God's imitator

Chapter 9 The Three Doors Problem
After thinking carefully for a moment, Li Renshu said, "You mean you can see through the linguistic trap that the designer buried in the rules, and then shoot yourself with all six shots?"

What everyone saw was the complete set of rules, meaning they knew the live bullet was in the innocent man's pocket, not in the gun cylinder.

The rules state: [A revolver cylinder has six magazines, five of which are empty and located at random positions on the cylinder.]

This is a pure linguistic trap.

Anyone who knows this can indeed complete the game without taking any damage.

Wang Yongxin immediately objected: "But that's because we've adopted a God's-eye view."

"Suppose we wake up knowing nothing and are told this rule while our lives are threatened, most people would not be able to think rationally as you say."

"You think you can recognize this trap? You're overestimating your own rationality."

Cai Zhiyuan shook his head: "No, I think that even if you don't notice the trap, it won't prevent you from completing the game."

"Let's analyze the probability issues involved here."

"First, the iron block mechanism is 6cm away from the player's head on both sides, which is an average of 3cm on each side. Shooting an innocent person will cause the iron block on each side to move inward by 1.29cm."

"This means that the first two moves were harmless, and the third move caused far less damage than the later moves."

"The fourth, fifth, and sixth movements will cause more severe damage to the head each time, and the danger level will increase exponentially. By the fifth movement, death is almost certain."

"Therefore, when considering the risk of death, we should not only consider being 'hit by a bullet,' but also 'being crushed by a trap.'"

"Assuming that the mechanism will kill you after moving it five times, we can roughly consider that each movement of the mechanism will accumulate 1/5 of the death progress bar. Of course, the death rate of the mechanism is not evenly distributed, but increases as time goes on."

"If you shoot yourself, there is a 1/6 chance of dying, that's for sure; but if you shoot the other person, there is a 5/6 chance of missing, and moving the mechanism will also bring a 1/5 chance of death."

"Whether you hit yourself or the other party, the actual risk is about the same."

"Since we could be crushed to death in five attempts, we must at least shoot ourselves twice."

"Assuming there is a live bullet in the gun, the probability of hitting the opponent with each shot is 1/6. Which two shots you choose to fire at the opponent does not actually affect the outcome of the game."

"But psychologically speaking, it's definitely better to choose the first two shots."

"Because in actual operation, if the first shot misses, the probability of the next shot will increase accordingly, which will bring huge psychological pressure."

"For example, if you miss the first shot without knowing it, the probability of each subsequent shot becomes 1/5. If you miss the second shot, the probability of each subsequent shot becomes 1/4, and so on."

"So, regardless of whether you think the probability of each shot is the same or different, you should prioritize shooting yourself in the first two shots."

"After the fourth shot, there will be a new prompt: the fifth shot is a blank."

"This hint is too kind; isn't it just the classic three-door problem?"

"This means that the probability of the fourth shot being live is still 1/3, while the probability of the sixth shot being live becomes 2/3. If one can make a rational decision, the fourth shot should still be aimed at oneself."

"If you can grasp this point, then even if you choose to shoot an innocent person with the last shot, plus the shot that shot an innocent person with the first three shots, the iron block mechanism will only move twice at most."

"From the distance, there wouldn't even be any superficial injuries."

"Moreover, from God's perspective, we know that there is not a single bullet in the revolver, so the possibility of being killed by a bullet simply does not exist."

Everyone fell silent for a moment.

Newspaper editor Jiang He frowned and asked, "I roughly understood the beginning, but I didn't understand the last three shots. What is the 'three-door problem'?"

Cai Zhiyuan was somewhat surprised: "You don't even know this?"
"Okay, let me explain it simply. This is actually a very classic probability problem."

It originated from a foreign television program:

"There are three closed doors in front of the contestants. Behind one door is a car, and the contestant can win by choosing the car behind it. The other two doors are empty."

"The contestant selected one of the doors, but did not open it immediately."

"At this point, the host opened one of the other two doors, and there was nothing behind it; no car. Please note that the host did not open a door randomly, because as the host, he knew in advance which door had a car behind it. The door he opened was the one he knew beforehand was empty."

At this point, the host asked the contestant: "Do you want to change the door?"

"If you were a contestant, would you switch?"

Jiang He thought for a moment, then said firmly, "No, I won't switch. I trust my first instinct. Besides, isn't the probability of a car behind each door 1/3? What difference does it make whether I switch or not?"

Cai Zhiyuan shook his head: "Then you're wrong."

"Because the probability of a car being at the original door remains unchanged at 1/3, but the probability of a car being at the other door has become 2/3, so it should be changed."

Jiang He was stunned: "Huh? Why?"

Cai Zhiyuan explained: "That's why the three-door problem has become a classic probability problem. It seems simple, but it is very counterintuitive."

"It's normal for you to feel confused, because this question sparked a heated debate at the time, and many scientists and scholars even opposed the conclusion."

"This issue is rather complex to argue, but I have a more easily understood explanation here:"

"Let's say we increase the number of doors to 10000 doors, with one door behind a car and the other 9999 doors behind nothing."

"You choose a door, the host knows the car's location in advance, and then he opens another 9998 empty doors, leaving only one door."

"At this point, the host will ask you again: Do you want to change the door?"

Should we change it this time?

Jiang He thought for a moment: "Change it."

Cai Zhiyuan asked, "Then why did you decide to change it this time?"

Jiang He lowered her head and thought: "Out of ten thousand doors, it is almost impossible to accurately select a car on the first try. The probability is one in ten thousand."

"The door I originally chose definitely didn't have any cars."

"So the car can only be behind the other door."

Cai Zhiyuan nodded: "That's right, the problem becomes much easier to understand once the number of doors increases."

"No matter which door the host opens, the probability of the original door remains unchanged because it was chosen from the beginning, but the probability of the other doors will increase."

"So we go back to the original three-door problem: the probability of a car being behind the door chosen by the contestant is 1/3, and if we consider the other two doors as a whole, the probability of a car being behind them is 2/3."

"After the host eliminates one door, the probability of having a car through both doors is equal to the probability of having a car through the other door."

"The probability of that door has changed from 1/3 to 2/3."

Fu Chen understood, and he nodded slightly, seemingly lost in thought.

"So, when the game got to the last three shots, the rules on TV were updated, and it actually became the 'three-door problem'."

"The fourth shot to be fired is the door that was originally selected; the fifth shot is the door that was eliminated by the host; and the sixth shot is the remaining door."

"When the host asks if you want to change the door, it means the player decides whether to change the fourth shot to the sixth shot."

"From these two shots, choose the one with a lower probability of hitting yourself, and the one with a higher probability of hitting an innocent person."

Cai Zhiyuan praised, "That's right, you're very smart, that's exactly it."

A brief silence fell over everyone as they processed what Cai Zhiyuan had just said.

After thinking about it carefully, Fu Chen said, "So according to this analysis, the 'Redemption Roulette' is actually a game that tests 'textual sensitivity' and 'probability'?"

"But can you get an S rating just for this reason?"

Li Renshu seemed to realize something, and 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 a matter of course: "Yes."

Lee In-sook agreed, saying, "I think so too, and it shouldn't be because of any probability issue."

Cao Haichuan seemed to be craving a cigarette and subconsciously reached for one, but ultimately resisted.

"Yes, I thought about it, and there's no particular reason why I survived, since I don't understand probability."

"I simply can't bring myself to point a gun at innocent people."

(End of this chapter)