Blackjack Mathematical Strategy

The mathematical way of playing Blackjack is known as the Blackjack basic strategy chart. This basic strategy has the ability for cutting the casino’s edge to 0.5%. The game’s chart was derived from a.

1. In blackjack, this means that one should evaluate the success of the Kelly Criterion over many hours and hands of blackjack play. One two-hour session at the blackjack table may not produce a profit with this system. Therefore, it is a system which is more useful for the professional blackjack player who plays the game full time.
2. From Griffin's table of 'Average Gains for Varying Basic Strategy' (p. 30, Theory of Blackjack), note that some hit-stand decisions alone are worth more than all pair-splitting decisions combined. Some of these most valuable hit-stand decisions, such as the 13 vs. 2 previously analyzed, can be most efficiently played in single-deck games.

There are different ways to become an expert blackjack player. If you watch tons of video tutorials or start reading various guidebooks on blackjack or spend hours reading online blackjack articles. But before you join a casino and invest some money, you must read a good casino review so that you do not lose any money.

All of these happen to be extremely helpful for a beginner and you should certainly try them. But here in this article, we will give you a few tips that will help you quickly to improve blackjack results in five minutes.

Learn Blackjack Rules to Influence the High Return to Player Numbers

Every blackjack rule can influence the return to player numbers. The return to player percentage gives an idea of how much of the money the player bets will be returned to him, and from this, he knows how much the casino is going to win.

Basically, the aim is to play at blackjack tables ensuring a high return to player numbers. At these tables, the player loses less money overall and has the best chance to win real money.

There is no need to remember the return to player numbers for each probable rules combination. But you must know which rules offer better results than others. When you learn to choose the best rules you can get a good idea which blackjack will be a good game for you.

All you need to do is some simple research and understand every rule. To begin with, follow the below-mentioned rules.

• When players double down after splitting it helps to make the return to a player go up.
• The general rule is for a dealer to stand on a soft 17 as this is better than when they hit.
• Surrender is a better option compared to the games that don’t offer surrender.
• Splitting pairs 4 times or more will be better than if splitting 1, 2, or 3 times.
• It is better to double down on any 2 cards than more restrictive rules.
• Use Blackjack Strategy Card

The Blackjack basic strategy Card is one of the most important things for any blackjack player. The strategy recommendation is derived from a mathematical point of view, and the blackjack strategy card is the table that includes all the solutions recommended by the blackjack strategy. This is the most convenient way to check with the strategy every time you play.

If you don’t use strategy cards there are high chances to lose more money than other players who do use strategy cards.

There are multiple blackjack hands and different hands are played in different ways. But the best way to play each hand will be to consider the card the dealer will show along with your 2 cards, and then decide which one will help to earn more profit in the long run.

For many years players couldn’t figure out the easy way to decide the best play. They needed to learn many mathematical factors to figure everything out. But things became easier when players started using computer programs to run all of the possibilities.

These computer programs helped to discover mathematically proven ways to find the best play. And these results were printed on a card in tabular form so that anyone can use as this will give the best chance to win.

Use Free Blackjack Software Program to Practice

Proficient blackjack gamblers practice a lot to improve their skills. Though you can practice while playing for real money, but if you want to practice without taking any risk of losing money there are various tools available that don’t charge money play to practice.

Even if you prefer to play for real money in a live casino, you can still practice Blackjack on your computer or mobile phone using software that will highly help you to improve your skills to a great extent.

You will find many software programs to help to learn how to count cards. If you make a small investment to purchase a good counting software program, it’s worth it as you can learn how to beat blackjack effectively.

Avoid Playing on 6 to 5 Blackjack Tables By All Means

The utter mistake a blackjack player can make is joining a table that pays 6 to 5 for blackjack. But solving the problem takes only a few seconds. Just make sure not to play a single hand blackjack at a 6 to 5 table.

You must be thinking why 6 to 5 is so bad. In fact, most blackjack players do not have any idea just how bad it is.

Usually, the majority of blackjack tables pay 3 to 2 for blackjack. Many tables still offer the traditional amount, but plenty of 6 to 5 tables are now available than ever before. The real reason is casinos make more profit when they pay 6 to 5 compared to when they pay 3 to 2. As long as blackjack players are interested to play on bad tables the casinos will keep offering them.

You can get an idea of how much you can win from this example. When you get a blackjack betting $100 at a 6 to 5 table, you win $120, which sounds good. But when the same amount you wager at 3 to 2, your chance of winning can be $150. If you play blackjack for an hour, the difference will be $30 an hour. That means you will give the casino an extra $30 per hour just to play blackjack.

Learn How to Count

Learning how to count cards is one of the most crucial steps to becoming a successful Blackjack player. It can take probably a few hours to learn how it is done. With a decent level of practice, you can even start counting cards. But to get really excellent at counting you will need to invest a lot of time.

So you have to be persistent in learning how to count cards and it’s going to transform your gambling life altogether if you do it well.

Interesting Related Article: ” Winning at Blackjack: 3 Important Things to Remember“

We first present the probabilities attached to card dealing and initial predictions. In making this calculus, circumstantial information such as fraudulent dealing is not taken into account (as in all situations corresponding to card games). All probabilities are calculated for cases using one or two decks of cards. Let us look at the probabilities for a favorable initial hand (the first two cards dealt) to be achieved. The total number of possible combinations for each of the two cards is C(52, 2) = 1326, for the 1-deck game and C(104, 2)=5356for the 2-deck game.

Probability of obtaining a natural blackjack isP= 8/663 = 1.20663% in the case of a 1-deck game andP = 16/1339 = 1.19492%in the case of a 2-deck game.

Probability of obtaining a blackjack from the first two cards isP= 32/663 = 4.82654%in the case of a 1-deck game andP = 64/1339= 4.77968%in the case of a 2-deck game.

Similarly, we can calculate the following probabilities:

Probability of obtaining 20 points from the first two cards isP = 68/663 = 10.25641% in the case of a 1-deck game andP= 140/1339 = 10.45556%in the case of a 2-deck game.

Probability of obtaining 19 points from the first two cards isP = 40/663 = 6.03318%in the case of a 1-deck game andP = 80/1339 = 5.97460%in the case of a 2-deck game.

Probability of obtaining 18 points from the first two cards isP= 43/663 = 6.48567%in the case of a 1-deck game andP= 87/1339 = 6.4973% in the case of a 2-deck game.

Probability of getting 17 points from the first two cards isP= 16/221 = 7.23981%in the case of a 1-deck game andP= 96/1339 = 7.16952%in the case of a 2-deck game.

A good initial hand (which you can stay with) could be a blackjack or a hand of 20, 19 or 18 points. The probability of obtaining such a hand is calculated by totaling the corresponding probabilities calculated above: P = 32/663 + 68/663 + 40/663 + 43/663 = 183/663, in the case of a 1-deck game and P = 64/1339 + 140/1339 + 80/1339 + 87/1339 = 371/1339, in the case of a 2-deck game.

Probability of obtaining a good initial hand isP= 183/663 = 27.60180%in the case of a 1-deck game andP= 371/1339 = 27.70724%in the case of a 2-deck game.

The probabilities of events predicted during the game are calculated on the basis of the played cards (the cards showing) from a certain moment. This requires counting certain favorable cards showing for the dealer and for the other players, as well as in your own hand. Any blackjack strategy is based on counting the cards played. Unlike a baccarat game, where a maximum of three cards are played for each player, at blackjack many cards could be played at a certain moment, especially when many players are at the table. Thus, both following and memorizing certain cards require some ability and prior training on the player’s part. Card counting techniques cannot however be applied in online blackjack.

The formula of probability for obtaining a certain favorable value is similar to that for baccarat and depends on the number of decks of cards used. If we denote by x a favorable value, by nx the number of cards showing with the value x (from your hand, the hands of the other players and the face up card in the dealer’s hand) and by nv the total number of cards showing, then the probability of the next card from the deck (the one you receive if you ask for an additional card) having the value x is:

This formula holds for the case of a 1-deck game. In the case of a 2-deck game, the probability is:

Generally speaking, if playing with m decks, the probability of obtaining a card with the value x is:

6 Deck Blackjack Strategy

Example of application of the formula: Assume play with one deck, you are the only player at table, you hold Q, 2, 4, A (total value 17) and the face up card of the dealer is a 4. Let us calculate the probability of achieving 21 points (receiving a 4).

Blackjack Strategy Card

We havenx = 2, nv = 5, so:

.

For the probability of achieving 20 points (receiving a 3), we havenx = 0, nv = 5, so:

.

For the probability of achieving 19 points (receiving a 2), we havenx = 1, nv = 5, so:

.

Blackjack Mathematical Strategy Tactics

If we want to calculate the probability of achieving 19, 20 or 21 points, all we must do is total the three probabilities just calculated. We obtainP = 9/47 = 19.14893%.

How To Play Blackjack Strategy

Unlike in baccarat, where fewer cards are played, the number of players is constant (two), and the number of gaming situations is very limited, in blackjack, the number of possible playing configurations is in the thousands and, as a practical matter, cannot be entirely covered by tables of values.

Blackjack Strategy Trainer