Li Renshu thought seriously for a moment and said, "Are you saying that you can see through the linguistic trap the designer buried in the rules, and then shoot yourself all six times?"
What everyone saw were the complete rules, which means they knew the live round was in the innocent person's pocket, not in the revolver's cylinder.
The rule stated: [The revolver's cylinder has 6 chambers, and five of them are empty, distributed in random positions within the cylinder.]
This line was a pure linguistic trap.
Anyone who knew this could indeed clear the game without getting hurt.
Wang Yongxin immediately objected: "But that's because we have a God's-eye view.
"Assuming we wake up knowing nothing and are told this rule with our lives on the line, the vast majority of people couldn't think as rationally as you say.
"To think you could spot such a trap is to have too much faith in your own rationality."
Cai Zhiyuan shook his head: "No, I believe that even without noticing this trap, it wouldn't prevent one from clearing the game.
"Let's sort out the probability here.
"First, the total distance of the iron block mechanism from both sides of the player's head is 6cm, which is an average of 3cm per side. Shooting the innocent person once moves each iron block inward by 1.29cm.
"This means the first two movements are harmless, and the damage from the third movement is far less than the subsequent ones.
"But the fourth, fifth, and sixth movements will each cause more severe damage to the head, with the danger level increasing exponentially. You'd almost certainly be dead by the fifth movement.
"So when considering the risk of death, we must not only consider 'being hit by a bullet' but also 'being crushed to death by the mechanism.'
"Assuming five movements of the mechanism will kill you, we can roughly see each movement as accumulating 1/5 of a death progress bar. Of course, the mechanism's mortality rate isn't evenly distributed; it gets higher and higher.
"Shooting yourself has a 1/6 chance of death, no doubt about that; shooting the other person has a 5/6 chance of being a blank, and the mechanism's movement also adds 1/5 to the death progress bar.
"Shooting yourself or shooting the other person, the actual risks are about the same.
"Since five times could crush you to death, we must choose to shoot ourselves at least twice.
"Assuming there really is one live round in the gun, the probability of getting shot is 1/6 each time. Which two shots you choose to fire at the other person doesn't really affect the game's outcome.
"But psychologically, it's definitely best to choose the first two shots.
"Because in practice, if the previous shot was a blank, the probability of the next shot being live will increase accordingly, which creates immense psychological pressure.
"For example, if the first shot is a blank without your knowledge, then the probability for each subsequent shot becomes 1/5. If the second shot is also a blank, then each subsequent shot becomes 1/4, and so on.
"So, whether you think the probability for each shot is the same or not, you should prioritize shooting yourself for the first two shots.
"By the fourth shot, there's a new hint: the fifth shot is a blank.
"This hint is just too merciful, isn't it the classic Monty Hall problem?
"This means the probability of the fourth shot having the live round is still 1/3, while the probability of the sixth shot having it becomes 2/3. If you can make a rational decision, you should still shoot yourself on the fourth shot.
"If you can grasp this point, then even if you choose to shoot the innocent person on the last shot, plus the one shot at the innocent person among the first three, the iron block mechanism would move at most twice.
"In terms of distance, you wouldn't even get a scratch.
"Not to mention, from our God's-eye view, we know there are no bullets in the revolver at all, so the possibility of being killed by a bullet doesn't exist."
Everyone fell silent for a moment.
Newspaper editor Jiang He frowned and asked, "I mostly understood the first part, but I didn't get the last three shots. What is the Monty Hall problem?"
Cai Zhiyuan was a bit surprised: "You don't even know that?
"Alright, let me give a simple explanation. It's actually a very classic probability problem.
"It originates from a foreign TV show:
"A contestant is faced with three closed doors. Behind one door is a car, which they can win if they choose correctly. Behind the other two doors is nothing.
"The contestant chooses one of the doors but doesn't open it right away.
"At this point, the host opens one of the other two doors, revealing it to be empty, with no car. Please note, the host doesn't open a door randomly, because as the host, he knows from the start which door has the car. The door he opens is one he already knew was empty.
"The host then asks the contestant: Do you want to switch to another door?
"If you were the contestant, would you switch?"
Jiang He thought for a moment and said firmly, "I wouldn't switch. I trust my first instinct.
"Besides, isn't the probability of a car being behind each door 1/3? What difference does it make if I switch or not."
Cai Zhiyuan shook his head: "Then you're wrong.
"Because the probability of the original door having the car remains unchanged at 1/3, but the probability of the other door having the car becomes 2/3. You should switch."
Jiang He was stunned: "Huh? Why?"
Cai Zhiyuan explained: "That's why the Monty Hall problem became a classic probability problem. It seems simple, but it's very counter-intuitive.
"It's normal for you to be confused, because at the time, this problem sparked intense debate, and even many scientists and scholars opposed this conclusion.
"The proof for this problem is rather complex, but I have a more easily understood explanation here:
"Let's assume we increase the number of doors to 10000. Behind one door is a car, and behind the other 9999 doors is nothing.
"You choose one door. The host knows where the car is beforehand, and then he opens the other 9998 empty doors, leaving only one other door closed.
"Now the host asks you again: Do you want to switch to the other door?
"Do you switch this time?"
Jiang He thought for a moment: "Switch."
Cai Zhiyuan asked: "Then why did you decide to switch this time?"
Jiang He looked down in thought: "With ten thousand doors, it's almost impossible to pick the car correctly right from the start. The probability is one in ten thousand.
"The door I originally chose definitely doesn't have the car.
"So the car can only be behind the other door."
Cai Zhiyuan nodded: "Exactly. Once the number of doors increases, the problem becomes much easier to understand.
"No matter how the host opens the doors, the probability of your originally chosen door remains unchanged because it was selected at the beginning, but the probability of the other doors will increase.
"So let's go back to the original Monty Hall problem: the probability of the contestant's chosen door having the car is 1/3. We can view the other two doors as a single group, and the probability of them having the car is 2/3.
"After the host eliminates one door, the probability of the two-door group having the car becomes equivalent to the probability of the remaining other door having the car.
"That door's probability changes from 1/3 to 2/3."
Fu Chen understood. He nodded slightly, lost in thought.
"So, when the game reached the last three shots, the rules updated on the TV, effectively turning it into the 'Monty Hall problem.'
"The upcoming fourth shot is the originally chosen door; the fifth shot is the door eliminated by the host, and the sixth shot is the remaining door.
"The host asking whether to switch doors is equivalent to the player deciding whether to switch the fourth shot for the sixth shot.
"You have to choose to shoot yourself with the one with the lower probability, and shoot the innocent person with the one with the higher probability."
Cai Zhiyuan said with approval: "Exactly. You're very smart, that's precisely it."
The group fell into a brief silence, all digesting what Cai Zhiyuan had just said.
After some serious thought, Fu Chen said: "So according to this analysis, 'Redemption Roulette' is actually a game that tests 'linguistic sensitivity' and 'probability'?
"But can you get an S-rank evaluation for just that reason?"
Li Renshu seemed to realize something. She looked at Cao Haichuan:
"Officer Cao, if you were a player in this game, do you think you could survive it?"
Cao Haichuan nodded as if it were a matter of course: "Yes."
Li Renshu agreed: "I think so too. And it probably wouldn't be because of some probability problem."
Cao Haichuan seemed to be having a nicotine craving. He subconsciously reached for a cigarette but ultimately resisted.
"Yes, I thought about it. There's no special reason I'd survive, since I don't understand probability.
"I simply couldn't bring myself to point a gun at an innocent person."