Wang Yongxin paused for a moment and continued:
"In this world, visa time is life.
"Quantifying the value of life to earn visa time is essentially trading life for life.
"As for whether this exchange is worthwhile, one must consider the specific risks, returns, and probabilities.
"Of course, this brings us to another trap in this game, which is the 'Chip Exchange Machine'.
"Players are thrown into a game against the Chip Exchange Machine right from the start, and the rules clearly state that it's an unfair game.
"The Chip Exchange Machine gets to draw an extra card, choosing three out of four to form the best possible hand. It's also always the dealer and always raises first.
"Generally, raising first puts you in a more passive position, but since the Chip Exchange Machine can draw an extra card, its hand is naturally stronger, which in turn increases our cost to call and show cards. If we want to show cards, we have to bear an additional loss of 500 chips.
"Most players lose completely in their first couple of rounds.
"They either fold without daring to call, or they call and still lose, suffering even greater losses.
"This severe negative feedback leads most people to naturally assume that playing against the Chip Exchange Machine offers no chance of winning and is purely a waste of chips.
"This is the biggest information barrier in the game.
"This barrier even kept out smart people like Cai Zhiyuan and Officer Cao."
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 every single one.
"The Chip Exchange Machine had almost a 50% chance of getting a pair, and even if it didn't get a pair, it would inevitably get a high card hand of J or better.
"Later on, I just gave up, folding immediately without looking at my cards, since looking at them would cost another 500 chips."
He looked at Cai Zhiyuan, "However, we did discuss the relevant probabilities at the time, and Cai Zhiyuan even did a rough calculation.
"But whether it was the calculated probability or the probability we experienced in the game, the win rate was very low."
As a programmer, Cai Zhiyuan was the most proficient in probability.
And this kind of poker game is strongly correlated with probability.
Because the probability of each hand type can be calculated precisely, the difference in probability between two hand types naturally determines the win rate.
Many people had originally thought that Cai Zhiyuan would surely be the best at this type of game.
But unexpectedly, his performance was not particularly outstanding.
Instead, Wang Yongxin, a boss who didn't know much about probability, and Lin Si, a liberal arts student, became the only two people in Community 17 to discover the Chip Exchange Machine's loophole.
Cai Zhiyuan sighed silently, "I did calculate the relevant probabilities.
"But the more I calculated, the more I ended up misleading myself."
Wang Yongxin suggested, "Why don't we take this opportunity to calculate the relevant probabilities thoroughly? Although the game is over, at least everyone can understand clearly, whether they won or lost."
Cai Zhiyuan nodded, "Okay."
He took a pen and paper and began to calculate rapidly.
The initial calculations weren't too complex, but when it came to calculating the probability changes of choosing three out of four cards, the amount of calculation increased sharply.
Although Cai Zhiyuan calculated quickly, he still used several sheets of paper before giving the final answer.
"This should be about right."
Cai Zhiyuan handed the papers filled with numbers to Wang Yongxin.
Wang Yongxin looked through it from beginning to end, with a look of considerable surprise appearing on his face from time to in time.
Then, he looked at the crowd, "Allow me to build some suspense first. In this game, what kind of hand do you think is worth betting heavily on?"
The crowd looked at each other and started guessing.
"A straight? A straight is a moderately strong hand."
"I don't think so, isn't a straight itself a very low-probability hand? I think a pair is enough."
"A pair of 10s or better? That should be about right."
"Wait, let's first clarify what 'betting heavily' means. If you're going all-in with your remaining chips, would you dare to bet that a single pair can win it all? I think you'd need at least a flush."
Clearly, even in this situation, everyone still couldn't reach a consensus.
Because each person's risk tolerance was different, and their estimates of the probabilities of various hand types were different, the combination of these two factors naturally led to vastly different decisions.
Wang Yongxin gave the answer, "Drawing any three cards from a 52-card deck, there are a total of 22,100 combinations.
"Among them, there are 52 three-of-a-kinds, with a probability of 0.24%;
"There are 48 straight flushes, with a probability of 0.22%;
"There are 1096 flushes, with a probability of 4.96%;
"There are 720 straights, with a probability of 3.26%;
"There are 3744 pairs, with a probability of 16.94%;
"There are 16440 high card hands, with a probability of 74.39%."
As soon as these words were spoken, everyone was very surprised.
"Huh? The probability of a pair is only 17%?"
"The probability of a straight flush is lower than a three-of-a-kind? The probability of a straight is lower than a flush?"
"The probability of a high card hand is 74.39%? Doesn't that mean that as long as you get a pair, even the smallest pair, you have a nearly 75% win rate in a one-on-one showdown?"
Clearly, this probability, to some extent, completely subverted conventional understanding.
Everyone knew that a high card hand was the weakest and that hands from a straight to a three-of-a-kind were strong, but what was the specific win rate? Few people had actually calculated it.
Most people estimated that the win rate of a high card hand was probably only around 50%, and even the win rate of a pair might not reach 60%.
But in reality, even the smallest pair had a win rate as high as 75%, and the win rate for hands starting from a straight was over 90%.
Wang Yongxin continued, "What do you think the win rate is for the Chip Exchange Machine after it draws an extra card and forms a hand by choosing three out of four?
"Forget it, I won't keep you in suspense, I'll just give you the results.
"The probability of a three-of-a-kind is 1.02%, an increase of 325%;
"The probability of a straight flush is 0.78%, an increase of 255%;
"The probability of a flush is 9.84%, an increase of 98%;
"The probability of a straight is 7.15%, an increase of 119%;
"The probability of a pair is 27.61%, an increase of 63%;
"The probability of a high card hand is 53.60%, a decrease of 28%.
"The advantage of drawing an extra card is indeed huge. Even if both sides have high card hands, the Chip Exchange Machine can likely optimize for a better high card hand.
"So in the actual process of betting against the Chip Exchange Machine, losing is indeed a high-probability event."
Cai Zhiyuan nodded, "Yes, I only calculated up to this point in the game, so I didn't continue to bet against the Chip Exchange Machine.
"However, if you know that the 'Chip Exchange Machine' will never fold, the strategy changes completely.
"Although the win rate seems low, once we get a relatively strong hand in a round, we can get double the return by continuously raising.
"Assuming we get a pair of Ks, then when facing the Chip Exchange Machine, we would actually have a win rate of over 70%.
"Assuming we get a flush, we would have a win rate of over 87%."
Jiang He frowned slightly, "But, isn't it hard to get that kind of hand?"
Wang Yongxin nodded, "It is hard to get, but the Chip Exchange Machine actually provides many opportunities.
"For every 100ML of blood drawn, you can play 1 to 20 rounds against the Chip Exchange Machine. If you draw 600ML of blood, you can play up to 120 rounds.
"This number of rounds is actually enough to get many strong hands. As long as you encounter one, you have a chance to double your chips.
"Not only that, if you can figure this out in advance, you can also fold immediately when you get a weak hand, minimizing the game time to the greatest extent."
Jiang He thought for a moment and frowned, "But probability can be unreasonable at times, and low-probability events are not entirely impossible.
"What if you run into a cooler hand? Wouldn't you still lose everything?"
Wang Yongxin shook his head dismissively, "You can't think of it that way!
"If you're always worried about low-probability events happening, then you'd just fold every hand. How would you make any money?
"Besides, there's another advantage to betting against the Chip Exchange Machine: as long as you choose to call, you can show cards at any time. Unlike betting against players, if two people take turns raising, you can never show cards.
"So, you set your own stop-loss limit and adjust your bet amount in real-time based on the win rate.
"Just like doing business, it's a simple matter of 'risk control'."
The crowd fell silent, clearly needing some time to digest this amount of information.
Fu Chen looked at the detailed rules on the big screen and sighed with emotion again.
This game didn't seem too complicated, but when carefully broken down, it had an unimaginable amount of detail.
"Alright, up to this point, we should have thoroughly dissected this game.
"So... does everyone think this game really served its screening purpose? In other words, do you think this method of distributing visa time is reasonable? Is it fair?"
Ding Wenqiang's face was still dark, "It's not fair."
The others remained silent.
A moment later, Lee In-sook said cautiously, "I think it's not fair, but it is reasonable."