God's Imitator

Wang Yongxin paused slightly and continued:

"In this world, visa time is life.

"Quantifying the value of life to earn visa time is essentially exchanging life for life.

"Whether this exchange is worthwhile depends on the specific risks, rewards, and probabilities.

"Of course, this brings us to another trap in this game: the 'Chips Exchange Machine.'

"Players are thrown into a gambling game with the Chips Exchange Machine right from the start, and it's clearly stated in the rules that this is an unfair game.

"The Chips Exchange Machine can draw an extra card and choose the best three out of four, and it's always the dealer, always raising first.

"Generally speaking, raising first puts you at a disadvantage, but since the Chips Exchange Machine can draw one more card, its hand naturally has a higher value, which instead increases our cost to call. Anyone wanting to reveal cards has to bear an additional loss of 500 chips.

"Most players lose everything after just a couple of games.

"Either they fold before daring to call, or they call and still lose, incurring even greater losses.

"The severe negative feedback makes most people naturally believe there's no chance of winning against the Chips Exchange Machine, and playing with it is just wasting chips.

"This is the game's greatest information barrier.

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

Fu Chen nodded after pondering for a moment: "Yes, the four of us gambled twenty-four rounds in total with the Chips Exchange Machine.

"We lost completely in the first few rounds.

"The Chips Exchange Machine has almost a 50% chance of getting a pair, and even if it doesn't, it will invariably have a high-card of J or better.

"I later gave up and folded without looking at my cards, since looking at them would still cost another 500 chips."

He glanced at Cai Zhiyuan: "However, we did discuss the related probabilities at the time, and Cai Zhiyuan made a rough calculation.

"But whether from the calculated probabilities or those experienced in the game, the win rate was very low."

As a programmer, Cai Zhiyuan is most adept at probabilities.

And this kind of poker game is closely related to probabilities.

Because each card type's probability can be accurately calculated, and the probability gap between two card types naturally determines the win rate.

Many originally thought Cai Zhiyuan would be the best at this kind of game.

But unexpectedly, his performance wasn't particularly outstanding.

Wang Yongxin, who doesn't really understand probabilities, and Lin Sizhi, a humanities student, turned out to be the only ones in Community 17 who discovered the Chips Exchange Machine's loophole.

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

"But after calculating and recalculating, I ended up misleading myself."

Wang Yongxin suggested: "Why not take this opportunity to thoroughly calculate the related probabilities? Even though the game is over now, at least let everyone be clear, win or lose."

Cai Zhiyuan nodded: "Okay."

He took paper and pen and quickly began to calculate.

The initial calculations weren't too complex, but the calculations suddenly increased when addressing the four-choose-three probability variation problem.

Though Cai Zhiyuan calculated quickly, he still used several sheets of paper before providing the final answer.

"It should be roughly correct."

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

Wang Yongxin skimmed it from start to end, his face occasionally showing considerable surprise.

Then, he looked to everyone: "Allow me to keep you in suspense for a moment. What kind of hand in this game do you all think is worth betting heavily on?"

Everyone looked at each other and began speculating.

"A straight? A straight is a moderate hand."

"That shouldn't be it, a straight is a low-probability hand, right? I think a pair would suffice."

"Pair of 10 or higher? Should be about right."

"Wait, first clarify what 'bet heavily' means? If you're all-in with your remaining chips, do you dare bet everything on just a pair and expect to win the whole game? I think you'd need at least a flush."

Clearly, even under such circumstances, everyone still couldn't reach a consensus.

Since everyone's risk tolerance and estimation of probabilities for various hands differ, combining these two factors naturally leads to varying decisions.

Wang Yongxin gave the answer: "Choosing any three cards from 52, there are 22,100 possible combinations.

"Among them, there are 52 three-of-a-kinds, with a probability of 0.24%;

"48 straight flushes, with a probability of 0.22%;

"1,096 flushes, with a probability of 4.96%;

"720 straights, with a probability of 3.26%;

"3,744 pairs, with a probability of 16.94%;

"And 16,440 high cards, with a probability of 74.39%."

Upon hearing this, everyone was surprised.

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

"The probability of a straight flush is lower than a three-of-a-kind? And straights lower than flushes?"

"The probability of a high card is 74.39%? Doesn't that mean that even if you get the smallest pair, you have nearly a 75% chance of winning one-on-one?"

Evidently, these probabilities quite effectively overturn conventional understanding to some extent.

Everyone knows that high cards are the smallest, and straights to three-of-a-kinds are bigger hands, but the exact win rates? Few have actually calculated them.

Most people estimated that the win rate for high cards might be around 50% and that even pairs might not reach 60%.

But in reality, the smallest pair's win rate is 75%, and starting from a straight, the win rate is more than 90%.

Wang Yongxin continued: "What do you think the win rate is after the Chips Exchange Machine draws an extra card and forms a hand by choosing the best three out of four?

"Forget it, I won't keep you in suspense. I'll just tell you the results.

"The probability of a 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%;

"And the probability of a high card is 45.60%.

"Drawing an extra card provides a significant advantage, so much so that even if both sides have high cards, the Chips Exchange Machine can most probably optimize for a better high card.

"Therefore, in practical terms, losing while gambling against the Chips Exchange Machine is indeed a high-probability event."

Cai Zhiyuan nodded: "Yes, I only calculated up to this point during the game, and then stopped gambling against the Chips Exchange Machine.

"But if you know that the 'Chips Exchange Machine' never folds, it completely changes the strategy.

"Even though the win rate looks low, in a match, once we get a sizable hand, we can continually raise to acquire double returns.

"If we assume getting a pair of K, our actual win rate against the Chips Exchange Machine will be over 70%.

"If we have a flush, our win rate will be over 80%."

Jiang He furrowed her brows: "But isn't it difficult to get such hands?"

Wang Yongxin nodded: "Yes, it's hard to get such hands, but the Chips Exchange Machine actually offers many opportunities.

"Every 100ML of blood drawn allows you to gamble with the Chips Exchange Machine for 1 to 20 rounds. If you draw 600ML of blood, you can gamble 120 rounds at most.

"That's enough rounds to get plenty of good hands, and if you encounter one, your chips could potentially double.

"Moreover, if you could think this through in advance, you can immediately fold when holding a weak hand, maximizing the game's duration reduction."

Jiang He considered for a moment, then furrowed her brow: "But probability is often unreasonable. Small probability events aren't impossible.

"What if you run into a cursed hand and end up losing everything?"

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

"If you're always worried about small probability events happening, you'd fold every hand, so how can you make money?

"Besides, gambling against the Chips Exchange Machine comes with the advantage that you can choose to reveal your cards as soon as you call. Unlike gambling against players, where if both players repeatedly raise, you never get the chance to reveal cards.

"So, set your loss limits, and adjust the bet amount based on real-time win rates.

"It's like running a business, a simple 'risk control' issue."

Everyone fell into silence, clearly needing some time to digest the information.

Fu Chen looked at the detailed rules on the big screen, feeling amazed once again.

The game doesn't seem very complex at a glance, but when dissected carefully, it contains an unimaginable amount of detail.

"Alright, at this point, we should have thoroughly dissected this game.

"So... does everyone think this game truly serves as a filter? In other words, do you think this method of distributing visa time is reasonable? Fair?"

Ding Wenqiang still had a dark expression: "Unfair."

The others continued to remain silent.

After a moment, Li Renshu cautiously said: "I think it's unfair, but reasonable."