"But that possibility didn't happen, so I can eliminate it from my calculations now."

"If that were true, you could eliminate the Carissa-Ione-Pilar-Asmodia possibility, since it didn't happen, and leave Conspiracy putting 100% on Carissa-Ione-Pilar again, and then Ordinary would also put 100% on that since everything else didn't happen."

"I'm confused.  Why can't I just say that Conspiracy gets to allocate 100% of its probability to whatever happened, but Ordinary doesn't?"

"I'm not sure what is going to be Lawful but I can very strongly guess that will not be what Lawfulness looks like."

"With ninety-nine point nine nine percent probability."

"There's a saying out of dath ilan, don't criticize people for using what you think are the wrong general principles for arriving to their correct answer; if you're right that they're using the wrong general principles, you can wait for an occasion when they're wrong, and point out the error then."

"So I'm not going to criticize you for claiming you could make ten thousand statements about that strong, as confident as you are now, and be wrong on average about once."

"I'll wait until you're actually wrong.  Which will take, say, somewhere about four more occasions.  Fewer if I actively try to lure you into it."

"I await your lures."

If she never flirts with Keltham, Sevar will know the tropes aren't real.

Meritxell feels that Asmodia doesn't even want Keltham and is just flirting with him to mess with Meritxell, and Meritxell is going to destroy her for it. Somehow.

A watching Security thinks Meritxell could stand to learn a valuable life lesson about the importance of visibly flirting literally at all.

Well someone obviously came to a fast decision about whether she wants to be his nearly-ace harem member.  Or maybe, only about whether she might want to be; but sufficient to start flirting about it, at any rate.

"But yes, you aren't particularly allowed to reallocate the probability of observations after you observe them.  One way of thinking about it:  Probability of Carissa-Ione-Pilar given Conspiracy is meant to capture the probability that Keltham would assign if you asked him beforehand about what was likely to happen at lunch.  And all of the possible mutually-exclusive observations you can consider explicitly, need probabilities summing to at most 1.  The probability that exactly Carissa-Ione-Pilar go off at lunch, that Carissa-Ione-Pilar-Asmodia go off at lunch, and that nobody goes off at lunch, must sum to at most 1.  Realistically less than 1 because, say, I should've assigned some probability that, for example, just Ione and Pilar would run off, or that the whole lunch would be disrupted by a Nidal attack."

"This is why, especially at your stage of learning, we'd consider it a much more believable probability estimate, if you say in advance what will probably happen, compared to if you look back afterwards and come up with a reason why that event was clearly very predictable."

"If I'd thought in advance about the probabilities that Ostenso wizard academy would have any available books listing cleric spells, I could have considered the possibility that it would, and that it wouldn't, in an Ordinary world, and then considered the probability that Governance would need to stall me, in a Conspiracy world, versus having appropriately doctored books already made up.  If I'd done that in advance, I couldn't be influenced, either when thinking about the Ordinary world, or the Conspiracy world, by wanting to make a world give the 'correct' result, because I wouldn't know, in advance, which result I would observe."

"Since I didn't think that quickly, I had to go back and make up the probabilities afterwards.  And then there's a risk that, for example, maybe you don't want to believe in the Conspiracy world, so once you know that the real result is no-book, you're tempted to twist things around inside your mind and come up with a story for how the Conspiracy world would definitely have finished making up a doctored book of cleric spells by then, because they would anticipate my question and not want me to be suspicious about an absent book."

"If I make my prediction in advance, my mind will be less tempted to do that because I won't know that an absent book is the particular outcome that the Conspiracy world needs to dispredict in order for me to end up not believing that unpleasant thing."

"Dath ilani do have any skills for fighting that, for being able to come up with reasonable probabilities even after the fact; but those skills are difficult even for average dath ilani, which you frankly are not at this point.  You can ask two groups of medium-rank Keepers for their conditional probabilities, one group before and one group after they find out the real answer on some problem, and there'll be no significant systematic difference between the groups.  Because Keepers, that's why.  You would not find zero detectable difference between groups of dath ilani with around my age and intelligence levels, asked to say the likelihood that there'd be no book of cleric spells available, in the Conspiracy world, and in the Ordinary world, both before and after they actually got that result."

"Everyone gets trained in skills that partially protect against assigning-different-conditional-probabilities-to-outcomes-once-you-know-what-the-outcomes-are, but that's, like, diminishing the distortion by a factor of five, not driving the distortion down to undetectable levels.  That's the realm of, I would expect, sufficiently old devils, or gods - but definitely, it is known, Keepers rank four and up."

"Because - I would assume, and among other reasons - they practice really really hard until they stop doing it wrong, and not everybody has the time for that."

"So even I try to make my predictions in advance, if I remember and I'm not too lazy and it's important.  So you at this point should strongly, though not invincibly, question and distrust any probabilities for observations that you make up after seeing the answer."

"What's the screening like to become a Keeper," says Tonia, "are you allowed to know?"

"Be smarter than us, learn faster than us, be better at this particular stuff than us, be twenty times more naturally Lawful than I am, and my guess is that there are at the very least different tracks for Keepers who don't lean pretty heavily Good."

That's so disappointing and she doesn't bother hiding it. 

"We'll get there eventually," says Carissa with cheerful determination. "...not the Good part."

"I think once your Good people have enough Law to, you know, not end up being incredibly destructive and tearing through any social order they find themselves inside, there is frankly a lot to be said for having the people who keep custody of dangerous information, probably incredibly dangerous information, probably even more so in Golarion than in dath ilan, being people who innately lean towards defending alike the welfare of all sapient life.  Provided those people are actually making correct predictions about what defends sapient life from harm without a bunch of terrible second-order effects, and not being systematically wrong in audience-predictable directions like fictional Good supervillains.  There are, even I think, any places for Good in the universe, and that sure seems like one of them.  If you have enough Law."

Actually, why isn't Otolmens classified as Lawful Good?  Maybe ask Broom that at some point?

Carissa can think of counterarguments but isn't sure this is a point it's wise to argue. "Everyone in Hell is Evil and it works out all right? I guess we're lucky Asmodeus wants the universe to keep existing and have lots and lots of people who can grow into devils in it."

"Yeah, what does Asmodeus actually get out of it?  Or is he just the god of Lawful Evil people, who, if he fell into the system himself, would actually be Lawful Good, but like actual Lawful Good and not whatever passes for horrible chaos-infused 'Lawful Good' in Golarion?  I haven't actually heard any motives or plans attributed to Asmodeus except for Good ones like wanting Cheliax to have better technology and governance etcetera."

Broom is worried about the sheer bizarreness of what Keltham is ending up believing; it seems one plausible way that Keltham could end up planning some very great deed about whose consequences he is very mistaken.

"I mean, He wants more people to become devils, so he wants Cheliax to be prosperous and have a large population; He wants other kinds of god-resources that are harder to directly explain but I think having more people and Lawfuller and Eviller people helps - like, He can pick them as clerics, He can interpret them better. He likes contracts - I think just in their own right, a contract that enables something weird and complicated is inherently pleasing to Him, which I suspect is why a devil took time out of his day to help you with ours - I think He's actually Lawful Evil, though, He's just pursuing his own ends, but it happens you can do lots more with a rich and Lawful civilization than with a weak and stupid one. I guess the gods who are Good would want a Lawful Evil god who had selfish goals that Good approves of, so maybe there was some selection operating long before recorded history."

Makes sense.  Well, sort of.  Wanting people to be devils still sounds kind of Good unless you're doing something else with them?  But Keltham wants to get back to math.

"To put Asmodia's argument into symbols, we could rewrite," after a quick Prestidigitation, he should really hang two of those so he's not stuck constantly asking for help if he fails to catch one, "like so:"

P(Carissa-Ione-Pilar ◁ Conspiracy) = 1/2000
P(Carissa-Ione-Pilar-Asmodia ◁ Conspiracy) = 1/2000
P(Everything else  ◁ Conspiracy) = 1998/2000

"Because in fact, I would have maybe assigned something like a 0.1% probability, if I'd had to start listing possibilities in advance, that either of those groups would go off by themselves at that particular lunch."

"But this doesn't completely trash the Conspiracy theory, because you could say something very similar about the Ordinary World; an Ordinary World wouldn't have given me any more reason to think a group of girls would go off by themselves at that particular lunch.  Right?"

P(Carissa-Ione-Pilar ◁ Ordinary) = 1/220,000

"And so, I claim, we end up in the same place as before."

Concerned silent students!

Pilar raises a hand.  "I think I have something I'd say, even if I didn't know anything about the actual story?"

"So you think you can successfully correct for knowing the real answer?  I'll let you try your hand at it, and see what I think.  Go ahead."

"I have a strong sense that rules are being broken somewhere.  Why is Carissa-Ione-Pilar 1 in 220,000 in an ordinary world and 1 in 2000 in a conspiracy world?  What are the rules that say that part?"

"Simplicity itself:  In either an Ordinary world or a Conspiracy world, there is, from my perspective, a 0.1% chance that some group of girls will mysteriously vanish at lunchtime.  In an ordinary world, the further chance that this group is exactly Carissa-Ione-Pilar is 1 in 220, via picking from 12 then from 11 then from 10, and there's six possible ways to pick Carissa-Ione-Pilar in any order, that way, which works out to 1 in 220 probability.  If there is a dark government conspiracy, on the other hand, the group must clearly be either Carissa-Ione-Pilar or Carissa-Ione-Pilar-Asmodia, and for simplicity's sake we'll say that either case has equal probability."

"By what rules does one get from the dark government conspiracy to Carissa-Ione-Pilar, or for that matter, Carissa-Ione-Pilar-Asmodia?"