God's imitator

Chapter 28 Probability of Card Patterns

Wang Yongxin paused slightly before continuing:
"In this world, visa processing time is life."

"Quantifying the value of life to earn visa time is essentially trading one's life for another."

"Whether such an exchange is worthwhile depends on the specific risks, benefits, and probabilities."

"Of course, here we have to mention another trap in this game, which is the 'chip exchange machine'."

"Players are thrown into a game with a chip exchange machine from the very beginning, and the rules clearly state that this is an unfair game."

"The chip exchange machine can draw an extra card and select three cards from four to form the best hand. And it's always the dealer, and always the one who raises first."

"Generally speaking, raising first puts you at a disadvantage, but since the chip exchange machine can draw an extra card, the hand is naturally stronger, which increases our cost of calling and showing our cards. If we want to show our cards, we have to bear the loss of an extra 500 chips."

"Most players played two rounds and basically lost every time."

"Either they folded because they didn't dare to call, or they called but still lost, suffering even greater losses."

"The severe negative feedback leads most people to believe that there is no chance of winning by playing with chip exchange machines, and that it is a pure waste of chips."

"This is the biggest information barrier in the game."

"This barrier even keeps smart people like Cai Zhiyuan and Officer Cao out."

Fu Chen pondered for a moment and nodded: "Yes, the four of us gambled on the chip exchange machine for a total of twenty-four rounds."

"We lost the first few games."

"The chip exchange machine has almost a 50% chance of giving you a pair, and even if you don't get a pair, you're guaranteed to get a mixed hand of J or higher."

"Later I gave up and folded without looking at my cards, since looking at my cards would cost me 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's the calculated probability or the probability experienced in the game, the win rate is very low."

As a programmer, Cai Zhiyuan is most proficient in probability.

And similar card games are strongly related to probability.

Because the probability of each hand type can be calculated precisely, and the probability difference between two hand types naturally determines the winning rate.

Many people originally thought that Tsai Chih-yuan would definitely be the most skilled at this type of game.

Unexpectedly, his performance was not particularly outstanding.

Wang Yongxin, a boss who doesn't really understand probability, and Lin Sizhi, a liberal arts student, became the only two people in the 17th community to discover the loophole in the chip exchange machine.

Cai Zhiyuan sighed silently: "I did calculate the relevant probabilities."

"But after all the calculations, I ended up misleading myself."

Wang Yongxin suggested, "Why don't we take this opportunity to thoroughly calculate the relevant probabilities? Although the game is over, at least everyone will understand the outcome, regardless of whether they win or lose."

Cai Zhiyuan nodded: "Okay."

He picked up a pen and paper and began calculating rapidly.

The initial calculations were not too complicated, but the computational workload increased dramatically when calculating the probability changes of choosing three out of four.

Although Cai Zhiyuan calculated very quickly, he still spent several sheets of paper calculating before giving the final answer.

"It should be pretty much correct."

Cai Zhiyuan handed the paper filled with numbers to Wang Yongxin.

Wang Yongxin read it from beginning to end, his face showing considerable surprise from time to time.

Then, he looked at everyone and said, "Let me keep you in suspense for a moment. In this game, what kind of hand is worth betting heavily on?"

The group looked at each other and began to speculate.

"A straight? A straight is a hand that's neither too strong nor too weak."

"It shouldn't be that bad. A straight is already a very low probability hand, right? I think a pair would be enough."

"For 10 or more? That should be about right."

"Wait, let's first understand what 'betting heavily' means? If you're betting all your remaining chips, would you dare to bet on a pair to win the whole game? I think it would have to be at least a flush."

Clearly, even under these circumstances, everyone still cannot reach a consensus.

Because everyone has different risk tolerance and different probability estimates for different hand types, the combined effect of these two factors naturally leads to vastly different decisions.

Wang Yongxin provided the answer: "There are 22100 possible combinations of any three cards drawn from a deck of 52."

"Among them, there are 52 species of leopards, with a probability of 0.24%;

There are 48 possible combinations of a straight flush, with a probability of 0.22%.

There are 1096 types of flushes, with a probability of 4.96%;

There are 720 possible straights, with a probability of 3.26%; there are 3744 possible pairs, with a probability of 16.94%.

"There are 16440 types of generic cards, with a probability of 74.39%."

Everyone was very surprised when they heard this.

"Huh? The probability of a pair is only 17%?"

Is the probability of a straight flush lower than that of a three-of-a-kind? Is the probability of a straight flush lower than that of a flush?

"The probability of getting a mixed hand is 74.39%? Doesn't that mean that as long as you get a pair, even the smallest pair, you have nearly a 75% chance of winning in a head-to-head match?"

Clearly, this probability completely overturns conventional understanding to some extent.

Everyone knows that a mixed hand is the lowest, and a straight to a three-of-a-kind is a high hand, but what is the actual winning probability? Few people have actually calculated it.

Most people estimate that the winning rate of a mixed hand is probably only around 50%, and even the winning rate of a pair may not reach 60%.

However, in reality, even the smallest pair has a win rate of up to 75%, and the win rate starting with a straight is even higher, exceeding 90%.

Wang Yongxin continued, "What do you all think the winning probability would be if the chip exchange machine drew one more card, allowing you to choose three out of four cards to form a winning hand?"

"Alright, I won't keep you in suspense any longer, let's just get to the result."

The probability of getting a leopard is 0.9%;

The probability of getting a straight flush is 0.85%;

The probability of getting the same suit is 16.8%;

The probability of a straight is 8.4%;

The probability of a pair is 27.3%;

"The probability of getting a generic brand is 45.60%."

"The advantage of drawing an extra card is indeed significant. Even if both sides have mixed hands, the chip exchange machine is likely to be able to optimize and draw an even larger mixed hand."

"Therefore, in the actual process of gambling against a chip exchange machine, losing is indeed a high-probability event."

Cai Zhiyuan nodded: "Yes, I only calculated up to this step in the game, and then I didn't gamble against the chip exchange machine."

"However, if you know that the 'chip exchange machine' won't fold, the strategy changes completely."

"Although the win rate seems low, in the game, once we get a relatively strong hand, we can double our returns by continuously raising the bet."

"Assuming we get a pair from K, then when facing the chip exchange machine, we will actually have a winning rate of over 70%."

"If we get a flush, we'll have an 80% or higher chance of winning."

Jiang He frowned slightly: "But, this kind of hand is very hard to get, isn't it?"

Wang Yongxin nodded: "It is difficult to obtain, but the chip exchange machine actually provides many opportunities."

“每抽100ML血液，可以和筹码兑换机对赌1到20局。如果抽600ML血液的话，最多可以对赌120局。

"This number of rounds is actually enough to get a lot of big hands. As long as you get one, your chips have a chance to double once."

"Moreover, if you can think this through in advance, you can discard your cards immediately when you get small cards, thus minimizing the game time."

Jiang He thought for a moment, then frowned and said, "But probability is often unreasonable, and low-probability events are not entirely impossible."

"What if you encounter a jinxed card? Wouldn't you still lose everything?"

Wang Yongxin shook his head dismissively: "You can't think like that!"

"If you're always worried about low-probability events happening, you'll fold every hand, and how will you make money?"

"Furthermore, there's an advantage to playing against a chip exchange machine: you can always reveal your cards as long as you choose to call. Unlike playing against other players, where if two people take turns raising, you can never reveal your cards."

"Therefore, set your own stop-loss limits and adjust the amount of chips you bet in real time based on the win rate."

"Just like doing business, it's a simple matter of 'risk control'."

Everyone fell silent; clearly, this amount of information needed to be digested.

Looking at the detailed rules on the big screen, Fu Chen sighed again.

This game doesn't seem too complicated at first glance, but when you break it down carefully, you'll find an unexpected amount of detail.

"Okay, so far we should have completely broken down this game, right?"

"So...do you all think this game really serves a filtering function? In other words, do you think this way of allocating visa processing time is reasonable and fair?"

Ding Wenqiang's face remained dark: "It's not fair."

The others remained silent.

After a moment, Lee In-sook said cautiously, "I think it's unfair, but reasonable."

(End of this chapter)