none of them can meaningfully damage the robot. So they volley their fire.

One shoots with a DR 15 gun (firearms Attack Total 18), one throws a DR 18 grenade (thrown weapons Attack Total 29), and another uses engineering to point out a weak spot (engineering Skill Total 15).

The highest Attack Total is a 29. This becomes the base Attack Total. The other Attack Total and the Skill Total both beat CR 0, so Coordinate. The final Attack Total is 31 (29 + 1 + 1).

This Attack Total of 31 is compared to the robot’s Defense Rating, with the Result being read as Damage.

Using this method, characters can work together to bring down a single, tough target with coordinated attacks.