God's imitator

Chapter 426 Practice
Zheng Jie's eyes lit up: "Huh? Really? That's great, I want to participate!"

The others were also clearly very interested and became very enthusiastic.

It's not surprising that people have similar ideas; in fact, it's quite late that someone in Community 17 has only made such a suggestion now.

But obviously, just because someone in the community has an idea doesn't mean they have to bring it up.

The premise for making such a suggestion is that you must have the corresponding plan or ability. If you just make a suggestion but do not prepare the corresponding test, it is somewhat superficial and meaningless.

Moreover, people who are capable of designing may not be willing to do it; and people who want to do it may not have the corresponding ability.

Regardless, Yang Yuting's proposal at this time was the first of its kind in the 17th community, and it sparked a very enthusiastic response.

The group quickly gathered around the long table and got ready.

Yang Yuting said, "The little game I prepared actually originated from a small 'paradox' problem that I came across while reading a book some time ago, and it is also somewhat related to mathematics."

"The rules of the game are actually quite simple, and the way I play the game with everyone is a little different from the mode in the arcade."

"Overall, I hope to get as much participation and interaction as possible, mainly to understand the mechanics and changes of the puzzle."

"After all, it's possible for a copycat to guess the arcade's game invitation, but it's almost impossible for a player to guess the copycat's design."

"Understanding the principles is more important."

Li Renshu nodded: "Yes, actually many simple puzzles often involve more strategic gameplay, and breaking down simple routines clearly should be the most beneficial for ordinary players in the community."

"This is our first attempt after all, and we don't expect any immediate results. We just hope that everyone will feel that they have gained something."

Clearly, the stronger players in the community don't actually need this kind of step, and they're not particularly enthusiastic about it.

The ones who really need improvement are the average players.

However, if the rules are too complex, these players may have already exhausted all their efforts to understand them and be unable to provide an effective solution on their own.

In this case, waiting for the standard answer will have minimal impact on your self-improvement.

If we can use simple questions to make everyone rack their brains to think, it should achieve better teaching results.

Yang Yuting took a piece of paper, tore it open, and made two small slips of paper. She then wrote some information on each slip.

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

"Suppose I am a copycat in the arcade, here are two notes."

"The rules clearly state that the amount on one slip of paper is ten times that on the other slip of paper."

"The specific way to play is that you randomly choose a piece of paper, and then open it to view it."

"After that, you can choose to change the note or not."

"That's it."

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

Yang Yuting said somewhat helplessly, "I haven't finished yet. Because this is the most basic model, there's no need to actually choose."

"After all, even if we choose now, it's just a matter of luck."

"In short, you can answer a few of my questions now."

"First question: Can any player who understands the specific principles behind this and is confident that they can find the optimal solution under any derived rules raise their hand?"

The group looked at each other, and sure enough, Lin Sizhi, Wang Yongxin, and Cai Zhiyuan all raised their hands.

Yang Yuting nodded: "Okay, then please keep quiet for now. I will ask you again if I need your answers."

"Next are questions for general players."

"Under the current rules, if you receive any slip of paper, will you choose to exchange it or not?"

"Just answer directly."

Zheng Jie was a little confused: "What's the difference? There are only two slips of paper. You draw one randomly, and whether you exchange the other or not depends purely on luck, right?"

Yang Yuting nodded: "Okay, now, let's assume you drew this slip of paper. Now, shall we exchange it?"

Yang Yuting handed over one of the slips of paper.

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

It says "1 minutes for visa processing".

Yang Yuting looked at everyone and said, "Everyone, tell me what you would choose. Just share your first impression."

Zhou Guifen said first, "Let's not change it. 1 minutes of visa time is not a small amount."

Dai Yifan paused for a moment: "But it's also possible that the other one has 10 on it."

Qin Yao objected: "That's unlikely, isn't it? Are copycats doing charity work?"

Dai Yifan thought for a moment: "But the rules don't say it can't be 10, do they?"

"In many high-yield games, there have been instances of earnings reaching 10."

Zheng Jie took a piece of paper: "Wait a minute! I need to calculate the expected returns."

Let me think about it...

"If we were to exchange, there are two possibilities: one is to exchange 1 for 10, and the other is to exchange 1 for 1000. These two scenarios should each have a 50% probability."

“那预期收益应该是（10万-1万）×50%+（1000-1万）×50%=40500，这明显是个正收益的预期啊！”

Qin Yao asked with some doubt, "Wait, is this the right way to do it?"

Zheng Jie checked it again: "Is there a problem?"
"Shouldn't expected returns be calculated this way?"

"The two scenarios, each with a 50% probability, are combined to determine the total expected return."

Anyway, I think it should be changed.

Lee In-sook thought about it carefully: "No, although it seems like there's no major problem from an algorithmic perspective, intuitively it's wildly wrong."

"Since we've already received the note with the value of 1, the other note could indeed be for 1000 or 10, that's fine."

"But according to your algorithm, no matter whether we receive 1000 slips of paper, 1 slips of paper, or 10 slips of paper, the expected return will be positive."

"Then should they all be replaced?"
"Something seems off, because there's always a 50% chance of losing money."

"The relationship between these two slips of paper should be a zero-sum game. But according to your algorithm, it has become a positive-sum game."

Zheng Jie was stunned. He scratched his head and said, "Huh? It seems so. What went wrong?"

"My formula for calculating expected returns seems to be correct in every way, doesn't it?"

The crowd was momentarily confused as to why this was happening, and they all looked at Cai Zhiyuan.

Yang Yuting nodded, indicating, "You can explain this issue now."

Cai Zhiyuan said to Zheng Jie, "Your formula is fine, but you substituted the wrong numbers."

"Because you mistakenly assumed two scenarios: 'more than 1' or 'less than 1', and calculated both scenarios in the same formula."

The correct method should be calculated as follows:
"Suppose that one of the slips of paper has a visa duration of X, and the other slip of paper has a visa duration of 10X."

“那么，拿到一个红包之后，交换另一个红包的期望收益应该是：（10X-X）×50%+（X-10X）×50%=0。

"The expected return is 0, so this algorithm is correct."

Lee In-sook joked, "So, it's not that we're afraid of not understanding, it's that we're afraid of being half-baked. If this little puzzle were hidden in the game in the arcade, and you made a decision based on your profit calculation method, you would probably lose a lot of money."

Zheng Jie felt somewhat ashamed.

Yang Yuting continued, "Okay, that was just the simplest case. This problem is called the 'Wallet Game' or the 'Double Envelope Paradox,' and it was proposed by a mathematician."

"Next, I'll present a derivative game based on this principle, so please pay attention."

(End of this chapter)