Star Wars: Age of Rebellion – A Deep Dive on Dice Probabilities

A little while ago, I gave Star Wars: Edge of the Empire a reasonably positive review. After another year of playing the game, it’s time to check in again see how it’s faring, and to try to pass along some playing tips for dealing with some of the game’s quirks. If you haven’t played Star Wars: Edge of the Empire or Age of Rebellion (they’re exactly the same game system), you might want to catch up by reading that review – this will go pretty deep into the game’s probabilities and what they mean for actual play.

The dice in Star Wars: Edge of the Empire, image courtesy FFG. Click for product page.

The central, most intriguing, and most opaque idea in the game is the set of customized dice that are used to form dice pools for task resolution. At their most basic, they are simple and elegant: just add positive ability (green 8-sided) and proficiency (yellow 12-sided) dice for your level of skill, negative purple 8-sided difficulty dice for the difficulty level negative red 12-siders for reasons, and then even some more dice (positive blue boosts and negative black  setbacks, both 6-siders) for situational modifiers (cover, time pressure, assistance from an ally), grab them all, and roll them. Net out success and failure icons, and advantage and threat icons. What you’ve got left is the result. If you end up with at least one success, you succeed. Remaining threat or advantage may give an additional bonus or penalty. It’s a pretty cool idea and rolling lots of dice is fun. However, as I played more, I kept noticing unexpected quirks in the results.

The big thing was that critical hits (which generally require a successful combat check with three advantages) seemed exceptionally rare, and even weapons special powers were hard to activate (they generally require successful check with two advantages). A little bit of analysis of the dice and this made sense. The dice faces never have more than two symbols and rarely show both success and advantage. Good dice only have good faces, and bad dice only have bad faces. So canceling out all the failures and all the threats while having surplus successes and advantages is obviously rare. While there are in theory four different possible “quadrants” the result of a dice roll could fall into (success or failure with advantage or threat), in practice two of them (success with threat and failure with advantage) are predominant, with critical success and critical failure seeming quite rare unless you have a big imbalance between good and bad dice in the pool.

Another odd thing was that it seemed like having high characteristics (Agility, Perception, Brawn, etc.) was a much bigger deal than actually having ranks in skills. A skilled character with a lower characteristic (so, say, a character with Piloting 2 and Agility 2) did not seem to do as well as a character with a slightly higher characteristic (so, no Piloting skill but Agility 3).

Then finally, because nobody really had any idea what the magnitude of the effects of adding various dice were, it made it hard to know what to do with the Destiny Pool, or how to rate the importance of boost and setback dice, or how to wisely spend advantages in combat. The rules seemed to imply that a boost/setback die was a lesser effect while upgrading a die (for example, turning green ability die into a yellow proficiency die) was a bigger deal. But is this really true? It didn’t feel like it.

Now, a little bit (or even a lot) of opacity in the odds is not a bad thing. In fact, a major appeal of the Star Wars system is that dice pools are so intuitive to construct but the probability curves they produce are so complicated as to be essentially incalculable.  That said, we still need to understand some basic things to play the game well. And the only way to get there seemed to be to run some Monte Carlo simulations and see what the numbers looked like. So that’s what I did. Knowing these details definitely improved my game, but they also raised some real questions about whether the designer understood how the dice pool actually works in practice, and if there are fundamental aspects of the game system that need to be re-calibrated.

The dice pool is extremely flexible and it can generate a huge range of probability curves. So I focused on a just few questions: how common are critical successes? What are the quantitative impacts on success and critical success of adding the various different dice to the pool? How big a deal are the challenge dice? To do this, I looked primarily at a few common cases:

  • A difficulty 2 check, which is a typical ranged combat check at medium range or when shooting at a similarly-sized ship
  • A check made by a moderately-skilled entry-level character, with two yellow and one green dice
  • A highly skilled character rolling one green and 3 yellow dice

For a look at a sampling of the numbers generated, you can check out this Google sheet. I’ve focussed on positive results, because they get the most attention from the system. The SUC+2 or SUC+3 columns give the percent chance of a successful check with at least that many advantages. I didn’t go deep, running stats for 2 or 3 or more boost, setback, or challenge dice, but this should give you a feel for how they work. You could really go crazy with the data, but the visualization problems get out of hand very quickly. Also, you need to run a surprisingly large number of iterations to get the results to converge. The numbers for the very large dice pools are not exact.

First a few general observations:

  • If you’re trying to activate weapon properties or score critical hits which require a success with +2 or +3 advantages, basically forget about it unless you have a very large dice advantage. The odds of a less-experienced character with good skill (a dice pool of 1g+2y) activating her twin-linked cannons on a typical shot (difficulty 2p) are only 9%. The odds of a crit are only 2%. A ridiculously skilled gunner on that same shot (5y) still only gets +2 advantages half the time, and a crit 30% of the time (remember a crit is generally not “you’re dead”, or even double damage, but something like reducing the target’s speed by 1 or removing a defense die). Also: reducing your crit rating is a really big deal. A vibrosword with a mono-molecular, serrated edge is extremely nasty (vicious 2, crit 1). Very nearly as good as a lightsaber.
  • Quantity of dice is better than quality of dice. In virtually every case, your odds of success with N green dice are better than with N-1 yellow dice. For Piloting checks, someone with Agility 3 and skill has worse odds than someone with Agility 5 and no training until the former has trained up to 5 ranks in Piloting. There are minor exceptions when a skill level is high and characteristic ratings are only different by 1, but they are quite small. A boost die has a bigger impact than a die upgrade, and it can significantly increase your chances of success and critical success.
  • In the same vein, upgrading a purple difficulty die to a red challenge dice just isn’t that big a deal. Outside of the triumph and despair symbols (see next), the effects of the yellow and red dice on your chances of success vs failure or advantage vs threat are negligible (they help; just not a lot). In most situations a challenge die is about a 5 percentage point hit on your chances of success, with minimal impact on your chances of critical successes (again, outside of despair, which I’m getting to). Adding a setback die is significantly more impactful than upgrading a check, in that it has a somewhat greater negative impact on your chances of success, and a much nastier hit to your chances of critical success (roughly halving them in the 1g+2y vs. 2p case).
  • By far the most important impact of the proficiency (yellow) and challenge (red) dice are the 1:12 chance for a triumph or despair.  The 1g+2y shot vs. 2p has only a 3% chance of a critical, but it has a 12% chance of a success + triumph. For anything that requires three or more advantages to activate,  triumphs are the way to go. Even when you are enormously skilled and the task is easy, you are still more likely to get triumphs than 3 advantages. The overall impact of the challenge dice on the game (and so the despair symbol) is less pronounced simply because there aren’t very many of them flying around. You’ll occasionally get them through the GM spending Destiny, and a Nemesis’ Adversary talent; that’s about it.
  • The bias for failure + advantage and success + threat is very noticeable when the pool is balanced (equal green and purple dice). Due to the extra threat and missing failure symbols on the purple dice (compared to the green dice), until you have a big dice imbalance success with threat tends to dominate the nontrivial results, with failure plus advantage coming next, and then failure plus threat and success plus advantage only filling up as the dice become overwhelming in one direction or the other.

Some of this makes sense, some of it is decidedly odd.

I am definitely not a fan of how it makes levels of skill relatively unimportant. You might think 3 ranks of Piloting gives you some niche protection in that area; but it does not, someone with 4 Agility is basically as good as you. High characteristics are a big deal, and spending any of your initial XP on anything other than characteristics doesn’t make a ton of sense, from a pure min-maxing perspective. This is not great from a “making characters interesting” perspective.

The flipside of the relative weakness of skills is the imbalance in the Destiny Pool. For the GM, spending a dark side Destiny Point to upgrade the difficulty of a skill check just doesn’t do a lot – it’s usually about a 5% hit, the equivalent of a -1 in a d20-based system, with a small (8%) chance of a despair symbol. Barely worth the effort. The FATE-like “Luck and Deus Ex Machina” function of the Destiny Pool is great and I like it a lot. But spending points to upgrade checks and difficulty is fiddly and low-impact.

In fact, many of the parameters of the game seem to be built on a profound misapprehension about how powerful the challenge and proficiency dice are and the frequency of surplus advantages. There are weapons with critical ratings of 4 or 5, as if the chances of that level of surplus did not round to zero. In table 7-5, which talks about how to spend advantage and triumph in starship combat, two options for spending triumph are: “Do something vital to turning the tide of the battle, such as destroying a capital ship’s shield generator or losing a pursuing ship in an asteroid field”, and “Upgrade an allied character’s next Piloting Gunnery, Computers, or Mechanics check”. Which is deeply weird. That first use of a triumph is obviously extremely powerful – much more powerful than a simple critical hit. Yet for a character with skill, getting a triumph is much more likely than rolling a critical hit! The second effect, on the other hand, is comparatively trivial. Not only that, but it’s usually weaker than adding a boost die to the same check, which you can do with a single advantage! The proficiency dice do come with triumph symbols which boosts do not, which complicates the comparison slightly, I think the general rule holds. Boosts increase you chances of success more than proficiency dice do.

One of the interesting ways in which the dice pool works that did make sense is how armor affects defense. Armor is generally modeled through setback dice, and the interesting thing as that while it’s generally a modest reduction in your to-hit chances (on the order of 8%), it really nerfs your chances of getting surplus advantages (the impact on triumphs is less noticeable).

At the end of the day I’m not sure what to make of all this. I like the dice pool mechanic quite a bit, and if you look at it as a core system, it has lots of interesting features and it’s fun to roll lots of colorful dice. For purely narrative checks it works great, as long as you have a basic grasp of the frequency of some combinations. However, a lot of the crunchy superstructure built on top of it seems deeply suspect.

In the long term, to make a more smoothly functioning game, I think we need a serious recalibration of many of the parameters of the game system. Fortunately, it’s not too hard to figure out some tweaks to make your game run better. Here is what I’ve taken away from it for my GMing:

  1. Be very generous in handing out setback and boost dice; they are the most interesting dice to add to routine checks. Use the boosts like candy; give them to players as a reward for trying something cool cinematic, in addition to their modeling function. They are fairly strong, and in order to get surplus advantage to trigger interesting game effects (primarily in combat), characters are going to need the extra punch provided by boosts. The point of diminishing returns on the chance of success is at about 85-90%, so dice beyond that point (roughly +3 dice, although obviously the system has a lot of variability) are mainly going into generating advantage. A lot of talents also remove setback dice, so in order for that to be interesting you need to be handing them out fairly routinely. As a corollary for players, all those things you can do to gain boost dice in combat (aim, spending advantage) are worth doing.
  2. Don’t overdo the triumph symbols, either narratively or in combat. When characters are skilled, triumphs are not that uncommon (12-15% for a balanced dice pool with a couple Proficiency dice). Feel free to go nuts with multiple triumphs, but a single triumph should not be allowed to dismantle a scene or conflict.
  3. Be aware of the system’s significant bias for success with threat and failure with advantage in routine checks. This is actually mostly a feature, not a bug, and allows you to make success more complicated and (more usefully) mitigate failure. But it does get repetitive, so don’t get too worked up about it; it’s OK for the benefits of rolling an advantage or two on a failed check to be small and transitory, since it’s very common. It also argues for rolling dice only when it’s genuinely interesting to do so, but that’s good advice for any game under any circumstances.
  4. The Destiny pool doesn’t really work, because the impact of a single challenge or proficiency die just isn’t big enough. I don’t really have a solution for this. The house rule I’m considering using is to have the GM spend them for Numenera-like intrusions as the flip side of the players’ “Luck and Deus Ex Machina”, but what the system seems to really want is just a much more potent die.
  5. Find ways to get more challenge dice into the game, just so you can play with despair. As written, the system favors adding setback dice to modify difficulty, which I think generally makes sense, but we’re just not rolling enough red dice and they don’t have enough impact on the game. While excess threat is generally easier to find then excess advantage, we still want to see those despair symbols occasionally! Consider giving more opponents the Adversary talent. Minion groups especially currently really suck, and giving more imposing ones (Stormtroopers, TIE wings) some kind of levels of Adversary would help mix things up.
  6. Speaking of Minion groups, they do really suck because the extra proficiency dice they get for being in larger groups just aren’t hugely significant. I think this is fine and generally the intent of the game, but just bear it in mind. Big groups of minions are far more imposing on the page than they are in actual play. The number of groups is far more important than the numbers in each group.
  7. During character generation, I like to give players an extra 40XP to spend after spending their initial allotment (I think this number could actually be even larger). The system is so heavily biased in favor of characteristics that players are going to sensibly spend as many of of their initial points as possible on those. Making sure your character has one characteristic of 4 is a huge deal. Low characteristics, 1 or 2, can limit you because they cap the number of yellow dice you can roll, and so in the long term limit your ability to generate triumphs no matter how skilled you become. Giving players some points they must  spend on skills & talents to differentiate the characters seems wise. In an unrelated point, characters need a lot more starting money – 1500 credits instead of 500 seems closer to right. Yes, there are options for spending Obligation or Duty for more equipment, but messing with this is awkward and 500 credits is just ludicrously low.

This may all sound negative, and I do think it’s true that there is too much in the game that just doesn’t make much sense as designed. Unfortunately, there are a lot of things in the game – weapon ratings, talents, advantage spends – that clearly are at least somewhat misaligned. But, the cool thing about the system is that fundamentally it’s quite simple and elegant and has a lot of potential. Once you’ve gotten a handle on how things actually work, it’s not that hard to hammer things into some form of order. I still need to find a fix for the destiny pool, but I feel like as I play more and get more of an understanding of how the pieces fit together, and how to use them properly (even if that’s not exactly what the rules say), I’m happier with the game. While it’s always going to be a game in need of constant tinkering to keep working, that tinkering is not particularly onerous, Star Wars is fun, dice are fun, and the core system is good.

Player Agency in boardgames and RPGs

Last week there was an interesting interview on Slate’s The Gist with Peter Mendelsund, an ex-concert pianist and current designer of book covers. The conversation turned to how much agency the audience/reader/player has when engaging with different types of entertainment, and the interesting quote that struck me and got me thinking about boardgames was this:

… we imagine reading as being a medium in which we have no agency, we’re passive recipients of the author’s work, and video games as being the opposite, where we’re active participants. And the more you examine, say, just those two media you find out it’s actually quite the opposite in some ways, that reading is way more active and we have way more agency than we think we do and in video games it’s sort of the opposite, we’re way more put in the runnels that the programmer has made for us.

The argument is that because literary descriptions are usually fairly economical, the reader does a lot of construction out of their experience and imagination to create the scene that is in truth only sketched in the text. Mendelsund calls out The Lord of the Rings specifically as a book that relies on the agency of the reader to create the full experience, and how for him the movies ruined the experience of reading the books – because now when Gandalf appears he just conjures up Ian McKellen instead of engaging his imagination. Mendelsund is a book cover designer, and he thinks about the fact that once you concretize a character through an illustration, you take away some of the reader’s agency.

This tweaked me immediately because I had been thinking about player creativity and its vital role in boardgames and RPGs. I have been getting back into MMP’s Operational Combat Series of wargames with the fantastic Reluctant Enemies, and as I was playing it reminded me why I love these games: they generally give the players a huge amount of latitude to do creative and expressive problem-solving, to change not just their chances of winning but the entire course of the game. It struck me as similar to the effect I aim for in the Star Wars: Age of Rebellion game I am running, albeit using a completely different set of tools in a completely different context. The recent release of the terrific Blue Moon Legends has me playing that again also, which has always struck me as a game that particularly rewards finding creative cardplay sequences and combinations, something above and beyond pure tactical analysis.

It became clear to me that a game that gave its players real agency is what divides the good from the great for me. Immediately after thinking this, though, I realized that what exactly agency is in this context is not so easy to simply express. Intriguingly, it seems to work in exactly the same way for both RPGs and boardgames, and so at first I thought of “agency” as “rewarding player creativity”. But as I thought about it more, it became more slippery. Creativity is clearly a very big part of it, but it’s not a sufficient description. Games from across the spectrum can reward various types of player creativity in a range of different ways: High Frontier, Race for the Galaxy, Lost Legends, Blue Moon Legends, Android: Netrunner, Battle Above the Clouds, No Retreat, Ashen Stars, The One Ring. But there are other games where the players clearly have what I think of as agency but which I can’t really see as creative per se, like Modern Art and Lord of the Rings. There are games where players need to be creative but it’s not clear they have agency, like Dixit or Telestrations. There are games which seem like they might reward creativity, but system imbalances or constraints mean they probably don’t, like X-Wing or GMT’s COIN games. And there are games which support or provide outlets for creativity in different ways but where it’s not really part of the game, like Arkham Horror or Games of Thrones: Westeros Intrigue.

This last category is intriguing to me, because it’s both a very large class of games and also the closest analogy to Mendelsund’s idea of how we interact with books: although the players’ choices don’t affect the course of the game, on the other hand the experience of playing provides a sketch in which you have to (and which the game allows you to) fill in with your imagination to move forward and bring the game to life. In a game, though, I find this form of agency the least compelling, least useful, and also the most technically difficult to meld with an interesting game. Games are different from books: they are shared with multiple people and require a shared framework, and they take place in strict time where everyone has to move at the same pace, more or less. They require a quite different sort of player agency to feed engagement. It’s clear that simply engaging the players’ imaginations can turn a so-so game (Grand National Derby) into a very good one (Titan: The Arena), or a non-game (Munchkin) into something people like a lot. But this is not a particular strength of the boardgame form, and I’m always far more interested in what games can do that other forms can’t.

To loop back a bit, in the realm of RPGs I’ve spent the last few years pursuing games that strongly encourage player agency. For me, RPGs aren’t fun – either as a player or the GM – unless the players are actively involved in the creative process, unless their decisions change not just their chance of success in any given scene but the entire course of the story. Thus I have been drawn to Ashen Stars, Night’s Black Agents, Numenera, and Hillfolk. For plenty of players, though, agency is not a feature and is in fact something they specifically don’t want. They want the GM to set up some scenes for them, and they want to interact with them. Just as in the world of boardgames, there are games that support both preferences. I think this may be part of the trap that 13th Age fell into for me personally: although it tries to give the players much more freedom to be creative, it is also clearly set in a genre where the main games (D&D and Pathfinder) are the games of choice for players who don’t particularly want agency.

I came away from all this thought without a clear definition of how agency works in boardgames, other than that it is important to me and some people like it and others don’t (the picture is obviously much clearer in RPGs). So I thought I’d close with a few capsule comments about boardgames where I feel like I have real agency and how I think it works.

Knizia’s Lord of the Rings is a game that is sending distinctly mixed messages, and presents a particularly difficult critical problem. On the one hand, with its fixed throughline, the players clearly have no ability to affect the overarching flow of the game. On the other hand, because the risk-reward probabilities are so complex and the thinking required frequently so long-term, the players do have a huge amount of flexibility in how they choose to attack the problems – far more meaningful flexibility than in any other cooperative game, even before you throw in the expansions. While the instances of truly creative problem-solving may be rare, they do exist; those occasional eureka moments where you realize that if I use the Miruvor, you can pass the Mithril to Frodo which allows him to use Gollum without dying and to escape from Shelob’s Lair are really cool. At the same time, the fixed throughline could be viewed as a list of checkpoints which allow all the players to stay on track together while still being able to construct their own internal narratives. I don’t think of Lord of the Rings as giving the players true narrative or creative agency; the real strength of the game is how it evokes the books in forging the players into a fellowship through the trials it sets up for them (and this is perhaps the greatest agency the players have, in how they relate to the other players in the game). On the other hand the game is also so much more than the sum of its mechanics, probabilities, and presentation, and it give the players the chance to decide what the game means to them.

Reluctant Enemies is the game that sent me down this path, because as I was playing it – even as the more reactive Vichy French who play primarily defense – I was impressed both by how much legitimate flexibility I had in deciding how to attack tactical problems, and how dramatically the choices of the players affects the flow of the game. Much of this is driven by how much information is concealed – available supply, so crucial to being able to do anything in this system – and so how much uncertainty there is. In a more traditional wargame like Roads to Moscow or France ’40 the players can see everything that matters and so it’s much harder for a game to get away from being strict tactical problem solving and allow players true flexibility and choice. Even in games like War of the Ring or Hammer of the Scots, where there is a lot of hidden information, right and wrong answers to the situation develop as players feel out the game and their flexibility and agency gets stripped away. By contrast, in Reluctant Enemies, right and wrong answers are created only out of the choices the players make and are largely unknowable in the moment.

Thinking of games where agency seems to start high but goes to zero over time, Dominion is to me a classic example. When you first play it there is this sense of endless possibility, that by creatively mixing and matching cards and ratios you can create interesting effects and control the game. As you gain even a little experience though, you find that the cards aren’t particularly well balanced, that some are worth the effort and many are not, that the game rewards simplicity to an extreme degree, and so each set tends to be an up-front tactical problem-solving search for the critical card or combination. Ascension (and similar games like Star Realms), by making you figure out how to take advantage of a constantly changing environment, is much better at tapping into player creativity and feelings of agency. It’s probabilistic – occasionally the exact cards you need are magically turned over off the deck, and everything just works out – but you earn your stripes in the game by turning what seems like a bunch of nothing into something.

Tales of the Arabian Nights is the game which is the obvious analog to the book-reading experience. As you string together these blocks of text you get to construct in your head the cinematic narrative. Because the ongoing story applies only to you, and only your choices affect it, it doesn’t matter if different players construct radically different ideas about what’s going on. Reading the paragraphs are also little bits of performance art (very little, but still). Additionally, and also cool, is that your choices of skills and how you develop them has obvious and significant effects on how the story unfolds. These elements are strengths and weakness, though. Because Tales is an analog to a book-reading experience (with each player individually developing his or her own story), and because book reading doesn’t scale that well past 1, having players beyond 2 or 3 simply degrades the experience.

Talking about Advanced Squad Leader in this context makes me sad because it’s a game I like, but at the end of the day I think ASL is much more of a game of tactical problem solving than it is about player creativity. The variety of tactical situations it puts you in is vast and it rewards being able to simplify very complex problems, but usually creative solutions are less important than correct solutions. The interesting counterpoint – which shows the huge range of the system and the difficulty of generalizing about it – is that the night rules change the texture of the game drastically. All of a sudden players have far less concrete information (and often more flexibility) and games can turn on creative bluffs and traps, which probably explains why I’ve always liked those scenarios.

Race for the Galaxy is game where I think this idea of agency is at the heart of why it is such a great game. You are always looking for creative ways to use the cards you’ve been dealt, reaching for combinations or strategies that will work, then trying them out and seeing what happens. Additionally, those choices have significant effects on how the overall game unfolds. If you go with a military strategy, that increases the number of Settle actions taken in the game in an obvious way, and so changes how the other players feel and choose in a way that simply isn’t true for the majority of purely tactical euros (Tzolk’in, Power Grid, Age of Steam). This feeling of control may age out after a long period of time as the contours of game balance become more fully explored, and the game’s expansions weren’t always handled adroitly, but introducing just the goal chits goes a long way by messing with that sense of balance and extending the creative phase of the game.

I’ve just started working with this idea in the realm of boardgames, so I’m sure my thoughts on it will evolve as I develop it. Maybe it will turn out to be a minor element of most boardgames, where it’s much harder to clearly see than it is in roleplaying, but it strikes me as an important intangible that helps separates the good from the great.