1) It's consistent with the way probability works.
2) It's consistent with the way Parson has used the bracer.
3) It's consistent with descriptions we've had of the bracer from other characters.
As I see it, the bracer is an ultimate Mathamancy artifact. It's great at doing math with odds. Therefore, it can automatically combine probabilities in the mathematically appropriate way - if you have three options, with probabilities A, B, and C, and each of those has sub-options, each with some probability of victory, it can automatically do all the math and say that the final probability of winning is [Something]. Or, if you ask it a question like "how many Archons does it take", it can instantly run the calculations for any number of archons.
It is able to do this for things other than battle calculations - since anything about which you're uncertain can be assigned a probability based on your uncertainty, questions about anything are fair game.
That part isn't controversial - I think everyone agrees that the bracer CAN do all those things. The question comes down to - what INFORMATION can it use as inputs to its calculations?
Obviously, it can't be omniscient. If it knew the future, it would give 0% or 100% as an answer to everything. But, it obviously knows more than what just Parson knows - after all, early in the story, Parson was asking it questions about units whose stats he didn't know.
So my preferred interpretation is that it can get the following information:
1) Whatever that Parson himself knows or thinks is relevant. That takes a little bit of thinkamancy, but it's not out of the ordinary - we've seen a lot of applications of "natural thinkamancy", and a worn item having access to its owners insight doesn't seem like it would be out of the blue. For this to be relevant, the bracer also needs to be able to turn Parson's intuitions into numbers - but that also makes sense, since it's supposed to be a Mathamancy artifact. It would give the sort of numbers that Parson WOULD come up with, IF he had infinite time, paper, and pencil.
2) Anything that is considered "basic knowledge" - the sort of stuff that any Erfworld unit would be popped with. So this lets it answer basic questions like "if a level 1 Warlord fights a level 2 stabber, who will win?"
Then, with these two inputs, it's able to calculate all the probabilities that we've seen, based on the rules of math and probability only.
This is consistent with its description as a mathamancy artifact - this interpretation doesn't have the bracer able to do any Predictamancy or Lookamancy (it doesn't get any knowledge of the future, or of anything in the present that's hidden). It does take a little bit of thinkamancy, but we've seen Natural Thinkamancy used pretty often to explain things like that.
This is consistent with numbers its given. For simple things that Parson's already thought a lot about, the bracer gives roughly the same numbers that Parson would. (Probability of success of a well-defined plan.)
It is consistent with the fact that the bracer HAS been wrong before. The incident with the gobwins - the bracer said that there should have been gobwins, but they weren't there. This would make sense if some of the inputs were wrong - if Parson hadn't considered the fact that someone would deliberately interfere with the gobwins. (This 'incorrect' answer COULD also be explained if the bracer is exquisitely sensitive to the details of how you word the question - if Parson wasn't actually asking the question he thought he was asking, and so the bracer didn't take into account information that it could have used had the question been better. However, I think this is unlikely - after all, the bracer communicates by subvocalization and reading thoughts/intent, like a unit being given orders, which makes it harder to argue that the exact phrasing is important.)
Importantly, this interpretation is consistent with how Parson uses the bracer. After a big fight and a long campaign, both of those AFTER Charlie gave Parson a bit of a bump about the bracer's abilities, I would find it hard to believe that Parson hasn't spent some time investigating its capabilities. It would be, in my mind, quite a plot hole if, a book down the line, there's another sequence of Parson "discovering" new Bracer abilities that he could have discovered earlier. He should have spent some time trying to exploit the rules, by now.
So yeah, that's how I think about the bracer. I think it's consistent and fits everything we've seen the bracer do, though that of course doesn't *prove* anything conclusively.
Responding directly to what some people before discussed:
It seems like anyone could just continue asking the bracer questions until you had a kind of brute-force outline of what's really going on.
Not necessarily. Asking any number of probabilistic questions can't give you more information than the bracer actually has available to generate answers. No amount of asking "What's the probability that this coin will land heads?" will give you anything better than "50%".
I would like to eventually see, in the text updates, some indication of what the bracer is not capable of.
I think we've had one example - the gobwins. The bracer said that they should have found gobwins by now; they didn't find the gobwins. That indicates that there ARE limitations to what it knows - that is, until the gobwins weren't gone for long enough for Parson to suspect something fishy, the bracer didn't suspect anything fishy either.
The bracer can clearly give probabilities of situations Parson doesn't fully understand. Its first noncombat application, whether it would be worth it for Charlie to end the Mathamancy deal to learn what happened to his Archons, how could Parson be expected to know what's going on there?
You can always, always, ALWAYS give a probabilistic answer to any question. The more information you have, the better the answer is - but even with very little information, you can still give an answer. It's just not a very useful one.
In that case, the bracer, at the very least, had the following information:
1) What actually happened to the Archons. Parson knew that.
2) What possible ways there were for Charlie to learn that information anyway. Parson could figure that decryption would eventually become known.
3) What COULD be done about it - or as much as Parson or Wanda knew on that matter.
Those alone would be enough to come up with pretty useful numbers for an answer, even if the bracer didn't know what Charlie intended to use the results for or what future questions he'd ask. (For both of those, my interpretation would involve the bracer using Parson's "best guesses").
how could the bracer know what is meant by a statement like 'behind the disappearance of?'
I'd guess it gets its instructions via natural thinkamancy from Parson; if Parson understands what he's asking, so does the bracer. Dwagons don't need to understand Language to follow orders issued in Language, because it's not the words that matter; as mentioned, good commanders can give orders without using words at all. Same thing would make sense here, I think. It interprets 'behind the disappearance of' however Parson intended it to be interpreted when he asked the question.
-Bracer has a thinkamancy-level link with Parson, able to alter it's calculations based upon his mental preferences, without the need for specific wording. (very impressive magic)
Hmm, I would disagree that this is very impressive magic. It's how orders work, in general. I'll quote the update where we learn this:
"Speaking or shouting the command will work, Lord," said Maggie, lurching a bit as she rounded the remains of the picnic and walked up beside him. Though he was not completely steady himself, he offered his right elbow and she grabbed it gratefully. "Not be- because they understand Language, but because it hhhelps you frame the intent in your mind. You see. Experienced-" she swallowed hard, or possibly hiccupped. "Excuse me. Experienced commanders can command stacks with few or no words. When you understand your command, the unit will. Yet another fo-horm of natural Thinkamancy, Lord."
So I would agree with the natural thinkamancy link, but would disagree that this is "very impressive magic".
I still see the Fate thing as a problem, especially if it is using Predictamancy (which is really the only thing that makes sense, given that it can answer and quantify distinctly non-mathematical questions).
Everything can be treated as a mathematical question. Seriously.
Just look at our world. People put "odds" on all sorts of things - you can make bets on sports, on politics, on everything under the sun. Lots of those things aren't fundamentally mathematical, but somewhere out there there's a bookie that has figured out the odds of the various possible outcomes, or thinks he has. Anything that has multiple possibilities, you can put an over/under on. There's absolutely nothing "fundamentally mathematical" about two people playing tennis with each other, and yet betfair odds predict winners fairly accurately.
So no, I don't think the bracer needs any predictomancy to do what it does; just mathamancy.
That's not predicting the future, that's the past. It either was Charlescomm or wasn't, and I don't see how that can be represented as a probability.
Again, I think I can refer you to the way probability works in our world. It represents uncertainty in your knowledge - and it doesn't matter whether that uncertainty is a fundamental part of the universe or not. If I ask you what's the probability that a coin LANDED on tails (and you didn't see the result), it'll give the same answer as asking whether it WILL land on tails (and the result didn't happen yet.)
...anyhow, gah! I always write forever about bracer stuff. I haven't been checking the board at all, and then when I get back first thing I see is a bracer discussion. Anyhow, hope some of this has been interesting for people, I don't claim to know the author's intent for the bracer but I *do* believe I have a pretty good understanding of probability.