"This is actually a game theory problem. If you're interested, you can read some related Muggle books."
But there was no response from Terry, only soft breathing.
He was already asleep; after a whole day of excitement, children his age would fall asleep the moment their heads hit the pillow.
Lucien closed the book and turned to look out the window. From this room, he had a perfect view of the Forbidden Forest.
The Forbidden Forest, right next to Hogwarts, was home to a large number of magical creatures.
There were Thestrals, visible only to those who had witnessed death; massive Acromantulas; Unicorns, which were Tom's blood-replenishing packs; and Centaurs, skilled in divination…
In the future, I want to specialize in the magical creature Transfiguration field, so I will inevitably need to observe these creatures. The Forbidden Forest is a good place to start.
However, I must first ensure my own safety. Spells are one aspect, and the proper potions must also be prepared. And the travel between the castle and the Forbidden Forest…
He turned to look at Terry on the bed, confirming that he was sound asleep.
Lucien turned back and continued to gaze toward the Forbidden Forest.
"Lumen."
A faint golden figure appeared directly in front of him.
The beautiful Quilin happily leapt into the air; it had been cooped up all day.
Lucien had kept it in the system's pet space all day. Although the system claimed there were mountains and water in that space, with Little Quilin as the only living creature, it was easy for it to grow bored and restless.
Gently stroking Lumen's head, Lucien fell into thought.
Qilins are born with the ability to Apparate, making them the perfect "transportation tool" for rushing to places or making a quick escape.
However, I don't quite remember if Apparition and similar magic are forbidden within Hogwarts Castle.
Thinking of this, Lucien sent a thought directly to Lumen:
"Try it and see if you can still Apparate."
The talent for telepathic communication let Lumen immediately understand his master's command.
In an instant, the little Quilin vanished before Lucien's eyes.
Before he could even blink, it reappeared.
"Master, it worked!"
A childlike voice echoed directly in Lucien's mind.
Lucien smiled, a hint of joy flashing in his eyes.
"Very good! By the way, where did you just go?"
Another childlike voice echoed in Lucien's mind: "Home!"
Lucien nodded and rubbed Lumen's head again in praise.
Hmm, there are most likely still restrictions within the castle. Otherwise, a school cultivating the future of all British wizards wouldn't just allow villains to come and go freely with Apparition and similar magic, would it?
Lucien believed the school's four founders, the legendary wizards of their age, would never have overlooked such safety concerns.
It must be that a Quilin's innate magic is fundamentally different from a wizard's.
After all, there are countless magical creatures in the wizarding world, each with its own unique talents. Wizards have never been able to fully analyze their abilities.
Moreover, Lumen was not an ordinary Qilin; it belonged to the true divine beast lineage.
It was entirely plausible that it wasn't subject to Hogwarts' restrictions and possessed extraordinary powers.
Lucien recalled Lumen's movement when it Apparated just now and realized it was completely unlike the toilet-flush-like vanishing that accompanied a wizard's Apparition.
The Quilin seemed to merge directly into space, the entire process natural and swift.
Indeed, the magic of wizards and magical creatures was quite different.
He looked down at Lumen, whose large golden-red eyes were fixed on him. The short horns had not yet grown on its forehead—only two slightly raised bumps.
Lumen is still too young. Even as a divine beast, its ability to protect itself in infancy…
I'm a bit worried about letting it run into the Forbidden Forest just like that.
Thinking of this, Lucien directly communicated with the system through his mind:
"System, is there any way to strengthen my Quilin's power?"
[Yes, Host, yes, I have nine methods for these OvO]
"…"
How should I put it… it feels like this system has become more active since entering the magical world.
"Uh, just tell me the most effective one."
[Okay, the system recommends: Pet Growth Loan]
[There are two types of this loan: allowing the pet to quickly reach its growth stage (monthly loan); or quickly reach its mature stage (annual loan)]
[Note: Pets in their growth stage will have initially awakened all racial talents; pets in their mature stage will have fully mastered their talents and will awaken unique individual talent abilities]
Lucien rubbed his chin and glanced at Lumen.
"What level is Lumen at in its growth stage? Are there any side effects to this rapid maturation for the pet? What are the tasks for the monthly and annual loans?"
Facing Lucien's three consecutive questions, the system quickly responded:
[A Qilin just entering its growth stage is equivalent to an excellent Auror among wizards, but it far surpasses wizards of the same level in the field of innate magic]
[There are no side effects; the pet only needs to sleep in the space for a week]
[After all, it's a product of our system(^///^)]
[Monthly Loan: Observe and record the abilities, characteristics, and habits of 5 magical creatures, for a period of 30 days]
[Annual Loan: Observe and record the abilities, characteristics, and habits of all magical creatures (including known and unknown species), for a period of 365 days]
Ignoring the system's cutesy interjections, Lucien frowned and asked:
"A divine beast just entering its growth stage is only equivalent to an excellent Auror?"
Although the system said it surpassed ordinary wizards in innate magic, Lucien still felt that was too low and didn't meet his expectations.
[The growth stage is the most significant and rapid period of a divine beast's power change, with a huge difference between the early and late stages]
[A divine beast about to enter its mature stage is already infinitely close to the level of a legendary wizard among humans]
Hearing the system's explanation, Lucien's brows gradually relaxed, and he nodded.
That was still acceptable. Lumen, in its growth stage, would at least have the ability to protect itself. As long as it didn't fight to the death with dangerous creatures in the Forbidden Forest, survival shouldn't be a problem.
Recording five magical creatures within a month was also manageable. Since there were no specific requirements for which species, he could prioritize less dangerous and more approachable ones in the Forbidden Forest.
As for the annual loan that would allow Lumen to directly reach its mature stage, Lucien only glanced at it before dismissing the idea.
The annual loan required recording information on all magical creatures, which was completely beyond his current ability.
Moreover, unlike fully mastering Transfiguration or refining potions with the Philosopher's Stone—things he could work toward while staying at Hogwarts—not all magical creatures lived in the Forbidden Forest. And with the condition specifying both known and unknown species, repaying this loan would mean traveling the entire world.
Heh, "Enroll at Hogwarts and become a magical creature expert"?
Lumen would also need to sleep for a week first.
Hmm, I'll use that time to practice practical spells and prepare more potions as backup.
"System, I want to take out the Pet Growth Monthly Loan."
[OK, hope Host has a pleasant repayment (• ᴗ •) ♡]
[Loan: Pet Rapid Growth (Monthly Loan)]
[Repayment Period: 30 days]
[Loan Content: Allows the pet to initially reach its growth stage]
[Loan Task: Observe and record the abilities, characteristics, and habits of 5 magical creatures]
[Evaluation: Keep it up, this is your first step to surpassing Newt Scamander!]
Seeing the system's evaluation, Lucien gave a knowing smile.
Why is it bringing up that introverted magical creature expert?
He looked up at the starlight outside the window, feeling it was time to rest.
Lucien patted Lumen's head.
"Good night."
…
Late at night, in the Hogwarts Headmaster's office.
Dumbledore walked to the shelf where the Sorting Hat was placed.
"Old friend, would you be willing to chat with me about that young man, Lucien?"
_____
Note for gamabunda4873, here's how the riddle works-
The Riddle Recap:
"If five exceptionally intelligent wizards obtain 100 Galleons and propose solutions in order: the first person proposes a distribution plan, then the five vote. The plan passes only if more than half agree; otherwise, he will be thrown into a dragon's nest.
As the first wizard, how should you distribute it to get the most Galleons?"
Objective:
As the first wizard, your goal is to:
Survive (i.e., get at least 3 votes including your own), and
Get as many Galleons as possible.
Rules:
There are 5 wizards, all very smart, and rational (they want to survive and get as much money as possible).
Wizard 1 proposes a distribution plan.
Everyone (including Wizard 1) votes.
If 3 or more vote YES, the plan passes.
If the plan is rejected, Wizard 1 is thrown into a dragon's nest, and Wizard 2 becomes the new proposer, and the cycle repeats.
Scenario: Only 2 Wizards Left (Wizards 4 and 5):
Wizard 4 proposes.
He needs 2 votes to survive — both his and Wizard 5's.
Wizard 4 keeps all 100 Galleons.
Wizard 5 gets nothing (0 Galleons).
Plan passes because Wizard 4 votes for it. Wizard 5 can't do anything.
Conclusion: In a 2-person scenario, the proposer keeps everything, and the other gets nothing.
Scenario: 3 Wizards Left (Wizards 3, 4, 5):
Wizard 3 must get 2 out of 3 votes.
He already has his own vote. Needs 1 more.
He knows:
If he's thrown into the dragon's nest, Wizard 4 proposes.
From earlier, Wizard 4 gives Wizard 5 nothing, and keeps all 100.
So Wizard 3 can bribe Wizard 5 with just 1 Galleon. Wizard 5 will accept, because 1 > 0.
Wizard 3 keeps 99, gives 0 to 4, gives 1 to 5.
Votes:
Wizard 3: Yes
Wizard 4: No
Wizard 5: Yes
Plan passes.
Scenario: 4 Wizards Left (Wizards 2, 3, 4, 5):
Wizard 2 needs 3 votes total (including his own).
He has 1 vote (himself). Needs 2 more.
From earlier, we know:
Wizard 3 would get nothing if Wizard 2 is eliminated (since in the 3-wizard case, only Wizard 5 gets a bribe).
Wizard 4 would get 0 in that case too.
Wizard 5 gets 1 Galleon in that case.
So:
Wizard 2 can bribe Wizards 3 and 4 with 1 Galleon each (better than 0), and give Wizard 5 nothing.
Wizard 2: 98 Galleons
Wizard 3: 1
Wizard 4: 1
Wizard 5: 0
Votes:
Wizard 2: Yes
Wizard 3: Yes
Wizard 4: Yes
Wizard 5: No
Plan passes.
Final Scenario: All 5 Wizards
Wizard 1 needs 3 out of 5 votes. He has his own. Needs 2 more.
From previous step, he knows:
Wizard 2 will bribe Wizards 3 and 4.
Wizard 5 gets nothing in that plan.
So Wizard 1 can bribe:
Wizard 3 with 1 Galleon (better than 0)
Wizard 5 with 2 Galleons (better than 0)
Wizard 4 gets 0, but wouldn't help him anyway.
Final distribution:
Wizard 1: 97 Galleons
Wizard 2: 0
Wizard 3: 1
Wizard 4: 0
Wizard 5: 2
Votes:
Wizard 1: Yes
Wizard 3: Yes
Wizard 5: Yes
Plan passes.
Correct Answer:
"Give the fifth wizard 2 Galleons, and the third wizard 1 Galleon.The remaining 97 Galleons… are all mine."
This is exactly the optimal answer for Wizard 1 using backward induction.