Wang Yongxin paused briefly, then continued:
"In this world, Visa Time is life.
"Earning Visa Time by quantifying the value of life means trading life for life.
"As for whether such an exchange is worthwhile, that depends on the specific risks, returns, and probabilities involved.
"Of course, this brings us to another trap in the game: the Chip Exchange Machine.
"From the very beginning, players are thrown into a gambling match against the Chip Exchange Machine, and the rules clearly state that it is an unfair game.
"The Chip Exchange Machine can draw an extra card and select three out of four to form the strongest hand. It is always the dealer and always raises first.
"Generally speaking, raising first puts you at a disadvantage. But because the Chip Exchange Machine can draw an extra card, it naturally has stronger hands, which instead increases our cost of calling to reveal the cards. If you want to reveal, you must accept an additional loss of 500 chips.
"Most players lost every round after trying it twice.
"Either they did not dare call and folded, or they called and still lost, suffering even greater losses.
"The severe negative feedback naturally made most people believe that they had no chance of winning against the Chip Exchange Machine and were simply wasting chips.
"That was the biggest information barrier in the game.
"This barrier even kept smart people like Cai Zhiyuan and Officer Cao out."
Fu Chen pondered for a moment and nodded. "Yes. The four of us played a total of twenty-four rounds against the Chip Exchange Machine.
"In the first few rounds, we lost them all.
"The Chip Exchange Machine had nearly a fifty percent chance of getting a pair. Even when it did not get a pair, it would definitely have high cards above J.
"Later, I gave up. I folded without even looking at my cards, since looking at them cost another 500 chips."
He looked at Cai Zhiyuan. "Still, we did discuss the relevant probabilities at the time, and Cai Zhiyuan made some rough calculations.
"But whether it was the calculated probabilities or what we experienced in the game, the win rate was very low."
As a programmer, Cai Zhiyuan was the most proficient in probability.
And poker games like this were closely tied to probability.
Because the probability of every type of hand could be calculated precisely, and the probability gap between two types of hands naturally determined the win rate.
Quite a few people had originally thought that Cai Zhiyuan would definitely be the best at this type of game.
Yet his performance had not been particularly outstanding.
Instead, Wang Yongxin, a boss who did not know much about probability, and Lin Sizhi, a humanities student, had become the only two people in Community No. 17 to discover the loophole in the Chip Exchange Machine.
Cai Zhiyuan sighed silently. "I did calculate the relevant probabilities.
"But the more I calculated, the more I misled myself."
Wang Yongxin suggested, "Why not take this opportunity to work out all the relevant probabilities properly? The game is over, but at least everyone can understand clearly, whether they won or lost."
Cai Zhiyuan nodded. "All right."
He took some paper and a pen and began calculating at high speed.
The initial calculations were not too complicated, but when he reached the probability changes involved in choosing three out of four cards, the amount of calculation abruptly increased.
Although Cai Zhiyuan calculated quickly, he still filled several sheets of paper before giving the final answer.
"This should be about right."
Cai Zhiyuan handed the number-filled sheets to Wang Yongxin.
Wang Yongxin read through them from beginning to end, an astonished expression appearing on his face from time to time.
Then he looked at everyone. "Let me keep you in suspense for a moment. What kind of hand do you think is worth making a heavy bet on in this game?"
Everyone looked at one another and began offering guesses.
"A straight? A straight is neither too big nor too small a hand."
"Probably not. A straight itself is already a low-probability hand, right? I think a pair would do."
"A pair of tens or higher? That should be about enough."
"Wait, first define what a 'heavy bet' means. If you mean shoving all your remaining chips, would you dare bet everything on a pair winning? I think it would have to be at least a flush."
Clearly, even under these circumstances, they still could not reach a consensus.
Everyone had a different tolerance for risk and a different estimate of the probabilities of various hands. With those two factors combined, their decisions naturally varied greatly.
Wang Yongxin gave the answer. "Choosing any three cards from a fifty-two-card deck gives a total of 22,100 combinations.
"There are 52 three-of-a-kinds, for a probability of 0.24%;
"There are 48 straight flushes, for a probability of 0.22%;
"There are 1,096 flushes, for a probability of 4.96%;
"There are 720 straights, for a probability of 3.26%;
"There are 3,744 pairs, for a probability of 16.94%;
"And there are 16,440 high-card hands, for a probability of 74.39%."
Everyone was extremely surprised when they heard this.
"Huh? The chance of getting a pair is only 17%?"
"A straight flush is less likely than three of a kind? A straight is less likely than a flush?"
"The chance of a high-card hand is 74.39%? Doesn't that mean that if you get any pair, even the smallest pair, you would have nearly a 75% win rate in a heads-up match?"
Clearly, these probabilities completely overturned conventional understanding to a certain extent.
Everyone knew that high cards were the weakest hands and that straights through three-of-a-kind were strong hands, but very few people had ever truly calculated the exact win rates.
Most people estimated that high-card hands probably had around a fifty percent win rate, and even pairs might not have a win rate above sixty percent.
But in reality, even the smallest pair had a win rate as high as seventy-five percent, while hands from straights upward had win rates above ninety percent.
Wang Yongxin continued, "What do you think the Chip Exchange Machine's win rate becomes after it draws one extra card and chooses three out of four to form its hand?
"Forget it, I will not keep you in suspense. I'll give you the results directly.
"The probability of three of a kind is 0.9%;
"The probability of a straight flush is 0.85%;
"The probability of a flush is 16.8%;
"The probability of a straight is 8.4%;
"The probability of a pair is 27.3%;
"The probability of a high-card hand is 45.60%.
"The advantage of drawing an extra card is indeed enormous. Even if both sides have high-card hands, the Chip Exchange Machine will most likely be able to optimize into a higher one.
"So in an actual match against the Chip Exchange Machine, losing is indeed the most likely outcome."
Cai Zhiyuan nodded. "Yes. I only calculated that far during the game, so I stopped gambling against the Chip Exchange Machine.
"But if you know that the Chip Exchange Machine will not fold, the strategy changes completely.
"Although the win rate looks low, once we get a relatively strong hand, we can keep raising to obtain multiplied returns.
"Suppose we get a pair of kings. Against the Chip Exchange Machine, we actually have a win rate above seventy percent.
"Suppose we get a flush, and the win rate is above eighty percent."
Jiang He frowned slightly. "But hands like that are hard to get, aren't they?"
Wang Yongxin nodded. "They are hard to get, but the Chip Exchange Machine actually gives us many opportunities.
"For every 100 milliliters of blood drawn, you can gamble against the Chip Exchange Machine for one to twenty rounds. If you draw 600 milliliters of blood, you can play up to 120 rounds.
"That number of rounds is actually enough to get strong hands many times. As long as you encounter one, your chips have a chance to double.
"More importantly, if you think this through in advance, you can immediately fold whenever you get a weak hand, minimizing the time spent in the game.
Jiang He thought for a moment, then frowned. "But probability is often unreasonable. Low-probability events are not impossible.
"What if you run into a cooler? Wouldn't you still Lose All Capital?"
Wang Yongxin shook his head dismissively. "You cannot think like that!
"If you are always worried about low-probability events happening, then you will fold every hand. How are you supposed to make money?
"Besides, there is another benefit to gambling against the Chip Exchange Machine: as long as you choose to call, you can reveal the cards at any time. It is unlike gambling against another player, where if the two sides take turns raising, you can never reveal.
"So set your own stop-loss limit and adjust the number of chips you bet in real time according to your win rate.
"Just like doing business, it is a simple matter of risk control."
Everyone fell silent. Clearly, they needed time to properly digest all that information.
Fu Chen looked at the detailed rules on the big screen and sighed again.
The game did not seem particularly complicated, but when carefully broken down, it contained an unimaginable amount of detail.
"All right, by now, we should have completely broken down this game, right?
"So... do you think this game truly served its purpose of screening people? In other words, do you think this method of allocating Visa Time is reasonable? Is it fair?"
Ding Wenqiang still had a dark expression. "It is not fair."
The others remained silent.
After a moment, Li Renshu said cautiously, "I think it is unfair, but reasonable."
Before you continue