TitansGrave, Fantasy AGE, and Stunt Dice -- Probabilties of Rolling Doubles on 3d6

Green Ronin's AGE game system is one of the more innovative role playing systems on the market and the company has begun a major marketing push to promote the system. As a part of their promotional campaign, or as a bit of wonderful serendipity, the AGE system was selected by Wil Wheaton as the role playing system that would be featured in his entertaining TitansGrave: The Ashes of Valkana webseries. I've begun reviewing the show episode by episode, and will continue to do so, but one thing struck me as I was watching the second episode that prompted me to do a post that wanders down Probability Lane in the middle of Statisticsville.

One of the things that really sets the AGE system apart from other systems is its "Stunt" system. This system allows for an increase in player agency at key moments during a game session. It's a mechanic that evolved from early Greg Gorden designs like James Bond 007 which had pools of points players could spend that would allow their characters to do special actions that were out of the realm of possibility for normal "non-player" characters. Some early games that were inspired/influenced by this mechanic include Marvel Superheroes (Karma) and DC Heroes (Hero Points). This mechanic has been very influential in the story game genre where player agency takes priority over game master storytelling. Modern games in this school include, but are not limited to, D&D 5th Edition (Inspiration), Through the Breach: The Malifaux RPG (Twist Decks), and Savage Worlds (Bennies).

While the "Stunt" system falls within this design school of modeling character heroics through the increase of player agency, the AGE take is relatively unique. Where most systems have a set pool of points, or have GMs give points to players, AGE allows probability to decide when players get points to spend. Additionally, and most importantly, many systems have either set effects like rerolls (Bennies) or allow for players to radically alter the elements of a scene (Hero Points and many story driven games). AGE takes a middle ground philosophically between these two extremes. While stunt points allow for more than "mere" rerolls, the Dragon AGE role playing game provides lists of effects that can be achieved by spending stunt points and assigns each a cost. For example, attacking two foes simultaneously might require 4 stunt points while adding a die to damage might only require 2. These are only two, of a large number, of effects that can be achieved. What is important here is that while AGE allows for increased player agency, it does so within constraints that are balanced to ensure players feel challenged.

So how does one acquire these extremely valuable stunt points?

In any AGE game when a player attempts to accomplish a task, that player rolls 3d6 and adds whatever attribute is relevant to that task. For example, when picking a lock a character might add her Dexterity score to the roll. This number is then compared to a Difficulty Number. If the roll plus bonus equals or exceeds that number, the action is successful. If lower, then the action fails. One of these die is of a different color and in Dragon AGE is called the "dragon die", but we'll call it the "stunt die." How successful a character was with the action is sometimes (in the case of extended actions) determined by the value of the stunt die.

If any two of the die come up doubles (or if all three come up as a triple), and the action is successful, the player acquires stunt points which may be spent to make that action special. Maybe the attack hit vulnerable spots or a lock is permanently disabled.  These things are determined by the expenditure of stunt points and a player acquires a number of these equal to the stunt die value. Note that this only occurs when a player rolls doubles (or triples) and is successful.

It's elegant and allows characters to feel extremely heroic in their actions, but this leaves open the question. How common are doubles on 3d6 and how do we even begin to think about these things. There are a couple of books that might be helpful. Chapter 3 of Reiner Knizia's classic Dice Games: Properly Explained is a good place to start, but I have found O'Reilly's Statistics in a Nutshell to be a wonderful resource to return to once the basic idea is understood.

The first way we can see how frequently doubles, or triples, turn up is to write out all the possible combinations.

In this case, it isn't too much work, but if more die had been rolled then it would have been far more time consuming and really we don't want to have to do this all the time. What we really need to understand is that this kind of problem is an example of an intersection of independent events. This means that it is an example where we are looking for matching results from things that are independent from on another. This is the case in all die rolls since what a die rolled on one roll does not effect what gets rolled on the next die roll. If you roll a six on a d6 and pick it up, you still have a 1 in 6 chance of rolling a six the next time you roll the die. These are independent events.

When determining the probability of independent events, we need to know the total number of combinations possible. In this case, that's simple because we are rolling 3d6. This makes the total number of combinations as follows:

6 × 6 × 6 = 216 

 Now we need to know the probability of rolling doubles (or triples) on 3d6. This is equal to:

P(Rolling Doubles) = 1 - P(Not Rolling Doubles)

Since this is a case of an intersection of independent events, we will use the following equation and modify it as a chance of not rolling doubles and then subtract that probability from 1.

P(D1 ∩ D2 ∩ D3) = P(D1) × P(D2) × P(D3)

We know that the probability of rolling a number on 1d6 is 100%. The first number we roll doesn't matter, so that makes D1 = 1.

We know that there are 5 ways to not roll the number rolled on the first die and that leaves us with D2 = 5/6.

We know that the chance of not rolling a number on either of the first two die is 4/6 which makes D3 = 4/6.

This gives us the following equation:

P(D1 ∩ D2 ∩ D3) = P(1) × P(5/6) × P(4/6) = .66667

P(D1 ∩ D2 ∩ D3) = P(1) × P(5/6) × P(4/6)  = .55554

The odds of not rolling doubles is .66667. Thus the odds of rolling doubles is:

P(Doubles) = 1 - (.66667) = .44443

P(Doubles) = 1 - .55554 = .44446

This leaves us with a 44.44% chance of rolling doubles or triples. If you want to double check the equation, you can count the 16*6 combinations above and divide that by 216. Another way of looking at this intersection is using this Venn diagram. As you can see, there are 6 ways of rolling triples and 30 doubles combinations at each intersection of any two dice (making a total of 96).

As for calculating the odds of earning stunt points at any given Difficulty rating, that is beyond the scope of this conversation and I'd leave such analysis up for those much better versed in probability and statistics than I am.

Titansgrave: Ashes of Valkana | Episode 1 Review

I was pretty skeptical when I first heard the news that Geek & Sundry would be running a Tabletop Roleplaying Game Let's Play with Wil Wheaton as the Game Master. I wasn't skeptical that Geek & Sundry would actually produce the show, rather I was skeptical that it would work as a piece of entertainment.

I've been a fan of playing RPGs since I was ten years old, but I've learned one thing from standing around watching RPGA sessions at various conventions. With the exception of the fictional world of the Gold web series, where roleplaying games are a spectator sport, it isn't often fun to watch other people play them. There are so many ways that the spectator experience can be fouled. The Game Master might not be willing to engage in theatrics. The Game Master may be bad at theatrics...although that can have its own short term entertainment value. The medium isn't very visual on its own and requires participants to fill in the "spectacle" of the tale. The players may not be evocative in their explanations of what their characters are doing. The game play might get caught up in the spiral of discussing things that aren't at all game related, and thus turn the experience into merely watching a conversation about which version of Highlander 2 is worth watching.

The answer is neither.

It's one thing for a roleplaying game session to be fun for the participants, which it can be with all the above failures, it's quite another for it to be fun to watch.

David Nett and his friends did a great job of creating an entertaining to watch roleplaying game experience with their second season of Gold entitled Night of the Zombie King, but they did so in an entirely scripted format where the roleplaying game session was merely the setting for a host of dramatic tensions. Being scripted, the session is also heavily edited and time compressed. The question is whether the entertainment value of a well-written and well acted "scripted simulation" of a roleplaying session can be recreated in a real gaming session where things are much looser.

If the first episode of TitansGrave: Ashes of Valkana is any indication, the answer is yes. I won't say that it is a "resounding yes," for reasons I'll articulate as the review goes along, but I will say that Geek & Sundry did manage to create an entertaining viewing experience.

WHAT'S GOOD ABOUT TITANSGRAVE

Before I comment on what I believe the show has done wrong, let me begin by praising what it got correct. A lot of work went into producing this web series, and it shows. Wil Wheaton has recruited a number of actors, of the tradition and voice varieties, to play the game with him. Before you assume that the "recruiting of actors" means the "recruiting of non-gamers/non-geeks," let me cue you in on a little secret. D&D is the secret language of Hollywood. There is an entire community of rpg geeks in tinseltown, and while not everyone games a lot do.

The show has also selected a game system, the AGE system from Green Ronin, that has a lot of improvisational narrative potential. All roleplaying games have at their root the potential for improvisational narrative, it is after all what really defines a roleplaying game, but given the tactical wargame roots of the hobby the game can sometimes descend into a series of "I roll a 13, I do 5 damage, You roll a 15, I take 3 damage" comments that are mindnumbing to watch. Roleplaying is best watched when "roles" are being "played" and that means that actions are being described rather than mere die rolls. AGE's "stunt point" system aids in making combat sequences more narrative, rather than quantitative, by mechanically encouraging players to create descriptions of their actions in return for benefits. Players respond to incentives, and if you incentivize narrative descriptions you tend to get more of them.

The show hired adventure writers from the game industry who worked with Wil Wheaton to bring about his world. It's one thing to hire talented writers, but it is another thing to hire people who can take a story and translate it into a game experience. Experienced adventure writers have a knack for it. It takes more than breaking a story down beat by beat and then creating stats to gamify a story. It takes an intuition regarding how players will respond to circumstances. You also need to be able to create a small enough segment of a story that it can be played (after being edited) in less than an hour and still have narrative movement. This includes taking into account the delay that mechanics will cause as actions are resolved. What separates roleplaying games from mere improvisational theater is the fact that actions are arbitrated by mechanics. This is something that not only is at the core of what makes roleplaying games "games," but is a key to ensuring that all players get an equal chance to participate/succeed.

Hiring Wes Otis for the sound effects and musical loops was wise. Otis has done good work as a sound professional, but he has also made some great effects for home play.

The show is well edited, which cuts down on the digressions that players are prone to making, and has incorporated sound effects and some minor animations to increase the visual appeal. The editing is key for this show, and they seem to know it. They have edited out the distracting digressions, while leaving some of the more entertaining ones in, which gives the session a nice play flow.

The cast does a good job of staying interesting without trying too hard. One of my person peeves when watching some episodes of Tabletop is that the players often seem to be trying too hard to entertain. They seem to have the sense that watching a board game isn't exciting in and of itself, and thus feel the need to spice it up. Wil Wheaton, Hank Green, Laura Bailey, Yuri Lowenthal, and Alison Haislip may be doing that a little in TitansGrave, but it is indistinguishable from the normal one-upsmanship I've witnessed in my playing experience.

WEAKNESSES

This show is not made for a wide audience. It's hard to tell if the show is meant to only appeal to those who are already gaming, or whether it is also meant to bring more people in. I say that because the first episode already has a couple of inside jokes that might appeal to long time gamers, but which will be missed by new viewers.  Additionally, the first story is "age confined" in that they had to bleep out profanity and that it's about drinking. This isn't a bad thing per se, and I found it quite entertaining, but it does limit your viewing audience.

Lack of use of voice actor talent. C'mon people! Let's get crazy! We've got funny people here, but they seem to be holding back a little in combat. This could partially be because they are still learning the AGE system, and don't feel comfortable with it, but I want more verbal sound effects from the players. Laura Bailey and Yuri Lowenthal are trending in this direction, but I want more as a viewer. You really can't "commit" too much for me. Think about it like a comedic role. You have to be willing to fully commit to the joke/process. That doesn't mean go over the top, but it does mean you have to immerse yourself in the play and lose the wall of "I'm being judged."

The show hasn't quite captured a way to make the depiction of combat visually interesting. I both like and dislike the battle display they are doing. I like that they aren't showing miniatures on the table, which can be good are bad for spectators, allowing the actors to free form act rather than move game pieces. What isn't working for me is how static the display is. If you are going to present a graphic virtual tabletop, have the images move about on the hologrid you've presented. I also noticed that Wil Wheaton began to fall into the "I roll an x and do y damage" drone. It's hard not to, and Wheaton was great most of the time, but it's something he'll need to fight.

The show isn't perfect, but it did entertain me. We'll see how the season progresses. One thing is certain, I will keep watching. I will also be buying the tabletop campaign supplement as soon as Green Ronin releases it.

Latest Wil Wheaton TABLETOP: FORMULA D

I don't normally post episodes of Wil Wheaton's GEEK & SUNDRY series TABLETOP. Basically, I figure if you already watch the show -- like me -- you already know about the episode, and if you don't then it's likely not something that would fall within your normal wheelhouse.

I decided to share this one because it features on of my favorite games FORMULA D, and given that TABLETOP games quickly become available at Target I thought this would be a good time to promote one of my favorite games.

I have only two minor quibbles with the episode.

First, the players are playing a bit too much to the camera and trying too hard to be funny. This is a more minor complaint than it sounds as a video watching a group playing a boardgame that wasn't playing to the camera would be terrible. Oh...and comedy is hard.

Second, Wheaton calls the game FORMULA Dé (DAY), and this is the new version FORMULA D (Dee). Yes, the game is produced by a French Company, but they have decided to market it distinctly from the earlier edition.

Formula Dé

Formula D

The original version features racing solely based on Formula 1 and the De stands for "dice," while the new version features both Formula 1 style racing and Formula Drift racing as well. The newer version has classic F1 tracks and adds some street races better suited to drifting as well. The original is a collector's item, the new one is something you should just go out and buy.

As usual, though I am somehow compelled to watch and read many things Wheaton, this video does nothing to mitigate my Sheldon-esque rage.

Magic Potions for Sale: Jones Soda is Offering "Dungeons and Dragons Spellcasting Soda"

For many this will be old news, as it has already worked its way around the geekernet Wil Wheaton and Felicia Day have already tweeted about it), but I think it is still pretty cool news. I first read the story on the excellent Nerdvana blog on the East Valley Tribune website. I have no idea why an eastern Phoenix newspaper is the home to this excellent blog, but maybe it has something to do with Flying Buffaloes.

To make a long story short, Jones Soda is offering a new limited edition 6-pack of sodas under the brand name Dungeons and Dragons Spellcasting Soda.



Each pack comes with six Dungeons and Dragons themed flavors, though not all the names are exactly "spellcasting" related. The flavors are:

Dwarven Draught

Healing Potion -- the one diet beverage

Sneak Attack

Bigby's Crushing Thirst Destroyer

Eldritch Blast

Illithid Brain Juice

The names of the flavors is pretty hit or miss. I could have done without "Sneak Attack" or "Eldritch Blast," but that is more than made up for by the 1st edition referencing "Bigby's Crushing Thirst Destroyer." Given that Bigby was famous for his hand/fist related spells, it is a little bizarre imagining drinking this soda being the equivalent of swallowing a liquid fist -- but that's beside the point.

I'll be ordering a couple of packs today and hoping that "Illithid Brain Juice" is a cool as it sounds.

Responding to Things We Think About Games -- Gaming Expectations: Heroic Endings or Doomed to Failure (Case Study One: Robotron 2084)

In 2008, game designers Will Hindmarch and Jeff Tidball released a very useful book entitled Things we Think About Games. The book contains 101 statements by the authors, with a couple of additional statements by guest gamers/designers. Some of the comments are common sense, some are blunt, and all are thought provoking. Things We Think About Games is a book that belongs on every gamer's bookshelf, and Will and Jeff's website belongs on every gamers rss feed.

At the San Diego Comic Con this year, I asked Jeff Tidball if he would allow me to write a series of posts featuring the statements from the book. Each blog post would be a gamer reacting to one of the statements in the book, and eventually I'd like to address all the statements made by the various game designers. I will also continually belabor the fact that Will and Jeff asked Wil Wheaton, and not me, to write the introduction to the book. While this is a common mistake, it is one that I will point out at every opportunity. Yes, Wheaton is more famous (and is in Secret of Nimh which I recommended as last week's Hulu recommendation), but I am less likely to use expletives.

This being a blog, and not a Thesis or Dissertation, I will address the statements in no particular order, but I do hope to address them all. Today's blog topic is inspired by the 101st entry in the book.

STATEMENT 101
Know Why You Play Games.

The statement is simple enough, and is a gamer's version of Oracle of Delphi's famous dictum Gnōthi sauton or "Know Thyself." It is a statement seems to have an underlying claim that some ludophile Socrates might adhere to, "the unexamined gaming experience isn't worth playing." That may, in one way, be the whole point of Hindmarch's and Tidball's book, but this quote provides a nice starting point for any discussion regarding games and spurs one on to think philosophically about the subject.

It was this thought that was lurking around my subconscious when I read an article at Gamasutra about Robotron 2084. The article is an historical article about the game and its legacy with regard to game play. A good amount of time is spent discussing the games innovative use of a two joystick system, an innovation that couldn't be accurately emulated in a "home experience" for many years. It makes for interesting reading, but there was one quote which mixed with STATEMENT 101 to inspire me to think about why I play games. The quote was a simple one, "The player is tasked with the grim, desperate, and ultimately futile task of saving the last family of Humanoids (emphasis added)."



Ultimately futile -- the words echoed in the back of my mind.

Why would I want to play a game that I cannot, no matter how skilled I get at it, "win?"

What particularly bothered me about this statement is that it pointed to a contradiction in my game playing habits. I have been a fan of Robotron 2084 for decades and have played it uncountable times. In that time my skill level has migrated, from poor to excellent to poor to average, depending on how often I have played the game during a given time period. I am not always in the mood for Robotron, but I never find the game -- as it was designed -- to be a bad game. As big a fan as I am of this particular futile effort, I was seriously disappointed by the end of Dawn Of War. After many hours of game play, and total victory over the forces of Chaos, I watched as all my hard work evaporated in a "1970s Satan has eaten your soul Bad ending" as my Space Marine Captain unwittingly released a new demon into the universe.

The futility of all my hard work playing Dawn of War was made clear to me during the final animated narrative sequence. Lucien Soulban's scripted ending undid everything I had struggled for in playing the game -- and it seriously aggravated me. I was all the more aggravated because an author/game designer I respect was the one who dropped the "futility bomb" on my head.

Why was I experiencing such a strong emotion that was, on its face, a contradictory sentiment to my thorough enjoyment of the equally futile Robotron 2084? To answer this, it was helpful to contemplate statement 101.

Why do I play games?

I play different games for a variety of reasons, but one reason that keeps me coming back is "story." I like the way that games, of all kinds, tell stories. It's one of the reasons I am a "good loser." I don't mind losing to someone who is better than me at Chess, all I want is my learning experience to be a good story. Candyland, with its pre-determined gameplay, taught me the importance of story in play and de-emphasized "winning." Both Robotron 2084 and Dawn of War contain story elements. Robotron's appear to be "weak" at first, but they are deeply embedded in gameplay -- if simple narratively. Both games contain narratives where the actions of the player, in the end, result in failure -- so there must be some element of the game and how it interacts with story that allows me to enjoy one in its entirety while feeling dissatisfied with the ending of the other.

Aha! It isn't the futile ending that is disappointing. It is the fact that the futile ending was not a part of game play -- it was a forced narrative tacked on to the end of the game. When the player inevitably loses in Robotron it is because the game has finally become too hard to finish, the game has literally beaten you. When you "lose" at the end of Dawn of War, it occurs after you have achieved "final victory." The contradiction lies in the interaction between the mechanics and the story -- a contradiction made even stronger by the underlying expectations of Real Time Strategy games. The underlying expectation of an RTS is that you can win, any advantage in supply or troops the computer opponent has is usually made up by an imperfect AI -- necessarily imperfect as a perfect AI would likely win all the time and lessen the fun.

Would I have felt differently if I had actually lost the final scenario of Dawn of War rather than have a scripted 70s ending? Not if the game had followed standard RTS genre conventions, the player "must" have a chance to win in the conventional. If the game progressed in a manner similar to other RTS games, each level getting slightly more difficult but winnable, with a final impossible level, the game would have likely been as unsatisfactory. This dissatisfaction would likely have been accentuated by the interstitial narrative clips.

On the other hand, if the game lacked interstitial clips and the narrative left only to game play I would probably have accepted an unwinnable level. At least possibly, especially if I knew going in that the game eventually becomes unwinnable as each level becomes more difficult than the last. But that isn't the central conceit of an RTS campaign, the central conceit of an RTS campaign is that the player is unlocking a heroic narrative. In this case, each victory leads to a new chapter in the hero's tale. A hero can hit a low point, like the one at the end of Dawn of War, but that ought not be the end of the story. In this case, it is. There is no sequel to the narrative, though there are many sequels to the game. My Blood Angels forever stand defeated in their victory, where my mutant defender of humanity just ends up dead after finally facing overwhelming odds.

I think it would be interesting for someone to design an RTS where each level becomes more difficult than the last, with no end in sight. Then the story changes from how my victory was taken from me, to how far I was able to get and who is able to get to the farthest level. I think I might prefer traditional RTS games -- with victorious endings -- to that "futile" RTS, but given my love of Robotron 2084 I'd probably like that killer RTS more than the end of Dawn of War because the ending would be driven by the mechanics of the game.

I don't mind losing when it's a part of the rules, but I hate losing when I won fair and square.