In this Crunching the Numbers review, we revisit fan-favorite Dungeon World (DW), which tries to port a Dungeons & Dragons-like setting into a traditional Powered by the Apocalypse format.

In this review, I want to talk about how the probabilities in Dungeon World (and by extension, most PbtA games) net out with respect to success at a cost.

You're Doing It Wrong

In one of several plays of the game, I noticed myself getting frustrated at the frequency with which I wasn't able to do the things in the fiction without something goofy or unexpected happening that I didn't intend as a player.

Now I've noticed a rebuttal to criticisms of PbtA in general is "You're playing it wrong" or "Your GM doesn't know what he's doing." That can be said of any playthrough, and it's true that it's impossible to really assess the degree to which a playthrough follows the rules-as-written without video evidence.

But to be fair to our GM in this instance, I think he did an exceedingly good job at running the game rules-as-written. Despite my gripes below about the numbers, we all had a fantastic time overall. Even so, I couldn't stop thinking about why I always felt like every move I made in the game seemed to be accompanied by a high likelihood of something going sideways... until I decided to crunch the numbers!

RE: Success at a Cost

Why is it important for players to feel confident that their rolls, on average, will have foreseeable consequences?

I think the answer to that has to do with one of the reasons we play RPGs to begin with: we want to do things in a fictional space, and we want to see our actions affect the fictional space in ways we intend.

In other words, when I roll well, I expect my actions to have an effect on the world that I intended. If most of my actions have effects I don’t intend, that frustrates my agency as a player of the game, and this is especially a problem for a game (such as Dungeon World) where my agency in the fiction is the principal way in which I contribute to creating the shared narrative outcome that is (arguably) the purpose of playing the game. 

Put another way by our resident designer Courtney Staples: "Players are (often) seeking to experience the game world as heroes, and it can feel very un-heroic/unsatisfying to have e.g. a trained warrior still have a fair chance of flubbing his sword swing even against a lowly criminal, or a highly observant character miss a basic clue."

She notes that in a system like Pathfinder, "you can of course still roll poorly and fail even if you're beefed up with a +14, but having that big bonus makes it very unlikely that you'll trip over yourself when facing a common situation." Just having that big number, she writes, "is probably psychologically satisfying/makes you 'feel' stronger and more advanced as a character."

So let's consider my probability of being able to completely foresee the consequences of an action I take in Dungeon World, based on an unmodified 2d6 roll (modifier “0” in the table below):

modifier	6-	7-9	10+	12+
-5	97.22%	2.77%	0%	0%
-4	91.67%	8.33%	0%	0%
-3	83.33%	16.67%	0%	0%
-2	72.22%	25%	2.77%	0%
-1	58.33%	33.33%	8.33%	0%
0	41.67%	31.67%	16.767%	2.77%
1	27.78%	44.44%	27.78%	8.33%
2	16.67%	41.67%	41.67%	16.67%
3	8.33%	33.33%	58.33%	27.78%
4	2.77%	25%	72.22%	41.67%
5	0%	16.67%	83.33%	58.33%

Taking a look at this table...

A 10+ result happens 16.67% of the time. I can gauge the consequences completely, because they are exactly as I intended, meaning there is no opportunity for GM fiat—that is, the GM gets no say in interpreting the outcome other than what I intend.

This is the equivalent of making a skill check with a binary outcome, or making an attack roll in a trad game where the consequence is completely predictable. The odds in these games are generally between 65% - 80% (except for certain types of horror and survival games), which is a I can't find any reliable source for this statistic in the form of a study. It’s basically received wisdom based on consensus everywhere in the RPG design space, and also in video games (the designers of X-Com refer to it, for example). If you reverse-engineer the success mechanics of pretty much all the most popular tabletops (including popular video games), this number consistently arises in conjunction with what’s considered the odds of clean success. chance of success typically needed for players to feel like they have a fair shake against random odds. .

On the flip side, a 7-9 result happens 41.67% of the time. This means I can't gauge the consequences for most rolls in the game, because most rolls will involve some form of GM fiat.

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Finally, a 6- result also happens 41.67% of the time. These are the sort of rolls where I can't gauge the consequences at all, as it's entirely up to GM fiat (it triggers a GM move). A few moves have more predictable exceptions, but with the exception of Take Watch, they all give the GM some latitude to fiat the result:

• Last Breath prescribes a 6- as basically your death is inevitable, but the when is left up to GM fiat.
• Take Watch prescribes what is effectively a surprise round. (So this one is not up to GM fiat.)
• Carouse just gives some guidelines for what a miss might look like, but still leaves it up to GM fiat.
• Recruit structures the "miss" to some degree but still largely requires GM fiat depending on the player's choice.

So overall, that's an 83.34% chance that I can't gauge the consequences of my action in any given unmodified roll in Dungeon Wold. Even if I'm an expert at what I do (say I have a +2), then that improves to a 58.34% chance, which is still more than half the time that my rolls have unforeseeable consequences.

“Failure” in Dungeon World

A 6- really boils down to either a "miss" as prescribed by the move, or a partial success with more negative consequences as prescribed by the GM. Either way, this is the least desirable of all the possible outcomes from the point of view of a player who wants to gauge the chance of success of their action before they take it.

That is, such a player would rather have a foreseeable outcome (which is the case in a handful of partial successes on a 7 through 9) than a partial success that's put entirely in the hands of the GM.

In this case, a 6- serves as a mechanism for the GM to make one of their moves. But of these moves, on a 6-, the move must always be "hard," which means it has immediate negative consequences: after all, in Dungeon World, "the world is a very dangerous place." Such hard moves are contrasted with "soft" in that soft is "not all that bad" and not immediate, so then hard moves must be "bad" and most definitely immediate (e.g., dealing damage).

All of this to say that a 6- is a less predictable version of success at a cost, which widens the gulf of unpredictability of any given roll in DW by a considerable percent, and the closest thing the game has to genuine failure.

Some Takeaways

I don't think it's a failing of PbtA games that to achieve a clean success is so difficult, on average. After all, part of the design philosophy of the PbtA is to "fail forward," and ensure that every roll is interesting, rather than just a binary pass-fail result. This is why most rolls result in success at a cost in these types of games.

In designing OSR+, however, I didn't want to burden the entire system with that much interestingness. Having played PbtA games, I came to the conclusion that I wanted the option to make rolls interesting while still being able to keep other rolls boring, in the sense that they're very predictable and straightforward, and don't require GM fiat. This is why we have success checks in OSR+ as a type of roll you can use instead of opposed or unopposed rolls, if you want to "measure success."

The option to use one of these three interchangeably when making resolutions gives the GM the flexibility to set the pace of the narrative as well as surface tension in the narrative as he sees fit, which understandably is a departure from the point of view of PbtA games, which generally seek to disempower the GM and distribute his authority to everyone at the table.