God's imitator

Chapter 428 An Assumption

Yang Yuting then looked at Qin Yao: "Qin Yao, what about you? Are you changing?"

Qin Yao hesitated: "Ah... I think I'll give it a try?"

Yang Yuting nodded and explained, "So, whether or not to make a change depends on the actual situation of the company and the boss."

"If the company's profits are consistently high and the boss is particularly generous with red envelopes at the annual meeting, then it's worth trying to switch things up and aim for even higher returns."

"But for the vast majority of people, their company boss will never give out a 10 yuan red envelope in their lifetime, so the wisest choice is to stop after getting 1 yuan. The other envelope will definitely be 1000 yuan, there is no other possibility."

Everyone nodded.

After considering real-world examples, it suddenly becomes much easier to understand.

Yang Yuting continued, "So, returning to the 'Choose Your Own Game' scenario, the best approach is as Zheng Jie suggested. Do you all understand now?"

"In this situation, we need to consider the expectations of the 'game designer,' that is, the 'money giver.' His expectations are the expected revenue of the game."

"Okay, let's try a different way of playing."

Yang Yuting made two more slips of paper and wrote numbers on them.

"Now let's assume that two players are playing this game against each other, and the specific rules will be changed:"

"One side is the 'defenders,' who is mainly responsible for writing numbers on slips of paper, and the other side is the 'attackers,' who is mainly responsible for drawing slips of paper and deciding whether to change them."

"But after the game ends, the gains and losses for both sides will be determined based on the 'difference'."

"For example, suppose there are two slips of paper with 1000 and 1 on them, and the 'attacker' originally drew 1000 and chose to change it."

"So the 'attacking side' took the slip of paper with 1, while the 'defending side' kept the slip of paper with 1000."

"The difference between the two sides is 9000. The 'attacking side' makes a net profit of 9000, while the 'defending side' is burdened with a debt of 9000."

"The units all have a 'minute visa time'."

"Now, if I were Lu Xinyi, as the 'defender' in this game, I would have already written two notes."

“Come on, Dai Yifan, you draw one.”

Zheng Jie was taken aback for a moment: "Huh? Assuming you're Lu Xinyi? That would be a lot of pressure."

Without thinking too much, Dai Yifan subconsciously chose Yang Yuting's right hand, which was closer to him, from her two hands.

When I took it and looked at it, it said "10".

Dai Yifan was stunned for a moment, his expression clearly stiffening. This meant 10 minutes of visa processing time, a number that far exceeded his expectations.

"Should we change it? Think it over before you decide," Yang Yuting said calmly with a smile.

She then looked at Zheng Jie: "You can also give him some ideas."

Zhou Guifen spoke first: "Should we not change it? No matter what, the company's 'visa time' is still valid!"

"10 visa processing time, that's probably the maximum return you can get in a game, right? It can't go any higher!"

But Zheng Jie immediately objected: "But the other party is Lu Xinyi!"

"Given an opportunity, she will always make the choice that maximizes her benefits."

"This game has no upper limit. If she writes 100 million on another piece of paper and you don't switch, she'll just earn 90!"

Would she let this opportunity slip by?

"I'll replace it 100%!"

Qin Yao thought for a moment: "But Lu Xinyi is very smart, right? Wouldn't she have thought of these things? If she wrote '100 million' and then you changed it, wouldn't that be a huge loss for her?"

Zheng Jie was speechless for a moment, but still said, "But wouldn't that be like nesting dolls?"

"If you always assume Lu Xinyi has thought one step ahead of you, how can you even play the game? Anyway, if it were Lu Xinyi, she could very well have written '100 million' on the other slip of paper."

Dai Yifan was clearly confused by the discussion.

According to the original theory, it doesn't matter whether you switch or not. But if you really put yourself in their shoes, it's precisely because it's all the same that the decision of "to switch or not" becomes much more difficult.

After considering for a long time, Dai Yifan said, "Change."

He handed back the note that originally read "10" and took another note.

Upon opening it, it indeed showed "1".

Zhou Guifen was somewhat puzzled: "Huh? Is it a coincidence? If that's the case, wouldn't it have been possible to win against Lu Xinyi if we hadn't switched in the first place?"

Yang Yuting shook her head: "No, I already guessed it. Dai Yifan will most likely change."

"Tell me your thoughts first."

Dai Yifan explained somewhat frustratedly, "Although statistically speaking, it doesn't matter whether you switch or not, the consequences of switching the wrong one are still very different."

"Lu Xinyi is a player with a high risk appetite, right? So the other note may very well have really said 100 million."

"If I don't switch, it's like taking on a debt of 90 minutes of visa time, which is really beyond saving."

“If I switch, and the other one says 1 million, then I will make a net profit of 100, which is definitely great; if the other one says 90, then I will only lose 9, and there is still hope after returning to the community.”

"So after thinking it over, it's better to change it."

The other players, acting as bystanders, quickly noticed that something was clearly wrong.

Zheng Jie spoke first: "Wait, didn't we agree that this is a 50/50 pure probability problem, and we shouldn't consider expectations?"
"If you think like this, aren't you still calculating the expected outcome of exchanging the notes according to my method?"
"This is already a corrected incorrect answer!"

Dai Yifan paused for a moment: "Huh? Yeah."

His previous thoughts were purely instinctive and he hadn't given them much thought.

But when Zheng Jie pointed it out, he realized that he had indeed subconsciously been thinking according to that flawed way of calculating.

But this kind of thinking is actually meaningless.

If Zheng Jie hadn't made a similar mistake before, Dai Yifan might not have realized the problem with his thinking at this point, and would have insisted that his choice was correct, just that he was unlucky.

But making the same mistake twice makes it even more memorable.

Dai Yifan was somewhat frustrated: "It's clearly the same problem, but after adding one condition, it becomes completely different..."

Qin Yao realized a new problem: "Wait, Yuting, did you guess Dai Yifan's choice from the beginning?"

"That's unlikely, isn't it?"
How can you be sure which note he'll choose?

Yang Yuting explained, "It's actually very simple. I just need to put the slip of paper I want him to choose on my right hand."

"Because of where we were sitting, my right hand was closer to his."

Qin Yao was somewhat incredulous: "Is it really that simple? But it's entirely possible that he deliberately chose the left hand, which is farther away, right?"

Yang Yuting shook her head: "No, he most likely won't."

"Because there is a very important premise when making a choice: 'Is it the same no matter which one you choose?'"

"Imagine there is no rule of 'determining income and liabilities by calculating the difference,' but instead, you directly receive the corresponding income based on whichever number you select."

"At this point, knowing the specific amounts on both slips of paper, if I deliberately bring my right hand closer to Dai Yifan, he is very likely to notice or become alert, and thus deliberately choose my left hand."

"However, in this game, everyone has already presupposed the concept that 'it doesn't matter which one you choose.'"

(End of this chapter)