"You shouldn't be able to be better off for points by not guessing at all, though."

"You should get the most possible points if you are - Nethys, and always give the right answer with perfect confidence, and the least possible points if you are .....Zon-Nethys, and always give the wrong answer with perfect confidence."

"Nethys still thinks in probabilities, they're just more extreme ones takaral."

(Ione does not appear to notice that she has said anything unusual.)

"...right."

"Well, those are all interesting rules, but the idea that two different people who give the same numbers should get the same points, seems to imply that everybody is, in some sense, using the same scale, in which case, that scale seems like it should maybe mean something.  The same way that, inside a language, the same sounds mostly mean pretty similar things to different people."

"But let's back up.  We can imagine that we've got this game which awards more points to people who put higher numbers on things that did happen, and lower numbers on things that don't happen.  You can't be better off by not guessing.  We don't have the Law for it, or any such thing, we just built a game that encourages numbers to go up or down in a way that matches what does and doesn't happen.  We play that game for a while, turns out somebody is really good at it, say Yaisa has the best score by far.  What" human capital "person-with-a-valuable-skill do we now have in the form of Hypothetical Yaisa?  Maybe Hypothetical Yaisa is just good at playing a strange game but the skills in that game aren't useful for anything else."

"I mean," says Yaisa, "I can branch out to predicting merchant ships and make a lot of money, if I've got a gift for something real."

"Who says the numbers you learned to assign are the ones that merchants need to decide whether to send out a ship?  You're slapping 3s on this and 9s on that and the merchant is like, 'uh, but do I send this ship or not' and you're like 'well I don't know what the numbers mean, I just learned what kind of number-assigning gets me a high score'."

"Well, if Yaisa can't explain herself at all, we can check how often she's right when she says 9, and then the merchant can do the translation from 9s to profits himself."

"These how-often-she's-right numbers sound quite interesting, maybe we should actually just be using them directly instead of the 12-point scale?  I mean, if we've got to translate the original scale into how-often-she's-right numbers, maybe we can skip the extra step and have the game just be about those?  Though first, right-oftenness numbers would have to be a thing.  Can you say more?"

"Well, it's kind of what we did with the gods prediction, right, 'one third' or 'one quarter', except wars with gods don't happen often enough you can figure out who is good at it, but if someone predicts whether a ship will come back, and if they say 'it'll come back a quarter of the time' and if they say that of four ships one comes back, then that's very valuable, pretty much as good as soothsayers used to be anyway."

"Even if something didn't happen very often, let's say a Nidal invasion instead of that other thing, I might go to the person who had a really good record about ships.  I mean, it might not be optimal, but at the very least they'd have a bunch of experience with how to hone and slice anything down to the difference between one-third and one-fourth.  And they'd answer in numbers that meant that, instead of saying 3 or 9 on a 12-point scale and then you've got to pause and ask them for a hundred predictions like that so you can even figure out what a 3 or a 9 mean."

"Well, anyways, let's say that in this game you give a number from 0 to 100, and those numbers are supposed to directly represent the chances out of 100.  If something happens 1 time in 4, you say 25, because something that happens 1 time in 4 will also happen 25 times out of 100."

"How do you score those numbers from 0 to 100?"

"...when it happens, you give them points or deduct points in proportion to how likely they said it was. So....if they said 25, and it happened, deduct 25 points? And if they said 25, and it didn't, add 25 points?"

"And if they said 24, and it didn't, add 24 points?"

"Nah, 26, because you should get more points for a more correct prediction."

So apparently his brain just registered a reluctance to shoot down his girlfriend too cruelly, and wow does that impulse need to get poisoned and handed off to the Surreptitious Head Removers, not just because entire integrity of the teaching process, but also because Keltham has ever met Carissa Sevar and if she could read his mind about that she would be cometary-impact levels of sad and possibly angry.

"Interesting, interesting.  Well, Carissa, want to play a few rounds with me of predict-if-the-coin-lands-Abrogail-twice-in-a-row?  It's a pretty simple game, on each round, we write down our numbers, Asmodia spins the coin twice, and if it's Abrogail both times that's a yes-event, and otherwise a no-event.  Which we also mark down.  After 12 rounds we reveal our numbers, score ourselves using your rule, and whoever has the highest score wins.  Anyone else in class is also welcome to play along."

"- sure." She's pretty sure that all guesses are equally good if you know nothing, which seems right, but maybe he's making a deeper point. 

Right then.  Here is the coin, Asmodia, this isn't even a loan you're just holding my coin.  Let's start.

Keltham writes down some numbers, not particularly showing them to anyone per se, just yet.

Ione writes down some numbers!  They're all 25s.

Pilar is actually going to try to guess those coin-spins because, like, also oracle?  25 or 75 depending on which she expects to happen next.  She's not doing too well so far but maybe she'll get the hang of it.

25, 25, 25, 25. 

Pilar's curse says no.

He didn't say not to cheat!  What manner of defective Chaotic Good oracular curse is this?

Time for everybody to add up their scores!  Double-Abrogail came up twice in the 12 rounds.

So, round 1, +25 points, round 2, +25 points, round 3, which is the first double-Queen, -25 points, it's obviously going to work out to +200 points at the end and also she's an idiot and is embarrassed to reveal what she wrote, maybe nobody will ask her.

She guessed neither of the two double-Queens, and also got -25 points the three times she falsely foretold them, so 5*-25 + 7*+25 = +50 points.  She probably just needs practice.

On the last round Carissa had an idea, and wrote a 0. 50 points if she's right, and -50 if she's wrong, but she's right more often than not.

Which is 225, on the whole, because the last one isn't an Abrogail.