It's not the ANSWERS that prove the Bracer has outside info, in addition to as Parson said the ability to "predict the future". The QUESTIONS THE BRACER IS ANSWERING is proof that it has info that neither Parson nor GK has.
No. You can answer ANY PROPERLY PHRASED QUESTION with a probability, no matter how low information you have on it.
This is a prime example: "Tell me the odds that learning what happened to my Archons right now will be worth giving up those calculations in the future." - Not only has to account for the world situation outside GK's sight, but predictomancy on odds Parson and Charlie will stay alive long enough to do the calcs.
No. Accounting for those things will give you more accurate answers. You can give a probability without accounting for any of it.
Example from real life: suppose I see two players playing chess. No further information - I can put a 52% probability on white winning, 48% on black winning.
Then I find out that Black is Kasparov, and White is my grandfather. Hey, now I put the probability of Black winning as 99%.
Same question, different information, different answers, both equally valid given the information at the time provided.
And let's look at your example. " His bracer put it at a 98 percent chance that the Archons should have spotted some Gobwins in the mountains or Sizemore found some below ground by now. They'd either rolled a critical fumble, or something weird was going on." Key word is SHOULD. Parson makes it pretty clear he's not asking what WILL the Archons and Sizemore find, but what they should they have found. The normal odds of that happening.
Right, and the "normal odds" of it happening depend on a multitude of factors, including what other sides are doing. If Parson asks "hey, what's the chance of us finding Gobwins this way" and the Bracer knows about Charlie, then it would put really low odds, because it would know Charlie's involved.
But it didn't. The answer to the question was 98% - it was extremely likely for them to find Gobwins. They didn't - therefore, there was information the bracer was missing.
Are you saying that Parson specifically told it to disregard information it had when making that calculation? The quote was "His bracer put it at a 98 percent chance that the Archons should have spotted some Gobwins in the mountains or Sizemore found some below ground by now." Not "should have found some if there was nothing fishy going on." Not "should have found some if nobody interferes." Just "should have found some." No specific information being removed from the calculation.
The next statements "One thing he never volunteered in these meetings was that the bracer gave a 78% likelihood that there was something fishy going on with the lack of Gobwins and prevalence of Marbits. And if there was, then there was a better than 92% chance that the agency behind it was Charlescomm." indicate the Bracer is indeed able to use info outside GK.
No, it does not. You can answer a probability question with any amount of information, from zero to perfect information. The more information goes in to the calculation, the more useful it is. But you cannot find out the usefulness by just looking at the answer, unless that answer is 0 or 100%.
How would the Bracer calculate the odds of "something fishy" unless it had info that GK didn't have?
By using whatever info GK did have. (Which is substantial. GK knows Gobwin spawn rates. Parson can easily find out a number of things about Gobwin mentality from Sizemore, Wanda, who have been around and worked with Gobwins. He can probably account for all the non-fishy ways that they might have missed Gobwins - thus, what remains is fishy. )
That it was more likely to be Charlie than say the Tardy Elves hanging around, Jetstone covertly tunneling the area, the Marbits themselves claiming the mountains as "natural territory", or some other detail the authors haven't given us yet? The bracer couldn't begin to calc those odds unless it had info that GK and Parson didn't.
No, it could. There's a laundry list of things it MIGHT be - but, in the end, the only agency around that's really LIKELY to do something tricky like that is Charlescomm. That is a conclusion that might happily have been derived from "rulebook + Parson" knowledge.
Heck, If the bracer knew substantially more info than GK and Parson did - such as info about Charlie - it wouldn't be giving "72" or "92" for "something fishy" or "Charlie". If it knew why the Gobwins were gone, it would answer either 0 or 100%. It's not a hard question to answer if you have priveleged information about Gobwins.