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.

Tim Kask: A Tale of Two Magazines

 

Back in July of 1981 Tim Kask launched the first issue of ADVENTURE GAMING magazine. It was a magazine dedicated to the entire gaming hobby. The magazine launched just as two of the largest "Industry Magazines" (DRAGON and WHITE DWARF) were beginning their slow migration from magazines that covered the entire hobby and into house magazines that covered primarily the products offered by the company publishing the magazine. Tim Kask had been the editor of DRAGON for the first 34 issues of the magazine, so if anyone was qualified to launch a new magazine for the growing hobby he was certainly on that list. Unlike the two previously mentioned magazines, and magazines like Space Gamer, Tim's new venture wouldn't limit what kinds of games it covered. To quote Tim from his "Off the Wall" editorial:

Do you really plan to cover it all? You betcha, Buffalo Bob! The lines that used to separate the types of gamers are becoming more blurred. The amount of crossover interest and participation has never been greater. There can be no disputing the fantasy phenomenon erased a number of those lines, as well as gave the industry an incredible boost in interest in sales. Fantasy remains the dominant force in the industry today, but all areas are showing increased interest and sales. We plan to accurately reflect the hobby whatever direction it may take.

 The words that Tim wrote in 1981 were true, but they weren't sufficiently true for him to launch a successful magazine that lasted years. ADVENTURE GAMING published only 13 issues. As a fan of the hobby as a whole, I find this to be a great loss. Magazines are one of the best ways for modern fans to learn the history of the hobby. They are the primary way we can cut through the "common knowledge" and assumptions about the history of the hobby we so often encounter in conversations across fandom. If you read the article in FIRE & MOVEMENT magazine about the TSR/SPI merger you get quite a different picture than what you hear from former SPI employees. That merger doesn't look to be a clean merger from either side, and one wonders if TSR's attempt to acquire IP while avoiding debt obligations that would have been demanded during bankruptcy wasn't poorly communicated. It certainly created bad blood, and TSR may have been being too "creative" for their own good. Add to that the state of nature-esque competitiveness of that growing market, and modern gaming historians are poorer for the fact that magazines like ADVENTURE GAMING, SPACE GAMER, and DIFFERENT WORLDS didn't do better outside their regional spheres of influence.

Let's just have a look at what ADVENTURE GAMING #1 had to offer:

1. Scepter & Starship -- A Traveller Variant article. Note that Traveller recently had a very successful Kickstarter over 20 years after this issues publication.
2. Starting Over: Some Points to Consider Concerning New FRPG Campaigns -- A good how to start a campaign article.
3. The Joys of Napoleonic Wargaming -- Here you begin to see the breadth of the magazine's coverage.
4. Reflections -- A "Gamer POV" article about the hobby.
5. The Adventures of space Trader Vic -- One of the obligatory cartoons.
6. Campanile -- A column by Kathleen Pettigrew that was a gamer opinion column.
7. CIVILIZATION: A Game Review -- What it says.
8. What Makes a Player Good? A DM's View -- An article that looks at a topic that is often under evaluated, that of what players can do to make a better game experience.
9. Heroic Combat in DIVINE RIGHT -- A cool variant rules article by one of the designers of the game.
10. Away to the Wars! -- A variant for the KNIGHTS OF CAMELOT game.
11. Cangames 81 and Canadian Gaming by John Hill -- Yes, that John Hill of SQUAD LEADER fame.
12. NPCs are People Too! -- An article on how to give more personality to NPCs.
13. On Being a Gamemaster -- A GM advice column.
14. Any News of the Questing Beast? -- An overview of KNIGHTS OF CAMELOT
15. Whither Boardgames -- A column dedicated to the discussion of boardgaming and about how RPGs are hurting boardgame sales and how boardgaming still has value.

It's a pretty interesting lineup and one that would be fun to see in a modern publication. Speaking of modern publications, Tim Kask and his merry band of adventurers are at it again. Late last year/early this year saw the launch of GYGAX Magazine, a quarterly "adventure gaming" magazine. A magazine with a distinctly familiar mission:

We've go material that reaches back to some of the earliest role-playing games, and some of the absolutely newest. Virtual tabletops, fantasy miniatures rules for toddlers, complicated mathematical answers to simple questions, even a city in a swamp...we've got it all here. If there's one question that's come up more than any other while we were making this magazine, it's been "what are you going to write about?" From here on out, we would like to direct a similar question at our readers. What would you like to read? Drop us a line and let us know. With your help, we want to see tabletop gaming thrive and expand.

 While the wording is more "marketing" oriented than the older editorial, the message can be said to be very similar to the older quote, "We plan to accurately reflect the hobby whatever direction it may take." The first issue of GYGAX features the following:

1. The Cosmology of Role-Playing Games -- An incomplete but interesting look at the role-playing game hobby as a cosmology. It has a lot of important games, but it misses a few games I would consider highly influential. Not to mention that it just ignores 4e completely.
2. Still Playing After All These Years -- An editorial by Kask. A very good one.
3. Leomunds Secure Shelter -- An article by Lenard Lakofka, of Bone Hill fame, that looks at the math of AD&D.
4. The Ecology of the BANSHEE -- With the demise of Kobold Quarterly, it's nice to see an ecology article.
5. Bridging Generations -- An article by Luke Gygax discussing the continuation of the hobby.
6. Gaming with a Virtual Tabletop -- What it says.
7. Keeping Magic Magical -- An article by Dennis Sustare the designer of SWORDBEARER a game that very much kept magic magical.
8. Playing It the Science Ficiton Way -- A discussion of METAMORPHOSIS ALPHA and its origins.
9. DMing for Your Toddler -- Cory Doctorow's less useful version of Highmoon Games RPG KIDS. Do yourself a favor and buy RPG Kids.
10. Greate Power for ICONS -- Steve Kenson article for the supers RPG.
11. The Future of Tabletop Gaming  by Ethan Gilsdorf -- The second "celebrity" article. It's a good article, but I'm wondering if Shannon Applecline couldn't have done a better job.
12. The Gygax Family Storyteller -- What you might imagine, in the best possible way.
13. Talents OFF the Front Line -- An article for GODLIKE by Dennis Detwiller.
14. D&D past, now, and Next by Michael Tresca -- A good article that none the less falsely states that 4e is the "first edition to explicitly require an objective environment." No, that would be 3e and both Line of Sight rules and Flanking rules.
15. Gnatdamp -- A city in a swamp. Good article.
16. The Kobold's Cavern -- Wolfgang Baur!
17. Magical Miscellany -- Support for Green Ronin's AGE.
18. An AGE of Great Inventions -- More support for Green Ronin's AGE, which is a wondrous thing.
19. Scaling Combat Feats for PATHFINDER -- A good article by someone who wants to address the "feat taxes" of 3.x and PATHFINDER. Insert my snarky remark about how PATHFINDER is already amped up, so why does it need to be turned up to 11. Answer with "because it's a game and there is no wrong way to play" response.
20. Marvin the Mage -- Obligatory Cartoon.
21. What's New -- Obligatory Cartoon.
22. Order of the Stick -- Obligatory Cartoon.

As you can see, Tim is being more conservative in the new venture. There are no mentions of Napoleonic games here and the focus is on fantasy. The magazine still covers a wide swath of the hobby though. It has yet to be seen if there is a market for this publication. I'm certainly the target audience, and I've already got a one year subscription to print and digital, but who else will be is the vital question.

Will GYGAX be the next ADVENTURE GAMING or will it be the first of a new breed of hobby based magazines? Only time will tell. It wasn't for lack of quality that ADVENTURE GAMING failed.

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