God's imitator

Chapter 471 The Secret of Strategy (Bonus Chapter)

Lin Sizhi paused slightly before continuing:

"This is the only optimal solution to this problem, and there is no better strategy than it."

"By implementing this strategy, the success rate can increase from 1/2 to the power of 100 to 30%, which is nothing short of miraculous."

"The principle behind this is ingenious, but due to time constraints, it is obviously too late to explain it now."

"And this set of 'digital prisoner' rules is clearly a direct modification of this rule:"
“把100名囚犯，变成了『窃贼的两次机会』；把原本编号1到100的盒子，变成了『1到22的木盒』，把原本编号1到100的纸条，变成了『木盒中100面值财富券的张数（1到22）』。

"Therefore, for players who understand the '100 Prisoners Problem,' they can simply copy this strategy."

"First, guess a number and open the wooden box with the number corresponding to that number;
"Next, count the number of 100-yuan wealth coupons in this wooden box, and open the next wooden box according to the number of coupons, and so on until you open 7 wooden boxes."

"Of course, this set of rules requires a little memory. You need to remember the seven wooden boxes you opened in the first chance and the specific number of 100-value wealth coupons in each box, so as to avoid opening the same wooden boxes in the second chance and wasting your chance."

"For the second chance, follow the strategy given by the sage and open seven more wooden boxes."

"If the boxes are opened completely randomly, the success rate for the first time is 7/22, and the success rate for the second time is 7/15. The expected reward is approximately 8.5 wealth vouchers from the wooden boxes."

"If this specific strategy is implemented, the expected return will also increase because the probability of guessing the number is greatly increased. It should be significantly greater than 8.5 wooden boxes."

"Therefore, using this strategy will definitely yield a higher expected return than the first conventional strategy of mindlessly taking away 10 boxes."

Lin Sizhi paused slightly before continuing, "My mask is the 'Wheel of Fortune,' so I should choose the number '10' and open 'Wooden Box No. 10.' Then, following this strategy, I should open them one by one until I find the box that contains '10 wealth vouchers worth 100 each.'"

But despite saying that, he didn't seem to have any intention of opening any of the wooden boxes.

Instead, the conversation took a turn.

"But this is also the trap of this strategy."

"In fact, my previous reasoning was completely wrong."

The “digital prisoner” rule and the “100 prisoners problem” may seem similar, but they are not the same thing at all.

"The most crucial difference is that it changed the original condition that 'victory is achieved when all 100 prisoners find their numbers.'"

"The original '100 Prisoners Problem' had a success rate that became 1/2 to the power of 100 because of this condition, which is why this strategy can significantly improve the success rate."

"In the rules of 'Digital Prisoner,' the 100 prisoners were changed to 2 chances, and a minimum reward of 'success only once' and 'failure at all' was added, which makes the probability of success not low. It is a completely different concept from '1/2 to the power of 100'."

"Therefore, this strategy can indeed increase the success rate, but in reality, the improvement will be negligible, or even insignificant."

"If the 'Sage' player randomly places different numbers (1~22) of 100-value Wealth Vouchers in the wooden box, then even if the 'Thief' executes this strategy, the expected profit will not be much higher than the original '8.5 wooden box Wealth Vouchers'."

"Therefore, this set of rules will actually confuse two types of players at the same time:"

"The first type of player is not familiar with the '100 Prisoners Problem,' and these players are often not good at probability or calculation."

"They just instinctively felt that since there was a guaranteed minimum of 5 wooden boxes even after two failures, why not give it a try? What if both attempts succeeded? Opening 7 boxes and guessing a number seemed like a pretty good deal. "So they would abandon the first strategy of reliably getting 10 wooden boxes and try a game with a lower expected return."

"The second type of player is good at probability and calculation, and can calculate the expected return of this game. However, at the same time, they have likely also encountered the '100 Prisoners Problem' and subconsciously applied it incorrectly, wishfully believing that copying the numerical cycle strategy of the '100 Prisoners Problem' can greatly increase their expected return."

"But they overlooked the fundamental difference between the 'digital prisoner' rule and the '100 prisoners problem,' and still chose a way of playing with lower expected returns."

Only a few players are able to clearly see the difference between the two rules in a short period of time and draw a conclusion:
"This is a trap that targets two types of people at the same time. The best choice is not to play it."

"We should continue with the first strategy and just take 10 wooden boxes at random."

Han Mengying was silent for a moment, then asked, "You mean you'll also choose the first strategy and take all 10 wooden boxes?"

Lin Sizhi shook her head: "No, I choose to play by your rules."

"Because I think you've probably already thought of this, and you think I'll be helpless because of it."

"However, there is no perfect winning strategy in this set of rules."

At this moment, Han Mengying, behind the '↑Lover' mask, widened her eyes and revealed a surprised and astonished expression for the first time.

In fact, given her abilities, she could create her own set of sage rules.

However, Han Mengying did not choose to create her own game. Instead, she played it according to the rules of "Digital Prisoner" because she believed that no matter how you analyzed the rules, it was a game in which the "wise man" had an absolute advantage.

The wisest choice for a 'Thief' player is not to play.

It was precisely for this reason that Han Mengying admired the player "↓Emperor" who proposed this set of rules even more, and further strengthened her resolve to recruit him to the 4th community.

Han Mengying had no confidence in winning against Lin Sizhi using her self-created rules, so in the end, she chose the method with the best chance of winning.

If Lin Sizhi chooses to take 10 wooden boxes and leave, then Han Mengying can still tell herself that this round is at least a draw.

But clearly, Lin Sizhi didn't want the match to end so boringly.

Lin Sizhi continued, "No matter how perfect a strategy is, it still needs people to execute it."

"Therefore, the flaws in the strategy are the flaws in the executor."

"For the 'wise man,' the optimal strategy is to randomly insert different numbers of 100-value wealth vouchers."

"But the most difficult part is that the 'wise man' will always subconsciously speculate on the possible behavior of the 'thief' and naturally make arrangements that are more favorable to himself."

"Just like when this set of rules first appeared, in the match between '↓ Emperor' and '↑ Demon'."

　This bonus chapter is extra and not included in the previously promised bonus chapters. There will be 6 more bonus chapters to come, but I have to catch a flight tomorrow, so it might take up to the next week to complete them all.

　　
　
(End of this chapter)