# According to this math, looks like Exponent 6 routine test should be 3, not 4

I did some math on Routine tests, because the numbers were bothering me.

Excluding Exponent 6, the odds for passing a routine test range from as low as 50% to as high as 75% (for exponent 2, otherwise it’s as high as about 68%)

However, exponent 6 has only a 34.38% chance of passing an OB 4 test - dramatically lower than anything else. But, if the routine test were to be changed to OB 3, it would be a 65.63% chance of success. This is right in line with the same range as all of the other exponents.

I’m thinking of, for our games, just changing it to OB 3 for Exponent 6 tests (we have a Google Sheets custom character sheet, so it’d be a piece of cake to change this for us).

I thought I’d share my findings, and also ask if there’s a chance I’m missing something. Is there some reason that Exponent 6 should be uniquely disadvantaged for routine tests?

Edit: I suppose the unique disadvantage isn’t about routine tests, but difficult. An OB4 test is, statistically, difficult for Exponent 6, but it only counts as a routine. Exponent 6 has to struggle, uniquely, compared to all other exponents, to get difficult tests.

Not particularly, Exp 9 and 10 have a tougher time getting difficult tests, and Exp 3 and 8 don’t have it much easier.
And check out what happens if you make Ob 4 difficult for Exp 6 as you suggest- it becomes the easiest exponent to get difficult checks for.
Unfortunately I think some amount of this is inevitable given the granularity of the system, but the current numbers seem to be the best given that granularity.
In practice, I don’t think this is that big of a deal since there are so many sources of bonus dice and die penalties- if you have an Exp 6 skill and want an easier difficult check, find a way to get an extra die.

Exponent 5+ doesn’t need Routine tests to advance… so I’m a bit confused why this is an issue.

Oh. I just saw your edit. I suppose Difficult tests are a different beast.

As Ctrail says, It’s 12.5% chance to hit difficult with 3 dice vs. 10.9% to hit it with 6 dice. Pretty small. Really it’s 4 dice that are the outlier, with a 31.2% chance.

blushes a deep shade of red

Guys, I screwed up my math in an incredibly fundamental way. I, er, may have somehow failed in my progression of possible combinations (2, 4, 8, 16, etc). I… somehow skipped 256, and went straight to 512, and onwards.

I was wondering why my odds were getting weird, when calculating later numbers. Erm. Sorry XD It’s fixed now.

Your spreadsheet is still looking at the upper end of routine difficulty. Why? That’s not an important value. If you want a routine test you can always go for Ob 1.

Actually, on the left is the upper end of routine difficulty, and on the right is the lower end of difficult difficulty. It’s to see more easily the barrier of probability between the two. I’d also like to add a third column for the highest end of difficult (that is, equal to the OB).

It’s a spreadsheet in progress, and it’s presently an absolutely hideous mess (Edit: I now have a prettier one, see bottom)

For difficult tests… Exponents 1 and 2, the odds are kind of weird, but that makes sense, there’s just not a lot of dice to work with. Exponent 10’s probability tanks to a paltry 5% - but as the left probabilities show, if it were an OB 7 instead of 8, for difficult, it’d be 17%. That’s much more in line with the rest of them.

Excluding the weird exponents (1, 2, and 10), the average chance of success for the easiest Difficult test is 17.08% Including them, the average chance for success is (oddly) exactly 20.00%.

I get the impression, looking at a lot of the numbers chosen for Burning Wheel, that the challenges assigned are designed according to a gut impression of balance, rather than the numbers.

The reason I started with Routine tests is because, according to the book (okay, I say that, but I can’t find it…) you’re supposed to be able to usually pass routine tests, and the simple fact is, you can’t. With the exception of Exponents 1 and 4, all other exponents have, at best, a 50% chance of success at a routine test.

Also, here’s a much, much prettier arrangement of data. I turned the old sheet into a “raw data” sheet, and the new one is actually readable, and has a “conclusions” section: https://docs.google.com/spreadsheets/d/1Jr4ecswn3Tzc3wT5hhUt5JawF6BEb0D0wOOIzOui_1s/edit?usp=sharing

Thanks Khana. Your math seems accurate, and I’m sure your chart will be appreciated by those who agree a system number change is in order here for their games.

Thanks! I hope it’s useful for everyone, even those who don’t want to tweak the numbers.

I’ll also go and double check how to do the math when the probability of a result isn’t 50% (black exponents are so easy that way!), and then I’ll make identical sheets in the document for Grey and White shade, for funsies.

Strangely, I’ve always gotten the opposite impression. I know Luke has shared that math went into deciding the breakpoints (https://www.burningwheel.com/forum/showthread.php?5098-Obstacle-vs-Number-of-Dice-Rolled) although he hasn’t shared what the criteria was.

-I couldn’t find anything in the book saying that you should usually be able to pass Routine tests either. I don’t get the impression that it was ever intended that you could.
-Your table has Ob 2 as a difficult test for 3 dice, it should be routine.
-I can see two simple rules that could have been used to get the breakpoint between routine and difficult. The one I suspect is correct is that if the chance of success is 1/3 or greater it’s routine, and if it’s less it’s difficult. This rule covers all cases except one die, which is a special case which counts as both routine and challenging for obvious reasons, and nine and ten dice which are a little harder for some reason. Another possibility is that the breakpoint happens at the lowest obstacle which still allows difficult checks to be passed more than 8% of the time, which works for all but ten dice. I suspect Ob 7 should be routine for 10 dice, but breaking the chart into four tiers instead of three just for that one case was not considered worth the extra complication,

You can use the BINOMDIST function in your spreadsheet. You’ll want something like BINOMDIST(Dice-Ob, Dice, .5, TRUE), and change the .5 to 1/3 or 1/6. (i.e. counting failures, not successes)

As number of dice go up the odds of hitting challenging and difficult tests goes down, mostly.

You can’t really say that routine tests become harder. The hardest routine tests are harder, but Ob 2 is Ob 2. It’s routine whether you’re rolling 6 dice or 600 dice. The more dice you have the easier those routine tests get. And there’s no incentive like for challenging and difficult to keep it hard for a better test to mark off. Once you know you’re rolling routine you want to just pile on dice.

So any given routine test get easier as you gain dice, and routine tests generally get easier, but some tests that would have been something else become routine. That’s the more useful way to look at it.

#1. After half an hour of digging, I give up. I can’t find it anywhere.
#2. Oops. I put the colour wrong on the table, but the math listed the correct difficulty for exponent 3 (in the Raw Data page, and in the breakdowns below the table). I’ve fixed the colour, thank you.
#3. Could be. For my part, it’s a very different mental meaning for the words “difficult” and “routine,” but hey, that’s okay

Oh my god, that’s amazingly helpful. That’s so much better than doing it manually! (At least I learned the math some)

You are correct - I wasn’t really trying to consider the difficulty of routine tests, for the reasons you said. I was more trying to look at the threshold from routine into difficult. The hardest possible Routine test, compared to the easiest possible Difficult test.

Obviously, for anyone with at least an exponent 2, OB 1 tests are pretty easy. They start at 75% chance of success and ramp up fast. Routine for everyone, no problem. No arguments.

However, saying that 34% chance of success is just too good of odds to count as difficult, your odds have to tank to 11% in order for a test to qualify as difficult (in the case of exponent 6, obstacles 4 and 5 respectively)… aii, that’s rough.

Granted, I’m coming from D&D (heavily modified, it really no longer suits us), so instinctively, I’m attached to the idea of failure as… well… failure. Whereas, in Burning Wheel, failure can still be a success, just with a hitch. Like, someone with a B10 skill, he could fail an OB1 test, but it makes more sense to say that someone bumped into him at a critical moment, messing up whatever he was doing, rather than him legitimately failing a task of that level of simplicity.

And as a GM (we’re all new to BW, and I love it most, so I’m GMing), I find myself giving a lot of grace with failures of small margins, especially with higher exponents. A B7 forte skill, she pushes herself absolutely ridiculously to keep walking when, by all means, she should pass out. I set the OB at 6, she gets 5 successes, I say she starts nodding off on her feet and smashing into trees - it’s up to the other player to convince her to sleep, else she’s going to get hurt.

I have to say, that was one of the most hilarious RP moments I’ve ever seen. She really got into it! (Smash I’m awake now! I’m totally… definitely… smash AWAKE!)

So part of it will just be… refining my concept of success a bit. Mind, I have no idea if I’m doing it right.

Maybe take difficult to mean outside your comfort zone, where failure and growth are both very likely possibiliites?
Also, remember Artha. This is a place you are heavily incentivized to engage with the reward system.
Also, it’s a reason to fight on when injured instead of retreating!

But if someone messes you up at a critical moment and you fail at the task you were doing, that is legitimate failure. Failure doesn’t mean you are incompetent- it could mean you ran into particularly bad complications. That’s why we roll for an Ob 1 test even for a B10 skill. It’s not to determine whether that character is skilled- we know they are, they have a B10 skill. What we are trying to determine is whether this is the one case in a thousand where everything goes wrong anyways. At least that’s how I’d interpret an unlikely failure by a skilled character. I’d only interpret a failure as due to incompetence if the skill was really low, and even then it seems like one that’s not always fun to go with…

Edit: One more thing I noticed- Ob 6 is crazy high. Ob 3 is difficult, Ob 6 is heroic. Are people going to be telling stories for years to come about how hard that character pushed themselves? I don’t know the context, maybe they would. But that one example seemed so extreme that it makes me wonder, if failure seems too common, double check that you aren’t setting obstacles really high.

I’ll emphasize again: routine, difficult, and challenging are terms that have meaning only for advancement and are derived solely from dice and Ob. Don’t let the names fool you; they’re not about whether the task is routine or difficult. The actual difficulty of the task, the Ob, must be set independent of skill or the system breaks down. Having higher skill doesn’t mean tasks that should be easy get harder. It means that more and more tasks are routine, which means you have trouble getting difficult and challenging tasks, which means if you keep doing the same things you do them safely but you don’t advance.

High skill means advancement gets harder and harder. You have to risk failure to get better, and yes, that means by the odds you will fail, and it will hurt. But that’s progress.

Also, remember that BW is not a game where you roll your raw skill against the Obstacle. Part of the game after the roleplaying is manipulating the dice so you get the test you want. Need a challenging test? Use your skill. Maybe wounded, so you have fewer dice to roll. Maybe what you really want is definite success and advancement can be saved for later? Use FoRKs, get help, start with a linked test for +1D, scrounge for advantages. You can have a ton of extra dice, often. That’s not cheating or power gaming or some terrible thing. That is exactly how BW is meant to be played.

In fact, take a look at the rules for help. You advance based on your skill vs. the Ob, not the actual dice rolled. That’s huge! Someone’s facing an Ob 3 test? It doesn’t matter if the guy’s got W8 skill and could do it with his eyes closed. If you help with your paltry B2, you get to log a difficult test. Often the person actually testing isn’t getting much out of the test, advancement-wise; it’s all the helpers who cash in.

Don’t get stuck on numbers for advancement. They matter less than you think. (On the other hand, combinatorics for calculating actual odds of success? Pretty useful! It’s good to know whether your have a snowball’s chance in hell or whether it’s time to plead for all help, desperately FoRK, blow all your artha, and pray to the random number gods!)

You’re right. This whole process seems to involve a great deal of trying to smash existing conceptions, rather than just learning a system. When I learned D&D, even though it was my first tabletop RPG, I still had this problem, but it was in bringing in expectations from video games. Now, rather than video games, it’s D&D influencing me.

Pretty much every time I give an obstacle, I look at the list of what the OBs mean, and go from there (like the OB 6, in my example above. It was referred to as “ludicrously difficult,” and I thought, “That sounds right.”)

This is one of the things that made me fall in love with BW, pretty much as soon as I found it. In D&D, we’re always scrambling for success - no matter what, we HAVE to succeed at everything we do. Failure hurts. BW failure doesn’t hurt nearly so bad - in D&D, it’s usually regarded as a complete, unmitigated failure, whereas in BW, failure can be a lot of fun.

This last game, I had a player argue with me about an OB - he was saying it was too easy! He was telling me about how his character should, because of X, Y, and Z reasons, have absolutely no chance of succeeding, but she’s going to try her damnedest anyway, because that’s who she is.

I just had to pause and marvel at the guy, who I’ve known and gamed with for years. When it came to important things, he always had to succeed. And now? Now he was embracing failure. It was beautiful.

Awesome.

One, BW failure should hurt. It needs to have teeth and move you away from your Beliefs or it doesn’t matter. What it shouldn’t do is stymie the game. It can leave avenues open but make them harder, or it can close off one and open another, but failure should never be a wall. One thing I stole from *World games is the rough idea of soft and hard moves. Not all failures should be catastrophic, and I tend to escalate the consequences in response to either a lot of failures or a situation that really seems do or die. Titrate the failure to the situation. And if failure just doesn’t matter, don’t roll; Say Yes.

Two, Ob 6 is impossible for all but the most X. Ob 6 Forte is going to be impossible for any but the most conditioned and tough Men, and it’s going to be damn hard for them. The Ob 1-3 is really where most things should fall, and Ob 3 is hard. Ob 6 is heroic and the stuff of stories.

I get a different feel for failures in Burning Wheel, as compared to D&D. It’s not that the BW failures don’t hurt, but it’s that they don’t… well, really hurt. From the way we read the rules, and have since run them, we’ve made BW failures a part of the story, rather than a roadblock. In D&D, failure hurts bad because it’s simple, unmitigated failure, on part of the character. Technically, according to D&D rules, I can’t get better than 95% accuracy against the broad side of a barn. If I roll to smash a hammer into the broad side of a barn, and I roll a nat 1, then - no matter how amazingly skilled and capable my character is supposed to be - somehow, my character screwed up this simple task and managed to miss the broad side of the barn.

In BW, it doesn’t work that way. Failure doesn’t mean “failure,” exactly, it means things just did not go according to plan. Maybe you overestimated the strength of that wall, and in smashing it down, managed to cut your arms up something fierce on the splinters. Or maybe your hammer got stuck in the wall. Either way, these things aren’t due to a failure on the part of the character - you can fail, and still be awesome, even though you’re now nursing a wound, or delayed by trying to get your hammer back.

That’s all I mean by BW failures not hurting the same way. Failures can still suck, but they suck in a way that makes sense for the characters and situation, which makes them feel real, and not like an arbitrary dice thing.

This mindset has completely transformed our gaming, and not just in BW. Like I said, D&D has been failing us for a while, so for our other games, we said “screw it!” to the normal rules, and have incorporated BW’s failure style as much as we can.

Sounds like I’ve been generally doing it almost right, then. I’ve run it more 1-4, rather than 1-3, but I’ve only used 4 when it should be really expected that almost no one could succeed. In this case, with a 6, it was more of a, “Erm, this should realistically be kind of impossible. Well, your forte is 7, so I guess if anyone has a chance, it’s you.”

I won’t deny that the difficulty scale for BW is what we’ve struggled with the most. We’re wanting to convert a very long running game to a BW “skeleton,” if you will, and for it, we’re using the magic burner to create the magic system that we’ve envisioned for it, rather than the butchered, hodge-podge mess of the D&D magic system we’ve been using. The single biggest challenge we’ve faced so far is trying to capture the difficulty curve. That’s the inspiration for making the probability sheet, actually. We’re absolutely loving the “test out the rules” BW game that I’ve been running, and our whole group is psyched to try to transfer the other game over. It’s going to be a very delicate process, and hopefully it goes well.