God's Imitator-Chapter 425: Practice

Sure, here is the translated text:

Zheng Jie’s eyes lit up: "Huh? Really? That’s great, I want to join!"

The others also seemed very interested and eagerly became more enthusiastic.

Actually, having similar ideas is not surprising, one could even say it’s relatively late that someone in Community 17 has proposed such a suggestion until now.

However, obviously, just because someone thinks of it, doesn’t mean they have to bring it up.

The prerequisite for making such a suggestion is having a corresponding plan or ability, if it’s just a proposal without the accompanying test, it feels a bit flimsy and meaningless.

Moreover, those who have the ability to design may not be willing to do it; and those who want to do it may not necessarily have the ability.

But no matter what, Yang Yuting’s proposal at this point was the first in Community 17, and it elicited quite a lively response.

Everyone quickly gathered around the long table, ready.

Yang Yuting said: "The little game I prepared actually comes from a small ’paradox problem’ I came across while reading a book recently, and it has a bit to do with mathematics.

"The rules of the game are actually quite simple, and my way of playing with everyone is a bit different from the pattern in the Walkway.

"Overall, I hope to have everyone engage and interact as much as possible, mainly to understand the mechanism and changes of the puzzle.

"After all, for an Imitator, guessing the game invitation from Walkway is possible, but for players to guess the Imitator’s design is nearly impossible.

"Understanding the principle is more important."

Li Renshu nodded: "Yes, actually many simple puzzles often have more strategies, and breaking down simple patterns clearly should benefit the ordinary players in the community the most.

"This is, after all, our first attempt; we don’t expect immediate effects, as long as everyone feels they’ve gained something."

Obviously, the stronger players in the community don’t actually need these sessions and aren’t very keen on them.

But it’s the average players who really need the improvement.

However, if the rules are too complex, these players might already be struggling just to understand them and can’t come up with effective solutions themselves.

In this way, even waiting for the standard answers would result in minimal improvement.

If simple problems can be used to make everyone rack their brains as much as possible, it should result in better teaching outcomes.

Yang Yuting picked up a piece of paper, tore it into two small strips, and wrote some information on each.

"Now let’s first play the most basic mode of this game.

"Let’s assume I am the Imitator in the Walkway, here are two pieces of paper.

"The rule can be clearly stated that the amount on one piece of paper is ten times the other.

"The specific gameplay is that you randomly pick a paper, then open and look at it.

"After that, you can choose to switch papers, or not.

"That’s all."

Zheng Jie was eager to try: "Really? Then I’ll go first! I choose the one to your left."

Yang Yuting was a bit helpless: "I haven’t finished talking yet, because this is the most basic mode, so there’s no need to really choose.

"After all, even if you choose now, it’s just about luck.

"In any case, you can now first answer a few of my questions.

"The first question is, players who know the specific principle of this matter and are confident in finding the optimal solution under any derived rule, please raise your hand."

Everyone looked at each other, and indeed, Lin Sizhi, Wang Yongxin, and Cai Zhiyuan all raised their hands.

Yang Yuting nodded: "Okay, then please remain silent for now, and I will ask you to answer when needed.

"Next is a question for general players.

"Under the current rules, once you have picked any paper, would you choose to switch or not?

"Just give a direct answer."

Zheng Jie was a bit puzzled: "Is there any difference? There are only two pieces of paper, randomly drawn one, whether to switch or not is just pure luck, right?"

Yang Yuting nodded: "Okay, now, assume you drew this piece of paper.

"Now, will you switch?"

Yang Yuting handed over one of the papers.

Zheng Jie reached out to take it, and the player sitting next to him also leaned over to take a look.

It said ’10,000-minute visa time’ on it.

Yang Yuting looked at everyone: "Everyone says how they would choose, just express your first feeling."

Zhou Guifen first said: "Don’t switch, 10,000-minute visa time is already quite a lot."

Dai Yifan was silent for a moment: "But it could also be that the other one is 100,000."

Qin Yao disagreed: "That possibility isn’t high, would the Imitator be doing charity?"

Dai Yifan thought for a moment: "But the rules didn’t say it couldn’t be 100,000?

"In many high-reward games, 100,000 level returns have also appeared."

Zheng Jie grabbed a piece of paper: "Wait a minute, I want to calculate this expected return question.

"Let me think...

"If you switch, there are two possibilities, one is switching from 10,000 to 100,000, and the other is switching from 10,000 to 1,000, each with a 50% probability.

"Then the expected return should be (100,000-10,000)×50%+(1,000-10,000)×50%=40,500, this is clearly a positive expected return!"

Qin Yao was skeptical: "Wait, is this calculated correctly?"

Zheng Jie checked again: "No problem?

"Isn’t that how expected returns are calculated?

"Two scenarios, each with a 50% probability, added together give the total expected return.

"I think it should be switched."

Li Renshu thought carefully: "No, although it looks correct algorithmically, it intuitively feels very wrong.

"Because now that we’ve got the 10,000 paper, the other paper could indeed be 1,000 or 100,000, that’s not a problem.

"But according to your calculation, no matter if we pick a paper with 1,000, 10,000, or 100,000, the expected return is positive.

"So, should we switch every time?

"That doesn’t seem right, as there should always be a 50% chance of a loss.

"Between these two pieces of paper, it should be a zero-sum game. But according to your algorithm, it becomes a positive-sum game."

Zheng Jie was stunned, scratching his head: "Ah? Seems like something’s wrong here?

"My formula for calculating expected returns seems flawless?"

People temporarily couldn’t figure out why, so they turned to look at Cai Zhiyuan.

Yang Yuting nodded as a signal: "You can begin explaining this issue now."

Cai Zhiyuan said to Zheng Jie: "Your formula is correct, but you plugged in the wrong specific numbers.

"Because you incorrectly assumed two scenarios of ’10,000 more’ or ’10,000 less’ and computed them in the same formula.

"The correct method should be calculated like this:

"Assuming one piece of paper writes a visa time of X, the other writes a visa time of 10X.

"So, after getting one envelope, the expected gain of swapping for the other should be: (10X-X)×50%+(X-10X)×50%=0.

"The expected return is 0, so this method of calculating is correct."

Li Renshu teased: "See? Not knowing isn’t scary, but half-baked knowledge is. If these little puzzles are hidden in the Walkway’s games, deciding based on your kind of return calculation, you’d probably lose big."

Zheng Jie was somewhat humbled.

Yang Yuting continued: "Okay, that was just the simplest scenario; this problem is called the ’Wallet Game’ or the ’Double Envelope Paradox’, proposed by a mathematician.

"Next, I’ve designed a derived game based on this principle, so please pay attention."