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## Successful choices have different probabilities

Mickey is a professor who has made a credit card counting technique using probability to detect the holes of blackjack and teach students math in a classroom during the day, but he learns the secrets of Blackjackjack. Mickey, who wants to create a new blackjack team, gives students a surprise quiz in class to pick out the talent of the " Kenyan. " The problem is as follows.There are three doors in front of you. Behind one door is a nice car, and behind the other are goats. The host says that if you choose a door, you will give the product behind it. Calm your pounding heart and you chose the number. The mischievous host then opens the door with a goat among the two doors you don't choose and offers you a chance to change the number you choose. What's your choice?

" Should I change it or not?Oh, what should I do? Just because the host opens the door with the goat doesn't mean the car behind the door I've chosen disappears. Unless the odds are different, I will believe my first choice! "

If this was the case, he would have been wrong earlier than Mickey. Of course, Ben, the main character, thought for a moment and said, " Change the door. " He gave Mickey the impression that he was a potential source for playing an important role in the blackjack team.

At first glance, what was Ben thinking? Say you have a new car behind door 1, and a goat behind door 2 and door 3. At this time, consider dividing the number by every number you select.

1) If you choose door 1 → The host will open door 2 or door 3. In this case, if you stand at door one, you will be in a new car, but if you change your choice, you will get a goat. → Do not change.

2) If you select Gate 2 → The moderator will open Door 3. If you stand at door two, you'll get a goat, but you'll get a new car if you change your choice. → Change it.

3) If you select Door 3 → The moderator will open Door 2. If you stand at door three, you'll get a goat, but if you change your choice you'll get a new car. → Change it.

You change the choices and drive your car twice in three attempts. The results are the same if the car is behind door 2 or door 3. The probability of choosing a new car when selecting the first door was $ \ frac} {1} {3}, but if the moderator opens the door and changes the choice {2}

## Memory is the best for non-residential extraction.

Blackjack is a game in which players are not driven by psychological warfare, but rather by competition between the dealer and the player. The key is fast calculation based on probability and how well you remember the card.

In blackjack, cards are mixed up. The dealer takes each card out of the mix and plays a game. The cards used in the game are not mixed again, but they are put together on the other side, and when the entire card is used, the card is filled again.

This method is called non-performing extraction. In non-performing extraction, the results of the first event affect the probability of the next event occurring. That is, if a player remembers all of the open cards and proceeds with the game, the lower the total number of cards the dealer distributes, the higher the probability is that the cards will contain.

If the game is played by " recovery-extracting " method, which is used once, mixed up and plays games, there is no information that can accumulate. In light of the fact that the Las Vegas casino is a non-residential system, Mickey's team teaches the team the technology to remember the card disclosed.

However, no matter how good his memory is, he can not remember all the cards that were released. Mickey has developed a " high-low system, " a card counting technique that he remembers by combining high and low cards. Calculate 2, 3, 4, 5 and 6 as - 1 for + 1, 7, 8, and 9 and for 0, 10, J, Q, and K. For example, if the cards currently open are ' J, Q, 2, 3, 10, 8 ' then the current count number will be - 1+1+1+0 = - 1.

The team of five engineering talented MIT students learns the high low school system and practices applying it every night, finishing its final training for Las Vegas.

In blackjack, cards are mixed up. The dealer takes each card out of the mix and plays a game. The cards used in the game are not mixed again, but they are put together on the other side, and when the entire card is used, the card is filled again.

This method is called non-performing extraction. In non-performing extraction, the results of the first event affect the probability of the next event occurring. That is, if a player remembers all of the open cards and proceeds with the game, the lower the total number of cards the dealer distributes, the higher the probability is that the cards will contain.

If the game is played by " recovery-extracting " method, which is used once, mixed up and plays games, there is no information that can accumulate. In light of the fact that the Las Vegas casino is a non-residential system, Mickey's team teaches the team the technology to remember the card disclosed.

However, no matter how good his memory is, he can not remember all the cards that were released. Mickey has developed a " high-low system, " a card counting technique that he remembers by combining high and low cards. Calculate 2, 3, 4, 5 and 6 as - 1 for + 1, 7, 8, and 9 and for 0, 10, J, Q, and K. For example, if the cards currently open are ' J, Q, 2, 3, 10, 8 ' then the current count number will be - 1+1+1+0 = - 1.

The team of five engineering talented MIT students learns the high low school system and practices applying it every night, finishing its final training for Las Vegas.

## Card count, number of cards is counted to calculate probability.

At last the day of the decisive battle came. The team flew to Las Vegas with a big heart. Professor Mickey raises funds, and the rest of the students play their roles as " Spider " and " Big Player. " Spider ' begins the blackjack game, betting a small amount of money, counting cards, and then gives a big player a password of when to join the game and the counting number he has calculated.In the movie, Spiderman crosses his hands back when a big player passes by, meaning ' Come in because the edition that's happening is in your favor. ' And when a big player enters the game, it provides password information about the remaining cards. He makes up his words by adding words that are linked to the counting number.

Spider, for example, pretended to have lost money and " I've written out " all the " checks I've brought. My girlfriend would try to kill me, which means the counting number is + 15. Spider's counting number is a lifeline for big players.

+ 15 means that the number of cards 2, 3, 4, 5, 6 is 15 more than the number of cards 10, J, Q, and K, so 10, J, K is likely to be distributed.

In this case, if a dealer's card is below 6, the player has a better chance of winning. Because, unless the Dealer's hidden card is A, the Dealer's score is less than 16, which means that the Dealer receives one more card, with 10, J, Q, and K, the likelihood of exceeding 21.

The Blackjack team makes hundreds of thousands of dollars in just one night through card counting technology, and those who are tempted to make more money go to Las Vegas every weekend.

But the casino's veteran security.The strongest blackjack team faces a crisis as Won finds out about their secret activities. Will they be able to overcome the crisis?

## Blackjack rules

Blackjack is a battle between a dealer and a player. Dealers run games by handing out cards, while players bet and compete with dealers. The cards used are 52 pages excluding the Joker, and between 2 and 8 people can do it.The dealer sends two cards, including himself, to all players, and the total score is close to 21. The cards count from 2 to 9, counting scores numerically, and counting K, Q, J and 10 to 10. However, A can be calculated to the convenience of one or eleven points.

If the score comes to 21, it is called " blackjack " and wins the game unconditionally. And if the total number of cards exceeds 21, the game is lost unconditionally regardless of the score (burst).

Players bet as much as they want to bet before they get their cards. At the beginning of the game, the dealer will share each card in the left hand direction without showing his card. The second chapter is distributed open to both players and dealers.

By dividing the cards into two, the player can view his card and the dealer's open card and receive a few more cards from the dealer to bring the total score closer to 21. However, if they are greedy, they will have to choose carefully since their scores will exceed 21.

After adding the cards, the dealer releases the hidden cards. If the total score is less than 17, the dealer receives one more card without fail, and if the score is 17 or higher, the player must win or lose.

## Card counting and conditional probability

The probability that the event A occurred is indicated by P (A). In real life, certain information is more often available when calculating probabilities, and reflecting them greatly changes the probabilities. When given information about the event B, the probability of the event A

P (A=B) = $ \ frac {P (A ∩B)}{P} $

Marking it as " conditional probability " for A when B is given. Where P (A ∩B) is the probability of having events A and B simultaneously occurring.

Consider dice games. A is the probability P (A) = a sixth of the six - side dice in which three is thrown. If someone secretly taught me that odd numbers came out, the odds are

P (A=B) = $ \ frac {P (A ∩B)}{P (B)} $ = $ \ frac {$ {1} $} $ {$ \ frac} {6} $}$ = $ \ frac {1} {3} $

Go up to The chances of getting three with an even number are P (A ∩B) = 0.

In the movie, Spider sees a card that is opened every time a plate is opened, counts the cards and tells the big player. In other words, it provides big players with information B that can calculate conditional probability.

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