Chapter 427: A Hypothesis

Yang Yuting looked at Qin Yao again, "What about you, Qin Yao? Would you switch?"

Qin Yao hesitated, "Ah... I probably would try switching?"

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

"If the company's profits have always been very high and the boss is especially generous with red envelopes at the annual party, then you can try switching to gamble for higher returns.

"But for the vast majority of people, their company's boss will never give a 100,000 red envelope in their lifetime, so drawing 10,000 and stopping immediately is the wisest choice. The other envelope must be 1,000, with no other possibilities."

Everyone nodded.

After connecting it to real-life examples, it suddenly became much easier to understand.

Yang Yuting continued, "So returning to the 'Self-Selected Game' situation, the best approach is like Zheng Jie said. Does everyone understand now?

"In this situation, we must consider the 'game designer,' meaning 'the person giving out money,' what their expectation is. Their expectation is the expectation of the game's final returns.

"Alright, now let's change the gameplay."

Yang Yuting made two new slips and wrote numbers on each.

"Now suppose two players are playing this game with each other, and the specific rules will be modified:

"One side is the 'defender,' mainly responsible for writing numbers on the slips. One side is the 'attacker,' mainly drawing slips and deciding whether to switch slips.

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

"For example, suppose the two slips have 1,000 and 10,000 respectively, and the 'attacker' originally drew 1,000 and chose to switch.

"Then the 'attacker' took the 10,000 slip, while the 'defender' kept the 1,000 slip.

"The difference between the two is 9,000. The 'attacker' nets 9,000, and the 'defender' bears 9,000 in debt.

"The unit is 'minutes of visa time.'

"Now, suppose I'm Lu Xinyi as the 'defender' of this game, and I've already written two slips.

"Come on, Dai Yifan, you draw."

Zheng Jie was stunned, "Ah? Assuming you're Lu Xinyi? That's a lot of pressure."

Dai Yifan didn't think too much and subconsciously chose Yang Yuting's right hand, which was closer to him.

Taking it and looking, it said '100,000.'

Dai Yifan was stunned. His expression was clearly somewhat stiff. This represented 100,000 minutes of visa time, a number completely beyond his expectations.

"Will you switch? Think carefully before deciding." Yang Yuting still smiled calmly.

She looked at Zheng Jie again, "You can also help him with advice."

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

"100,000 visa time, this is already the top for returns in one game, right? It can't be higher!"

But Zheng Jie immediately objected, "But the opponent is Lu Xinyi!

"As long as she finds an opportunity, she'll definitely make the choice that maximizes benefits.

"This game has no upper limit. If she writes 1,000,000 on the other slip and you don't switch, she directly earns 900,000!

"Would she pass up such an opportunity?

"I'd 100% switch!"

Qin Yao thought about it, "But Lu Xinyi is very clever, right? Wouldn't she think of what you're thinking? If she wrote '1,000,000' and you switched it away, wouldn't she lose big?"

Zheng Jie was momentarily speechless but still said, "But doesn't this become an infinite loop?

"If you always assume Lu Xinyi thinks one level more than you, how can you play?

"Anyway, if it's Lu Xinyi, the other slip could completely have the number '1,000,000' written on it."

Dai Yifan was clearly confused by everyone's discussion.

According to the original theory, switching or not switching made no difference. But when actually putting himself in the situation, precisely because they were the same, the decision of 'whether to switch' became even more difficult.

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

He handed back the slip with '100,000' written on it and took the other slip.

Opening it, it indeed said '10,000.'

Zhou Guifen was somewhat puzzled, "Huh? Was it a coincidence? In that case, if he hadn't switched at the start, wouldn't he have beaten Lu Xinyi?"

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

"You explain your thinking first."

Dai Yifan explained somewhat dejectedly, "Although probabilistically, switching or not switching makes no difference, the consequences of switching wrong still have a big difference.

"Lu Xinyi herself is a high-risk preference player, right? So the other slip might really have 1,000,000 written on it.

"If I don't switch, that would be equivalent to directly bearing 900,000 minutes of visa time debt. Even immortals couldn't save me then.

"If I switch, and the other one says 1,000,000, then I net 900,000, which would definitely be very good. If the other one says 10,000, I actually only lose 90,000, and after returning to the community, there's still hope.

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

Other players, as observers, quickly heard something obviously wrong.

Zheng Jie said first, "Wait, didn't we agree this was a pure 50% versus 50% probability problem and not to consider expectations?

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

"This is already a corrected wrong answer!"

Dai Yifan was stunned, "Hey? That's right."

His earlier thinking was completely an instinctive reaction without much thought.

But when Zheng Jie pointed it out, he realized he had indeed subconsciously thought according to that erroneous expectation calculation method.

And this kind of thinking was actually meaningless.

If Zheng Jie hadn't already made a similar mistake earlier, Dai Yifan might still not realize the problem with his thinking and would insist his choice was correct, just with bad luck.

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

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

Qin Yao realized a new problem, "Wait, does that mean you guessed Dai Yifan's choice from the start, Yuting?

"That's unlikely, right?

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

Yang Yuting explained, "Actually, it's very simple. I just had to put the slip I wanted him to choose in my 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 completely deliberately choose the left hand that's farther away, right?"

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

"Because there's a very important prerequisite when making a choice: 'does it matter which one you choose?'

"Suppose there wasn't a rule about 'calculating the difference to determine gains and debts,' but rather you directly receive the corresponding number's return based on which you choose.

"Then at that time, with me knowing the specific amounts on both slips and deliberately putting my right hand close to Dai Yifan, he would very likely notice or be alert and specifically choose my left hand.

"But in this game, everyone has already preset the concept that 'choosing either one makes no difference.'"