God's Imitator-Chapter 426: Guessing Expectations

Zheng Jie was a bit curious, "Hey, is the game just starting?"

"But hasn’t the fundamental principle and logic of this game already been revealed?"

Clearly, what Yang Yuting was talking about, this ’wallet game,’ or ’two-envelope paradox,’ its principle is not complex.

Simply put, it’s about two slips of paper with different amounts written on them, one being ten times the amount of the other, and the question of whether to switch after drawing one.

If there’s an error in calculating expected returns, it would lead to the wrong conclusion of ’no matter how you switch, it’s a positive return.’

But upon digging deeper, it just goes back to the original point where it doesn’t matter whether you switch or not.

It’s merely a 50% chance to switch from a small envelope to a large envelope, or a 50% chance to switch from a large envelope to a small envelope.

So, once you’ve understood that ’in terms of probability and expected returns, it’s the same regardless of switching,’ it’s not really a mystery.

Then what else is there to test on?

Yang Yuting smiled and continued, "Let’s keep listening.

"Now, I am still an Imitator.

"At this point, in the ’Self-Selected Game,’ I must follow the basic rules in the ’Self-Selected Game’ hall.

"The specific gameplay is to select one from the two slips and then decide whether to switch to the other, and once decided, it’s irreversible or unchangeable.

"What’s written on the slips are ’chip’ values, in ’Self-Selected Game,’ chips can be exchanged for visa time, but they are affected by inflation.

"However, every time you play this game, the two numbers change. This means you cannot use the previous experience to judge the next values.

"Now, let’s draw."

Yang Yuting placed the two written slips in her left and right hands respectively.

Zheng Jie volunteered, "I’ll do it!"

He pretended to consider for a moment, then took the slip from Yang Yuting’s left hand.

Upon opening, the number ’10,000’ was written on it.

"Do you want to switch?" Yang Yuting asked.

Zheng Jie hesitated, "This..."

Clearly, even though the principle was understood, once truly putting oneself in the specific game scenario, hesitation still occurs.

Because the principle of this strategy is affected by the specific rules of the game.

Dai Yifan was a bit puzzled, "Since the principle is that switching or not is the same, just go with your mood.

"If it were me, I would switch, since it’s the same, switching gets more information."

Yang Yuting asked, "What if it switches to 1,000? In ’Self-Selected Game,’ these two chip values can differ greatly, potentially leading you into a disadvantage in subsequent games."

Dai Yifan was stumped by the question and fell silent again.

Zheng Jie seemed to have thought of something, he earnestly said, "If it’s the early stage of the game, don’t switch. If it’s the mid to late stage, perhaps observe other players first, then decide whether to switch."

Yang Yuting nodded and asked, "Why make such a decision?"

Zheng Jie was a bit excited, "Because this issue has become a ’guess the Imitator’s psychological expectation’ problem rather than the original ’two-envelope paradox’ question!

"In the original problem, drawing ’10,000’ makes it impossible to judge whether it’s a smaller or larger number.

"The other number could be 1,000 or 100,000.

"However, when this issue gains a specific context, it becomes different because an ’expected range’ appears!

"So, if encountered in ’Self-Selected Game,’ first guess the maximum amount of chips the Imitator is willing to place in this game, then use this expectation to judge whether the drawn number is large or small.

"Consider the situation in ’Self-Selected Game.’ Though the Imitators can issue unlimited chips, they can’t really do so.

"If, at the beginning, I draw ’10,000,’ and the other slip is ’100,000,’ it means players could easily gain 100,000 chip levels early in the game room.

"This would cause severe inflation in the room, significantly shrinking the chips’ value for exchanging visa time.

"It would directly repel players who enter the room later, leading to a collapse of the room’s price system.

"Hence, if the Imitator indeed designed such a rule in ’Self-Selected Game,’ they would strictly limit chip output initially.

"These two numbers could only be ’1,000’ and ’10,000.’

"It’s equivalent to... if a player draws ’10,000,’ they have essentially found the sure-win method in this room.

"Yet, as the game progresses, to attract more players in, the Imitator might change the values midway.

"For example, change ’1,000’ and ’10,000’ to ’10,000’ and ’100,000.’

"Since the rules have no restrictions, the Imitator can change at any time.

"After modification, some players might draw ’100,000’ chips. If others preserve their room chips, their wealth gets diluted, akin to reshuffling.

"Although it’s a predatory tactic, it gives late-joining players more reasons to play a few more rounds.

"So, considering the Imitator’s thoughts, in the early game, drawing 10,000 means stopping; in the mid to late game, observe other players or try switching, there might be a chance to switch to 100,000."

Yang Yuting applauded approvingly, "Very well said, exactly!"

Qin Yao remarked, "So that’s how it is, impressive, Zheng Jie!"

Zheng Jie was a bit embarrassed, "No, no, mainly the question guided well, from simple to complex.

"If there hadn’t been an analysis of the principle initially, I wouldn’t have thought of it if encountered in the game suddenly."

Yang Yuting continued, "Thus, the first variation of this problem is ’guessing expectation.’

"If we use a real-world example, everyone might understand better.

"Suppose it’s your company’s or unit’s annual meeting now, and the company boss or your superior wants to play this game with you, and the drawn amount is your year-end bonus or welfare.

"Similarly, two slips are present, and the slip you draw reads ’10,000,’ and now the boss asks if you want to switch.

"Would everyone switch?

"Aunt Zhou, would you like to speak first?"

Zhou Guifen was suddenly questioned, somewhat surprised. But after thinking for a while, she said, "Don’t switch!"

Yang Yuting nodded, "Hmm, why?"

With firm conviction, Zhou Guifen replied, "Our school barely pays salaries on time, let alone giving out 100,000 bonuses at year-end! That’s absolutely impossible; 10,000 is already extraordinary."