God's Imitator-Chapter 470: The Secret of the Strategy

Lin Sizhi paused slightly and continued:

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

"By executing this strategy, the success rate can increase from 1/2 to the 100th power to 30%. This is simply miraculous.

"The principle behind this is very clever, but limited by time constraints, obviously there's no time to explain it now.

"And this set of 'Number Prisoners' rules very obviously made corresponding changes to these rules:

"Changing 100 prisoners into 'the Thief's two chances,' changing the originally numbered 1 to 100 boxes into '1 to 22 wooden boxes,' changing the originally numbered 1 to 100 slips of paper into 'the number of 100 denomination Wealth Vouchers in the wooden boxes (1 to 22).'

"So, for players who understand the '100 Prisoners Problem,' they only need to copy this strategy.

"First, guess a number and open the wooden box corresponding to that number.

"Second, count the number of 100 denomination Wealth Vouchers in this wooden box, and according to the number, open the next wooden box, continuing to open 7 wooden boxes like this.

"Of course, in this set of rules, a bit of memory is needed. You must remember the seven wooden boxes opened in the first chance and the specific number of 100 denomination Wealth Vouchers in the wooden boxes, avoiding opening duplicate wooden boxes in the second chance and wasting your opportunity.

"For the second chance, according to the number given by the Sage, continue executing this strategy and open seven more wooden boxes. 𝕗𝐫𝚎𝗲𝘄𝐞𝕓𝐧𝕠𝘃𝕖𝐥.𝐜𝚘𝚖

"If opening boxes completely randomly, then the first time's success rate is 7/22, the second time's success rate is 7/15, and the expected return is roughly Wealth Vouchers from 8.5 wooden boxes.

"But if executing this specific strategy, because the probability of guessing the number greatly increases, the expected return will also increase and should be significantly greater than 8.5 wooden boxes.

"So playing with this strategy will definitely obtain higher expected returns than the first conventional strategy of mindlessly taking 10 boxes."

Lin Sizhi paused slightly and continued, "My mask is 'Wheel of Fortune,' so I should choose the number '10' and open 'wooden box number 10,' then according to this strategy, open them one by one until finding that box 'containing 10 vouchers of 100 denomination.'"

But although saying this, he didn't seem to have any intention of opening any wooden boxes.

Instead, he changed the subject.

"But this is precisely where the trap of this strategy lies.

"In reality, my previous reasoning was completely wrong.

"The 'Number Prisoners' rules and the '100 Prisoners Problem' only look similar. In reality, they're completely different things.

"The most critical difference is that it changed the original condition of 'all 100 prisoners must find their numbers to count as victory.'

"The original '100 Prisoners Problem' was because of this condition that the success rate became 1/2 to the 100th power, and this strategy could greatly increase the success rate.

"But in the 'Number Prisoners' rules, changing 100 prisoners into 2 chances, and adding guaranteed rewards for 'only succeeding once' and 'not succeeding once,' causes the probability of success to not be low. It's a completely different concept from '1/2 to the 100th power.'

"So, this strategy can indeed increase the success rate, but in reality, the improvement effect becomes negligible and can even be ignored.

"If the 'Sage' player completely randomly places different numbers (1 to 22) of 100 denomination Wealth Vouchers in the wooden boxes, then even if the 'Thief' executes this strategy, the expected return won't be much higher than the original '8.5 wooden boxes of Wealth Vouchers.'

"So this set of rules will actually simultaneously confuse two types of players:

"The first type of player isn't clear about the '100 Prisoners Problem,' and these players often also aren't good at probability and aren't good at calculations.

"They just instinctively feel that since failing both times still has a guarantee of 5 wooden boxes, then why not try? What if both actions succeed? Opening 7 boxes to guess one number seems quite worthwhile.

"So they'll give up stably taking 10 wooden boxes according to the first strategy to try a gameplay with lower expected returns.

"And the second type of player, they're good at probability and calculations and can calculate the expected return of this gameplay, but at the same time, they've most likely also encountered the '100 Prisoners Problem' and instinctively match it incorrectly, wishfully believing that copying the number cycle strategy from the '100 Prisoners Problem' can greatly increase their expected returns.

"But they overlook the essential difference between the 'Number Prisoners' rules and the '100 Prisoners Problem,' and still choose a gameplay with lower expected returns.

"Only a minority of players can see clearly the difference between the two rules in a short time and reach the conclusion:

"This is a trap targeting both types of people simultaneously. The best choice is not to play.

"They should continue choosing the first strategy and just casually take 10 wooden boxes."

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

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

"Because I feel you've most likely also already thought of this level and believe I'll be helpless because of it.

"However, in this set of game rules, there's no perfect winning strategy."

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

Actually, with her capabilities, she could create her own Sage rules.

But Han Mengying didn't choose to create her own. Instead, she played with the 'Number Prisoners' rules precisely because she believed that after analyzing this set of rules to the end, no matter how one thought about it, it was a game where the 'Sage' held absolute advantage.

The wisest choice for the 'Thief' player was not to play.

It was precisely because of this reason that Han Mengying appreciated the '↓The Emperor' player who proposed this set of rules even more and further strengthened her idea that she must poach him to Community 4.

Han Mengying had absolutely no confidence in beating Lin Sizhi by relying on self-created rules, so ultimately, she chose the method with the greatest chance of winning.

If Lin Sizhi chose to take 10 wooden boxes and leave, then Han Mengying could still tell herself that this match they were at least tied.

But very obviously, Lin Sizhi didn't want to end this match so boringly.

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

"So, the flaw of a strategy is the flaw of the executor.

"For the 'Sage,' the optimal strategy is to completely randomly place different quantities of 100 denomination Wealth Vouchers.

"But the most difficult point is that the 'Sage' will also always instinctively speculate about the 'Thief's' possible actions and naturally make arrangements more favorable to themselves.

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