God's Imitator-Chapter 427: A Hypothesis

Yang Yuting looked at Qin Yao again: "Qin Yao, what about you? Will you switch?"

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

Yang Yuting nodded and explained: "So, to decide whether to switch, you have to consider the actual situation of the company and the boss.

"If the company’s profits have always been high and the boss is particularly generous with bonuses at the annual meeting, then you could try switching to aim for a higher return.

"But for the vast majority of people, their boss would never give a 100,000-yuan bonus in a lifetime, so taking the 10,000 yuan and stopping there is the wisest choice. The other envelope is surely 1,000, there’s no other possibility."

Everyone nodded in agreement.

After relating it to real-life scenarios, it suddenly became easier to understand.

Yang Yuting continued: "So back to the situation in the ’Self-Selected Game,’ the best approach is just like Zheng Jie said. Can everyone understand?

"In this situation, we have to consider the ’Game Designer,’ that is, the ’person distributing the money,’ and his expectations. His expectation is the expected value of the final game profits.

"Okay, let’s change the gameplay this time."

Yang Yuting made two paper slips again, writing numbers on each.

"Now suppose two players play this game against each other; the specific rules will change:

"One side is the ’Defensive side,’ responsible for writing numbers on the slips, while the other is the ’Offensive side,’ primarily drawing slips and deciding whether to switch them.

"But after the game ends, both sides will determine the profit or loss based on the ’difference in value.’

"For example, suppose the two slips have 1,000 and 10,000 on them, and the ’Offensive side’ originally draws the 1,000 and chooses to switch.

"Then the ’Offensive side’ takes away the 10,000 slip, and the ’Defensive side’ keeps the 1,000 slip.

"The difference is 9,000; the ’Offensive side’ earns 9,000, and the ’Defensive side’ bears a 9,000 liability.

"The unit is ’minutes of visa time.’

"Now, assuming I am Lu Xinyi, acting as the ’Defensive side’ in this game, I have already written two slips.

"Come, Dai Yifan, you draw one."

Zheng Jie was taken aback: "Uh? Suppose you are Lu Xinyi? That’s a lot of pressure."

Dai Yifan didn’t overthink it and instinctively chose the right hand of Yang Yuting, which was closer to himself.

When he took it and looked at it, it said ’100,000’ on it.

Dai Yifan was momentarily stunned, his expression evidently tense, representing 100,000 minutes of visa time, a figure completely beyond his expectations.

"Would you like to switch? Think about it before deciding." Yang Yuting still smiled calmly as she spoke.

She looked at Zheng Jie again: "You guys can also give him some advice."

Zhou Guifen said first: "Don’t switch, right? No matter what, the unit is ’visa time’!

"100,000 visa time, that must be the maximum in a game’s profit, it can’t be higher!"

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

"If she ever finds a chance, she will definitely make the choice that maximizes profit.

"There’s no cap in this game; if she wrote 1,000,000 on the other slip and you don’t switch, she walks away with 900,000. Would she miss that chance?

"I’m 100% switching!"

Qin Yao thought for a moment: "But Lu Xinyi is very smart, right? Wouldn’t she think of what you’re considering? If she wrote ’1,000,000’ and you switched it, wouldn’t she be at a huge loss?"

Zheng Jie was momentarily speechless but still said: "But wouldn’t that be overthinking it?

"If you always assume Lu Xinyi is thinking one layer deeper than you, then how could you play?

"Anyway, if it’s Lu Xinyi, there is absolutely a chance the other slip says ’1,000,000.’"

Dai Yifan was visibly confused by everyone’s discussion.

According to the initial theory, whether to switch or not was the same, but truly being in the situation meant that precisely because it was the same, the decision of ’whether to switch’ became more difficult.

After much consideration, Dai Yifan said: "Switch."

He handed back the slip that said ’100,000’ and took the other slip.

When he opened it, indeed, it said ’10,000.’

Zhou Guifen was a bit puzzled: "Huh? Was it a coincidence? In that case, if he hadn’t switched, wouldn’t he have beaten Lu Xinyi?"

Yang Yuting shook her head: "No, I had already guessed that Dai Yifan would most likely switch.

"You should first explain your thoughts."

Dai Yifan explained, somewhat frustrated: "Although, from a probability standpoint, whether to switch or not is the same, the consequences of choosing wrong are very different.

"Lu Xinyi herself is a high-risk tolerant player, right? So the other slip is likely to really say 1,000,000.

"If I don’t switch, it’s as if I am automatically bearing a debt of 900,000 minutes of visa time, and not even a deity could save me.

"If I switch and the other one says 1,000,000, then I net 900,000; that’s excellent. If the other says 10,000, I actually only lose 90,000, and I’d still have hope back in the Community.

"So, after thinking it through, switching is still better.

The other players, as spectators, quickly noticed something was off.

Zheng Jie first said: "Wait, wasn’t this supposed to be a pure 50% vs 50% probability problem, without considering expectations?

"Thinking like this, aren’t you still calculating the expectation for switching slips according to my method?

"This is already the corrected wrong answer!"

Dai Yifan was stunned: "Huh? Yeah."

His previous thought was completely a reflex response, without much thought.

But upon Zheng Jie’s point, he realized he indeed subconsciously used that incorrect expectation calculation method to think it over.

And such thinking actually had no real significance.

If not for Zheng Jie having earlier made a similar mistake, Dai Yifan might not have realized there was an issue with his line of thought and would continue to believe his choice was correct, just unlucky.

But making a mistake twice leaves a deeper impression.

Dai Yifan was somewhat frustrated: "It’s clearly the same problem, but adding one condition changes it completely..."

Qin Yao realized the new issue: "Wait, Yuting, did you already guess Dai Yifan’s choice from the start?

"Is that even possible?

"How could you be sure which slip he’d choose?"

Yang Yuting explained: "Actually, it’s simple, I just had to place the slip I wanted him to choose in the right hand.

"Because of where we’re sitting, my right hand is closer to him."

Qin Yao found it hard to believe: "Is it that simple? But he could also deliberately choose the further left hand, couldn’t he?"

Yang Yuting shook her head: "No, he very likely wouldn’t.

"Because a crucial premise in decision-making is: ’Does it matter which one you choose.’

"Assuming there was no ’deciding gains and liabilities with the calculated difference’ rule, and whichever you picked directly gave you the corresponding gain...

"Then at that time, knowing the specific amounts on the slips, and deliberately holding my right hand closer to Dai Yifan, he might be suspicious or cautious, and then purposely choose my left hand.

"However, in this game, everyone had already established the concept that ’it doesn’t matter which you choose’."

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