The Whip of the God of Basketball

In the luxury suite on the 31st floor of the Mohegan Sun Hotel, the Celtics players sat in a circle around the bed, and Fox Leon sat on the bed with a deck of cards in his hand. Just as he was explaining tactics during training, he was giving a unique gambling lesson to these little gamblers who hadn't gotten started.

"First, I went from $100 to $10,000 using roulette, and while it's basically a game of pure luck, that doesn't mean he's out of luck. Two things to note about roulette , First of all, the roulette wheel of Mohegan Sun Casino rotates very fast, faster than the general roulette wheel, which means that the randomness of the distribution of small balls will become higher; Being completely in the roulette wheel and only betting on the boundary spins is really key, and the few times I've won big stacks I've bet on the small balls on the boundary spins."

Leon started by explaining how he used roulette to win $10,000 from $100. The roulette wheel of Mohegan Sun Casino is not only luxurious in specifications, but also rotates fast, making it extremely difficult to judge the position of the ball from the probability. So in the first few minutes, Leon wanted to use his memory statistical probability to bet and win chips, but this high-quality roulette made him have to choose to give up.

"Next, I began to observe the croupier's kick-off habits and the strength of the kick-off. For an excellent dealer, he needs to try to make the kick-off as random as possible, but this is impossible for humans. Numerous kicks every day will allow him to develop muscle memory to achieve the most suitable and durable kick. Then I found that with this croupier's kick, the ball appeared in the third, fourth and sixth The probability of blocking is higher." There are multiple metal blocks on the track of the outer wall of the roulette, in order to increase the randomness when the ball falls into the roulette, but the inertia of the croupier's force is overwhelmed by Leon. Catch, knowing which block the ball will fall on means that you can judge which color zone the ball will fall on based on the rotation speed and initial orientation of the roulette wheel.

But this is still far from enough, Leon continued: "After the ball hits the metal block, its trajectory is very difficult to judge, and although the strength of the croupier is fixed, it really determines the position of the ball. It's still his initial velocity and acceleration. So next I started to measure the initial velocity and acceleration of the ball - draw a picture for you, when the ball rotates on the side wall, the component of gravity provides the centripetal force, assuming that the initial ball falls The speed is θ, the radius of the roulette is r, then according to the basic mechanical formula, the square of the first derivative of θ is greater than g/r*tanα, α is the angle between the position of the ball and the tangent line of the side wall, and the horizontal line. Assuming that the friction force between the ball and the side wall remains constant, the resulting acceleration is constant, the speed of the ball will gradually slow down, and it will fall downward when it reaches a critical value. Based on this, we can predict that the ball How long will it turn, how many times will it turn, and where will it fall, then the formula can be deduced: t is equal to the negative reciprocal of the second derivative of θ, multiplied by the first derivative of θ minus the root sign g/r*tanα... ………”

Once he comes into contact with mathematics, sometimes Leon will enter a state of ecstasy, and start to paint and draw on the paper, completely unaware that his disciples are the most outstanding basketball players in the world Instead of being the most outstanding person in mathematics, Walker has closed his eyes, he feels that his head is bigger, and Joe Johnson, who listened intently and tried to understand the secrets, quickly chose to give up.

Leon quickly noticed this, he put away the blueprint with some embarrassment, coughed and said: "Sorry, I shouldn't be so long-winded, simply put, I can roughly calculate based on the formula, the team's initial speed, and acceleration. Determine which baffle the ball will fall on, and then judge which number the ball may fall on based on the rotation speed of the roulette wheel and the timing of the intersection of the two. It took me about ten minutes to make a prediction, and I feel like guessing five One number is a relatively safe way to bet, and then I took the risk of trying a combination of three numbers and succeeded. Then I ended the roulette game, because the calculation was too tiring for me, and the luck component is indeed very large , so after amassing a small stack, I went to my favorite blackjack."

Leon finished talking about his roulette game experience in an understatement. Everyone stuck out their tongues, knowing that they would never learn this method in this life. Except for a machine brain like Leon, who else can do such a complicated game in a short time? Calculate and judge the speed and position of the ball?

"Blackjack... This is the simplest trick, a game that no longer relies on luck but on probability. You must know that if one thing can control him in terms of probability, then you have won half of the game... …Including your shot, Antoine. The dealer will continue to follow the card until it reaches 17 points, and the deal will end when it reaches 17 points or more, because the number of cards is limited, so the various combinations are also limited, These matrices can cover various situations in which players take cards."

As Leon spoke, he took out another piece of paper and painted on it, but this time it was not as complicated as a roulette wheel. He drew a few matrices, the horizontal rows represent the cards in the dealer's hands, and the vertical rows represent the cards in the players' hands , from the first round to the third round of three matrices, there are about two hundred situations, and each situation has two options of "continue to draw cards" and "end to take cards", and Leon filled these options go in.

"What does this mean? The choice in every situation is fixed?" Walker couldn't help asking, looking at these dizzying tables and figures, Walker had already forgotten the fact that he lost hundreds of thousands of dollars in the stud table before. Gotta clean it up.

"That's right, this is a game of probability, because Mohegan Sun Casino does not allow splits, so the situation is even simpler. For example, if the sum of the cards in your hand is 12, then if the dealer's card If it is 2 or 3, then you have to continue to draw cards. If it is 4 or 6, then please stop taking cards. If you don’t continue to ask for cards after 12 o’clock, you can only hope that the dealer’s cards will blow if you want to win. First of all, if the dealer is greater than or equal to 17 points, you will not get a card. OK, so you will lose. If the dealer’s starting point is 16 At this time, the dealer will continue to draw cards, and it will explode when it draws 6~10. We know that the probability of drawing cards of different sizes is equal to 1/13. Let F(x) be the current point and be x Continue to draw the probability of exploding, then: F(16)=8/13=0.61538, the probability is 0.61538, we then calculate F(15), F(14), and then combine the various probabilities... …………”

Leon started his probability class again, but this time his explanation was simple and easy to understand, and the details were appropriate. With the poker cards in his hand, several players quickly understood the general idea. Then he said: "In this way, considering all kinds of probabilities, if you strictly follow the method given in this table to make choices in blackjack, then the probability of you winning the dealer is about 49%."

As soon as he heard this, Antoine Walker, who was so focused on hearing this and wished to immediately take this watch to the gambling table below, suddenly looked like a wilted eggplant. He held his head and said: "Four percent Nineteen? Less than half of it, which means that you still lost a lot in the end!"

Leon shook his head and said: "The probabilities just now are based on the consideration of the sufficient number of cards. In fact, the number of cards will only become less and less. Mohegan God Casino has to deal out more than half of the cards before reshuffle the cards, so just write down which cards. If you have used it, you can change your selection strategy, the fewer cards you have, the greater your chance of winning!" Leon's memory ability has played a huge role in the blackjack game, which is why he is invincible in blackjack , this game that relies on probability and memory is really suitable for him.

Next, Leon taught the players the high-low memory method of 21 points, and how to observe micro-expressions, how to memorize cards, and how to guess cards in the stud game. For a moment, these guys who gambled only by luck felt that they had learned peerless gambling skills in an instant, and they wished they could go downstairs to the gambling table and make a killing.

But after a while, they found that Leon was sitting on the bed without saying a word, which was completely different from the one who was talking endlessly just now. His eyes were still cold, and he quickly cooled down the excitement of everyone. He got up from the bed, walked to the cabinet, picked up the large nylon bag that was set aside, and threw it on the bed, which contained the million dollars Leon had won.

He said to everyone: "After teaching you this, let's take a gamble. This is my bet, one million dollars, and your bet is your career!"