If things continued this way, after the next five rounds, with both players having roughly the same odds, it would all come down to luck drawing 10 cards.
So here's the question: if Rhomann has better luck than Bruce, why is Bruce still the wealthiest man in the world, and he's become a prisoner?
Bruce yawned and said, "This game is putting me to sleep. How about this? You give me three cards, I take three cards; next time, I give you three cards. If I take two, next time I give you two, and vice versa."
Rhomann was thinking. He knew that Bruce had seen through his weakness of not being able to afford a loss, so no matter what he said, it would be very hard to shake Bruce. But the current situation was unfavorable to him; without a change, he was going to be in big trouble.
With the initiative in Bruce's hands, he could only accept the terms proposed by Bruce, so he nodded and said, "Then let's do that."
They had only five rounds left. If they exchanged three cards per round, they would exchange a total of 15 cards—a not insignificant number, which could completely influence the odds and even decide the final winner.
Rhomann steadfastly stuck to his plan. When Bruce sent over three cards, he took the ones he needed to complete his hand and returned the rest, supplementing any shortfall with low cards.
To Rhomann's surprise, Bruce didn't send back the low cards, and even the cards he was sending over were increasingly larger, starting with larger numbers and eventually including J, Q, and K.
Overjoyed with the high cards, Rhomann began to calculate in his heart. Originally, there were four of each picture card in every suit. If he could get two extra in each suit, making it six of each suit, a total of 24 cards, the probability of drawing these cards would greatly increase.
In that case, the probability of getting a Royal Flush would increase, and even if not, the probability of getting a high Straight Flush would be greater. Even if it wasn't the highest, having a Straight Flush with Q, J, 10, 8, 9 was almost unbeatable.
What's more, with six cards of each suit, it's very easy to draw three of a kind, also known as trips, and with ten cards, drawing a pair of trips with picture cards greatly increases the winning probability.
Then Rhomann began to wonder why Bruce would do such a thing.
But the pressure didn't allow him to think too much; he just wanted all the high cards from Bruce's hand. But according to the rules they had established, if he took three cards, he had to give three cards. If he wanted to take all three in each round, he would have to give three as well.
After weighing his options, since he already had so many high cards, why not take the chance? He might as well give away all the low cards.
"Why would he do that?" the man wearing the Megalodon mask raised his question again, "Why give all the high cards to someone else?"
Stark sighed again and said, "The guy on the right has lost."
He was referring to Rhomann, and the audience in the VIP seats all turned to look at him, but Stark shook his head and said, "I'll explain after the reveal."
After the five rounds of card exchange, Rhomann incredulously looked at his neatly arranged hand of high cards, having kicked out almost all of the low number cards.
In his mind, he silently counted the number of high cards in his hand, thinking that as long as he could draw certain combinations, he was sure to win, like a Straight Flush or trips of K and Q, or he might even get a Royal Flush.
Although Rhomann wasn't as intelligent as Bruce, he was at least able to clearly calculate the probabilities of drawing different combinations. He found that the chance of his current hand was at least tripled compared to the base probabilities, as having more of the same rank increased the chances of certain combinations.
With that in mind, he sorted the cards in order, watched as his and Bruce's cards were all put into the machine, and the old card shuffler drew 10 cards for the showdown.
The revealing of the cards was done simultaneously—both would flip the first card at the same time, then the second, and so on.
After the first card of Rhomann was revealed, his heart immediately rose to his throat because his first card was the King of Spades, which was a pretty big card. But that was normal, given that his hand didn't contain many small cards.
Then came a spade 10, and Rhomann felt his heart pounding because he now had the chance to make a Royal Flush, which is a spade 10, J, Q, K, A.
The third, fourth, and fifth cards were a spade 10, a diamond 9, and a heart J. Rhomann now had a 9, 10, and a J, completing half of a straight.
Next were a spade 8, a heart K, a heart 6, a club Q, and a diamond 10.
Which means that Rhomann now had a straight consisting of a spade 8, diamond 9, spade 10, diamond J, club Q, and spade K, with the remaining high cards being 10, 6, 10, 8, K.
The hand was already quite large, not only a straight up to K but also high cards; in terms of sequence, its priority was quite high.
Meanwhile, Bruce's cards were also flipped.
A heart 2, club 5, club 7, club J, spade 9, diamond 3, club 3, club 4, club 6, diamond A.
Bruce won with a club 3, 4, 5, 6, 7 straight flush.
Rhomann stared at these 10 cards incredulously, then rushed to the machine like a madman to retrieve his own cards, searching through the entire deck, only to find four clubs.
In two decks of cards totaling 108, excluding the four jokers, there are 104 cards left, which means there are 26 cards of each suit.
If Rhomann only had four clubs, it would mean that Bruce had 22 clubs, almost half of the 54 cards.
Upon closer inspection, Rhomann saw he had 15 diamonds, meaning Bruce had 11 diamonds, and Bruce's spades and hearts together only amounted to 19 cards, 10 of one and 9 of the other.
Which means that the probability of Bruce drawing a club, diamond, spade, or heart was approximately 22:11:10:9, with about a 0.42 chance of drawing the most numerous clubs.
Whereas Rhomann's probability was 4:15:16:17, with the chances of drawing a diamond, heart, or spade all between 0.2 and 0.3.
Stark spread his hands and said:
"He forgot the most important thing, a straight flush absolutely surpasses a straight."
"The one on the right does have a lot of high cards, but with equal probability for three suits, the chances of getting a flush are reduced, whereas the one on the left, though holding low cards, has a higher probability of drawing clubs than any other suit. If you have sufficient numbers even with lower cards, you can make not only a straight but also have a higher probability of making a straight flush."
"Even if he's unlucky and doesn't get a straight flush, he will at least get a flush, which is still bigger than a straight. That's why I said that guy is bound to lose; he was completely fooled by the opponent."
"This is just the simplest color-probability problem, you don't even have to consider the size of the numbers; the higher the probability of drawing the same suit, the better your chances of winning."
"The guy on the left first creates pressure, making his opponent feel they must win, then reveals high cards, all to distract the opponent, making them only think about desperately putting together high cards for a gamble, without noticing their own control over the suit probability had been manipulated."
Stark pointed at Bruce on the right and said.
"He's just like all bankers, first applying pressure to the opponent, making them desperately crave victory, then giving them a taste of sweetness, ensnaring them in the illusion of victory. Once they've lost their reason and cannot calculate soberly, they fall victim to the simplest rule that can't get any simpler."
"The greater the pressure, the heavier the gambling, the desire to go big, the more insane one becomes, the less lucid one is, the more one loses—this is the eternal curse of the gambler."