When I was young, everyone had a gambling dream. When we grow up, we know that there are gambling and gambling losses. Think about it too, and win what the dealer eats. It is not bad to say that "the casino is a board set up by others." There is no game where the player wins 50%. Even so, there are still a few people who can earn a lot of money. They are professional gamblers, with Blackjack as their core business.
Blackjack is the game that is most likely to win in the casino. It is also the only relatively fair game there. With the best gameplay, the player wins 49%. However, if you want to win in the long run, the 2% disadvantage can't be tolerated. High-end gamblers will use the change bet or group combat method to bring this disadvantage back.
How to play blackjack
Although there are often 21 scenes in various movies, it is only popular in casinos. There are not many people actually playing. Let us introduce 21 points.
This game is divided into two groups. Usually, the dealers deal with 5 to 7 players who are fighting each other at a semi-circular table. The props are multiple playing cards that are mixed with the size of the ghosts. The player's goal is to make the card's points more than the dealer, but if this is more than 21 points, it will go straight out (that is, burst). The flower card counts 10 points, and A can be counted as 11 points or 1 point as needed.
Both the first round player and the dealer will get two initial cards, each of which will only open one. After each round, the player can choose:
● Take a card (Hit)
● Ending the card (Stand)
● Double the bet and take a card (Double)
● If the two cards you get are the same, the player can separate the two cards, press another same bet, and get two more cards from the dealer, which is equivalent to playing two games at a time (Split)
● Admit defeat, surrender half and start the next game (Surrender)
It should be noted that Double, Split, and Surrender can only be selected in the first round. Some casinos allow Double after the split or continue to split, and some casinos do not allow Surrender.
When all players have finished winning the card, the dealer opens the card covered in the first round. If the number of points is less than 17, the card is taken until the number of points is greater than or equal to 17, and the dealer does not double, split or Surrender. If the dealer explodes, all players win. If the dealer does not explode, the player with more points than the dealer wins, the same number of points is a draw, and the number of points is lost.
Of course, there are some special rules about blackjack, such as Insurance and Blackjack (getting an A and a 10 ), so I won't go into details here.
How do high-end gamblers want cards?
It can be seen that the 21 points are not complicated, and it is easy for mathematicians to find the best card strategy. Calculations show that the best gameplay results in a player win rate of around 49%. For professional gamblers, there is no difficulty in doing this. The so-called best gameplay is just three matrices. Just write it down.
The above three matrices cover almost all the situations that may occur on the gambling. The top horizontal coordinate indicates the number of points (T is 10 points) that the dealer has opened in the first round. The leftmost column of the first matrix vertical row indicates the player's current hand point sum, H is Hard, that is, the A in the hand card is counted as 1 point (if any), and the other two matrix vertical column is the leftmost column. What are the two cards on the player's hand.
The remaining matrix elements are the best actions for the player. Where H is Hit, S is Stand, P is Split, D is Double (if the rule does not allow Hit), and Ds is Double (Stand if the rule does not allow).
Looking closely at the three matrices above, many of the card strategies can be understood with a little thought. But there are also some interesting places. For example, when the hand is 12, the dealer's face is 2 or 3 to Hit, 4 to 6 to Stand, and when the dealer's face is bigger, the card should be determined.
Why is this happening? When do you want a card when you don’t want it, the probability is over. Let's take a look at the player's winning percentage at 12 o'clock. After the dealer starts to draw, the number of points and greater than or equal to 17 will stop. At this time, the player must win the game and only hope that the dealer will explode.
If the starting point of the dealer is greater than or equal to 17, no draw is required at all. When the sum of points is H16, the 6~T will be blown up. We know that the probability of drawing cards of different sizes is equal (1/13), let F(x) be the probability that the current number of points and the continued draw of the card is x, then:
F(H16) = 8/13 = 0.61538
When the dealer's hand score is H15, 7~T is blown out; when A is drawn, it is turned into H16:
F(H15) = 7/13 + 1/13×F(H16) = 0.58580
Similarly, the probability of explosion of H14 to H6 can be calculated. When the dealer's hand is H5, the situation is different. At this time, A can be counted as 11 points. After taking this change into consideration, it is not difficult to calculate the situation of H2—H5.
So what if the player chooses Hit? There are two kinds of wins at this time:
The player did not explode but the dealer broke the card
The player and the dealer are not exploding, but the dealer has a small number of points.
The probability of a beep has already been counted, so let's consider the case of size. If the first card of the dealer is 2, let G(x) be the probability that the dealer will get the number of points and the hand of x, then G(H2) = 1.
If the dealer's hand becomes H3, only one A can be drawn in the case of H2, namely:
G(H3) = 1/13×G(H2) = 0.07692
Similarly, the probability of H4 to H 21 can be calculated, and it is still necessary to pay attention to the case where A is calculated as 11 points. In the case where both sides have not exploded, there are only a few possibilities for the player to win by the size:
The player gets 21 points and the dealer gets 20~17 points.
The player gets 20 points and the dealer gets 19~17 points.
The player gets 19 points and the dealer gets 18 and 17 points.
The player gets 18 points and the dealer gets 17 points.
The player draws from 12 o'clock and gets 18 points, which is equivalent to starting from H2 and getting H8, so the probability is G(H8), and the dealer gets the probability of 17 points G(17). According to this situation 4 the probability is:
P4 = G(H8)×G(17)
Similarly, P3, P2, and P1 can be calculated. Therefore, in the case where the player's hand is H12 and the first card of the dealer is 2, the player's probability of winning Hit is:
P(H) = P1 + P21 + P22 + P23 + P24 = 0.36958
As previously calculated, the probability of winning Stand is selected in this case P(S) = F(H2) = 0.35831
P(H) > P(S), so Hit is the optimal strategy.
In the same way, we can calculate the probability that the player chooses Hit to win when the player's hand is the H1 and H11 when the dealer's first card is H12. To get everything calculated, you get the following form:
Change the bet to win
As I said before, even if you master these three matrices, the winning percentage can't be more than half. The best strategy can only make you not lose so fast, there is no way to help you win. In 1963, Professor Edward Thorpe of the Massachusetts Institute of Technology had experimented and found that the more cards (7 and below) in the remaining cards, the easier it is for the dealer to win, and the remaining big names (9, 10, J, Q) The more K, A, the more players, the easier it is to win. This is actually easy to understand. The dealer will draw the cards until the number of points is greater than or equal to 17. If there are more cards in the remaining cards, the possibility of the banker exploding will be greater. And it's easier for players to take the Double strategy to increase revenue when they are big.
Speaking of this, you may have guessed it. If you want to win, you have to change your bet. Bet a little bigger when it's favorable, and bet a little when it's bad. But the question is, how do you know when the remaining cards have more big names? The answer is - record cards.
There is a basic method of calling cards called the high and low method. Its strategy is to make 2~6 to -1 points, 7~9 to 0 points, 10, J, Q, K, and A to 1 point. The scores of the cards are added up. If the score is large, it means that there are fewer big cards in the remaining cards. However, the 15 points accumulated after the completion of 1 deck of cards and the 15 points accumulated after the completion of 3 decks are obviously different, so the following adjustment formula is also available:
For example, when there are 6 cards in the opening, 15 points are accumulated after 3 pairs, the real value is 15/3 = 5.
The book Lost Genius describes the story of a group of MIT high-school students earning 3 million in 21 in the 1990s. This group of people is using the high and low method to record cards. Although this method ignores the difference between 2 and 6, it is not perfect, but it is at least not easy to be wrong. It is better to know that it is better to lose less than to lose.
In reality, the MIT team will disperse several investigators to sign cards at different tables. Once a table is found to be hot, it will signal the companion to make a big bet. The investigator will keep quiet. bet. The teamwork model makes it easier to win big money, but it is also difficult to cause doubts in the casino. The movie "Decisive Victory 21" tells a story like this.