"I guess we'll just have to wait and see what happens tomorrow at orientation."

After the train arrives in Hope City, Edwin disembarks and checks into his inn. Maxwell follows him, checking into the same inn, having... already booked a room there as well?

Edwin doesn't try to figure out whether Maxwell went to the same inn as him deliberately. He collapses into bed.

Orientation day! 

The gates to Hope's Peak Academy are still barred (She checked! Of course she did!). Which means she's got about—let's see, 2 hours to burn before orientation begins.

Eden wanders for a bit, circumnavigating around campus outskirts and meandering through the local shops. After all, since she'll be living here for a while, it's only proper that she familiarize herself with the community. She purchases a few trinkets here and there—Ooh, a pack of scented candles!—as well as a pastrami sandwich from a deli. She chats up the clerk for a while, before heading back towards Hope's Peak entrance.

She spots another prospective student sitting at a table outside the academy, gazing at some sort of notebook. She sidles up to him and sits next to him.

"Whatcha reading?"

"Oh, numbers, numbers, numbers."

"What sorts of numbers?"

Didn't get the joke, it seems. That's ok.

"Mm, just working on one of my side projects."

Edwin sighs, and launches into a rehearsed explanation.

"Pi is infinitely long, which means it must necessarily contain every possible sequence of numbers. These numbers can then be translated, using a simple function, into text. This would contain everything ever written in human history: the full works of William Shakespeare," ("such as Hamlet," he resists the urge to say), "Fermat's original proof of his last theorem, the lost works of Homer, or even things yet to be written, future scientific discoveries, great works of literature, and so on."

He pauses for breath.

"I'm looking into tapping the potential knowledge contained within pi, although I haven't been seeing much hope: the most promising avenue of research are probabilistic tests for discernment, but progress on that has been slow, and the disjunctivity proofs have been eluding me as well..."

She blinks.

"Well, I didn't quite catch all that, but it sounds rather interesting, and the best of luck to you. 

So you're also a student at Hope's Peak? I take it you're the Ultimate Mathematician, or something of that sort, then?"

While she's talking, she takes a pastry out of her bag and offers it to him.

"Scone?"

"...is it poisoned?"

...it's possible Maxwell is rubbing off too much on him. 

"Never mind." He takes the scone and bites into it.

"Yes, I am the ULTIMATE MATHEMATICIAN. Edwin."

...

He takes another bite

"This scone is incredible."

"Lots of butter, that's the secret. Oh, and, moving quickly.

Eden Baker, pleased to meet you. Ultimate Baker."

"Appropriate name."

"You know, they say your family name used to come from what you did. I like to think I have some of that Baker blood in me."

While most of each cohort is filled by students who are scouted out by direct observation of their skills, there is one particular Ultimate Talent which Hope's Peak identifies with a different method.

Each year, the Ultimate Lucky Student is selected by lottery. In a way, it's the most pure test possible: you become the Ultimate Lucky Student if and only if you're lucky enough to be the Ultimate Lucky Student.

Gustavo is not himself the Ultimate Lucky Student, but he is looking for the Ultimate Lucky Student. While the list of Ultimate Talents for this year hasn't been publicized yet, there's almost always an Ultimate Lucky Student. And, as the Ultimate Forecaster, Gustavo bets he can identify them in advance.

Gustavo leans against a wall, listening closely to all students who pass by. There's still a couple hours before they're due to meet for orientation.

There are many keys to being a successful forecaster. But the most important one, Gustavo knows, is to always stay ahead of the competition. You can't be satisfied with one successful forecast: as soon as you make one prediction, you have to be ready to extrapolate and answer the next question. And luck, Gustavo predicts with 95% credence, will be a key contributing factor to many further questions. In the past, he's almost never found luck to be a very helpful consideration—but events at Hope's Peak are a different distribution, and it would be beneath Gustavo's pride to stick to old methods in a new situation.

Footsteps. He begins internally weighing the counterfactual odds from the scenario where he hadn't just observed strong evidence that this person would be attending Hope's Peak. There was... about a 40% chance they'd be chosen. Not the Ultimate Lucky Student. Hope's Peak hadn't ever explained precisely how they determined the random pool, but they do always say that the Ultimate Lucky Student is selected from a group of over a million candidates. So Gustavo's looking for someone who had a one-in-a-million or lower probability of being selected to attend Hope's Peak.

Gustavo continues waiting.

After a few minutes, another student walks by. Once again, nowhere near the one-in-a-million odds he was looking for.

There's not really that much point in narrowing in on a number, here, when it's about a counterfactual situation anyways and he can't check his calibration later. But he doesn't have anything better to do. He's feeling... 95%?

He tosses it around in his head a little longer. Isn't 95% kind of high? Is that really the number he'd've gone with, if he'd gotten the chance to consider it in advance?

...What do you mean, 100%?

Emma takes a deep breath. Ok, it's 9 AM, so she steps out to the gates, and, yeah, they're open now. They were closed when she got there, so she just... skulked around awkwardly near a building, trying her best not to look out of place and like she was doing something. (A task she likely failed at, but, anyways. Not that it matters.)

What does she see?

There's a sign directing her to an auditorium for the beginning of orientation.

Ah.

Well, alright then. She navigates over to the auditorium, enters, and... takes a seat? Grabs a pamphlet, if that's available? Schools really like giving out pamphlets at orientation.