Chapter 425: Practice

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

Others were also clearly very interested and became enthusiastic and eager one after another.

Actually, having such an idea wasn't strange. It could even be said that Community 17 only now having someone propose a similar suggestion was already relatively late.

But clearly, just because someone in the community thought of it didn't mean they had to propose it.

Because the prerequisite for proposing such a suggestion was that one had to have the corresponding plan or ability. If one only proposed it without preparing corresponding tests, that would be somewhat empty and meaningless.

Moreover, people with the ability to design might not be willing to do this. And people who wanted to do this might not have the corresponding ability.

But in any case, Yang Yuting's proposal at this time was the first in Community 17 and triggered quite an enthusiastic response.

Everyone quickly gathered around the long table, ready.

Yang Yuting said, "This little game I've prepared is actually derived from a small 'paradox puzzle' I happened to see while reading a book some time ago. It also has some relation to mathematics.

"The game rules are actually quite simple, and the way I play games with everyone is somewhat different from the Gallery's mode.

"Overall, I hope to get everyone to participate and interact as much as possible, mainly to understand the puzzle's mechanism and variations.

"After all, for God’s Imitators, it's possible to match Gallery game invitations, but for players to match a God’s Imitator's design is almost impossible.

"Understanding the principles is more important."

Li Renshu nodded, "Mm, actually many simple puzzles often have more game theory involved, and breaking down simple patterns clearly should also provide the most improvement for ordinary players in the community.

"After all, this is our first attempt. We don't expect immediately dramatic effects. As long as everyone feels they've gained something, that's good."

Clearly, those relatively strong players in the community didn't really need such sessions and weren't too enthusiastic about them.

The ones who truly needed improvement were ordinary players.

But if the rules were too complex, these players might already exhaust themselves just understanding the rules and couldn't provide effective answers themselves.

In that case, they'd still just wait for the standard answer. The improvement effect on themselves would be minimal.

If they could use simple questions to get everyone to rack their brains as much as possible, it should achieve better teaching effects.

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

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

"Assume I'm a God’s Imitator in the Gallery. Here are two slips of paper.

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

"The specific gameplay is, you randomly choose a slip and then open it to check.

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

"That's it."

Zheng Jie was eager to try, "Is that so? Then let me go first! I choose the one on your left."

Yang Yuting was somewhat helpless, "I haven't finished speaking yet. Because this is the most basic mode, you don't need to actually choose.

"After all, even if you chose now, it would just be luck.

"Anyway, you can now first answer a few of my questions.

"First question: Players who know the specific principle of this matter and are confident they can find the optimal solution under any derived rules, please raise your hands."

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

Yang Yuting nodded, "Good, then I'll trouble the three of you to stay silent for now. If I need your explanations, I'll ask you again.

"The next questions are for ordinary players.

"Under the current rules, after you've obtained any slip, will you choose to switch or not switch?

"Just answer directly."

Zheng Jie was somewhat confused, "Is there any difference? There are only two slips total. After randomly drawing one, whether you switch the other one or not is pure luck, right?"

Yang Yuting nodded, "Good. Now, assume you drew this slip.

"Now then, will you switch?"

Yang Yuting handed over one of the slips.

Zheng Jie reached out to take it. The player sitting next to him also leaned over to look.

It read '10,000 minutes of visa time.'

Yang Yuting looked at everyone, "Everyone say how you'd choose. Just say your first feeling."

Zhou Guifen said first, "Don't switch, right? 10,000 minutes of visa time isn't little."

Dai Yifan was silent for a moment, "But it's also possible the other one has 100,000."

Qin Yao objected, "That possibility isn't high, right? Is the God’s Imitator doing charity?"

Dai Yifan thought about it, "But the rules didn't say it couldn't be 100,000, right?

"In many high-reward games, there have also been rewards at the 100,000 level."

Zheng Jie took a piece of paper, "Wait, everyone! I need to calculate this expected return problem.

"Let me think...

"If I switch, there are two possibilities. One is switching from 10,000 to 100,000, the other is switching from 10,000 to 1,000. These two situations should each have 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 somewhat doubtful, "Wait, is this calculation correct?"

Zheng Jie checked again, "No problem, right?

"Isn't this how expected returns should be calculated?

"Two situations, each 50% probability. The sum is the total expected return.

"Anyway, I think we should switch."

Li Renshu thought seriously, "That's not right. Although the calculation method seems fine, intuitively it's completely wrong.

"Because we've already obtained the 10,000 slip. The other slip could indeed be 1,000 or 100,000, that's fine.

"But according to your calculation method, whether we got the 1,000 slip, the 10,000 slip, or the 100,000 slip, the calculated expected return would all be positive.

"So should we always switch?

"Something seems wrong, because there's always a 50% possibility of losing.

"Between these two slips, it should be a zero-sum game. But according to your calculation method, it becomes a positive-sum game."

Zheng Jie was stunned. He scratched his head, "Hey? That's true. What went wrong?

"My formula for calculating expected return looks correct everywhere, right?"

Everyone temporarily couldn't figure this out and looked toward Cai Zhiyuan.

Yang Yuting nodded in indication, "You can explain this problem first."

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

"Because you incorrectly preset the two situations of '10,000 is more' or '10,000 is less,' and calculated these two situations in the same formula.

"The correct method should be calculated like this:

"Assume the visa time written on one slip is X, and the visa time written on the other slip is 10X.

"Then, after getting one red envelope, the expected return of exchanging for the other red envelope should be: (10X-X)×50%+(X-10X)×50%=0.

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

Li Renshu teased, "So you see, it's not scary to not understand, but scary to have half-baked knowledge. If this little puzzle was hidden in a Gallery game and you made decisions based on your return calculation method, I'm afraid you'd lose big."

Zheng Jie was somewhat embarrassed.

Yang Yuting continued, "Alright, before was just the simplest situation. This problem is called the 'Wallet Game' or 'Two Envelope Paradox,' proposed by a mathematician.

"Next is the derivative game I'm giving based on this principle. Please everyone focus."