How To Deal Blackjack At A Casino – Do you think you can win at Blackjack? What is the best way to play? In this article we solve these and other questions with the help of mathematics.
The objective is to get 21 or a value higher than the dealer’s with our cards, without going over the number.
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When placing bets, each player is dealt 2 cards face up and only one card is dealt to the dealer.
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Players have to decide based on their cards and rackets whether they want to hit, stand, double or split their hand.
All cards are worth their numerical value, ie. from 2 to 10, except the figures that are worth 10, and the Ace that is worth 1 or 11 for our benefit
The payments are made at the same time, and we can get 21 with more than two cards but it will only be considered blackjack when it is made with two cards.
The house cannot hit or stand, and only hits when your hand is below 17, so if it reaches or exceeds that value you will automatically stand.
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In case the dealer exceeds 21, the players still at the table will win their bets and in case of a tie, the player will get his bet back.
American Blackjack has several different rules that allow you to modify whether the dealer hits or how players can split their hands. Additionally, a second card is dealt covered and you can watch in case your first card gives you the opportunity to play blackjack. If you roll 21, players will lose their bets before even playing. This speeds up the game and also reduces the house edge.
First of all, we can get it right, even if our sum does not exceed 21, depending on the card they give us, we will be closer to 21, or on the other hand, we will lose the bet if we manage to exceed it.
To double our bet it is necessary to have any hand and obligation sum 9, 10 and 11 and individual as a whole and spin principles. If you double your bet you will only be able to receive one more card.
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To double we need a hand that has a sum of 9, 10 or 11 and you can only do it at the beginning of the round. If you double your bet, you can only get one more card
If our cards are of the same value we can divide each card into different hands to play them at the same time, but for this it is mandatory to also bet as the first one. You should also know that within a split hand, even if we do not count the sum of 21 with the next card as blackjack.
After a split, most casinos allow doubling of the resulting new hands, and this gives us some advantages. (That increases the house edge by 0.12%) if not allowed.
If the card revealed by the dealer is an Ace, we can bet safely, if we believe that the house will get blackjack with the next card. If we bet and finally succeed, we will be rewarded.
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And finally leave, something that is only possible in American Blackjack and if the player leaves he only loses half of the bet.
–3 to 2 (three chips, for each bet of two chips or one and a half for each chip bet) if we beat the dealer with Blackjack (as long as there is no tie). In American Blackjack in Las Vegas it pays 6 to 5.
In the case of American Blackjack, it is also common that if the player has a blackjack and if the dealer has an Ace visible, he is offered the possibility of cashing a blackjack with 2 to 1 (instead of the usual 3 to 2). . to the insurance bet.
After that, there are only 4 cards left that are an Ace so if we want to get blackjack we need one of them but… what is the probability?
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The probability of getting Blackjack are the ways we have to get 21 with 2 cards of each possible combination to get 2 cards from the deck.
Or put another way, favorable situations among possible situations, which are not equal or odd, even related.
To get 21 with 2 cards we need an Ace and a 10. And in the deck there are 4 Aces and 16 tens (between face cards and 10 value cards).
On the other hand, all combinations of 2 cards, combinations of 52 elements taken 2 at a time (when the order is not relevant and cannot be repeated),
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4.16/C52, 2 which equals 64/1326 or 4.8% chance of getting a Blackjack (which was logical since we know that we always need an Ace to have a blackjack and there are only 4 in the deck).
In the case of playing with several decks, each figure or number has the same proportion, because 4 aces in 52 cards are the same as 8 in 104. But the probability of obtaining a certain result varies slightly, since it influences having fewer cards in a deck of 104 than in one of 52. So each game has its own probability study with different decks.
To calculate the probability of busting from 21, we need to calculate the probability of busting from any hand and for that we need to do a heads-up analysis.
As we see initially, there are 4 cases out of 13 in which 21 is exceeded. This is approximately a 30% chance, which means that with a value of 12 only 30% of the time we get it right we will exceed 21.
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(The calculation of this probability is a simplification because we really have to take into account that the cards that make up 12 change the probability of the card we ask for a little bit, but the difference with this calculation is not very big and it is also much more complex to study and understand).
Also keep in mind that if our sum is 11 or less, we cannot go over 21 with one more card, so the probability is 0.
As we just saw, if we don’t want to lose most of the time, we have to always ask for the sum of our hand to be less than 14. The question is… If we limit it to 14, do we have a chance of winning?
Considering that the dealer always hits a card with a sum of 17 or more, a position with a value less than 17 only makes you a winner when the dealer beats you.
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Or put another way, if the dealer does not exceed 21, his hand will always have a value equal to or greater than 17, so players who were left with a hand less than 17 will lose their bets.
Well, according to the mathematical study carried out, the chances of the dealer going over 21 depending on the card he has (and his strategy) are the following:
We see that the probability of a high card coming down is quite low because the Ace is the card that gives the most advantages to the house.
For a low card the probability is greater, but be careful that in no case does it exceed 50%
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If we average them all, we conclude that the dealer beats 21 28.35% of the time (368, 67/13), which means he loses his bet the remaining 71.65% of the time. stays with more than less than 17. .
As we have just seen, there is no point in setting a limit below the dealer’s limit, since we will lose in most cases.
If you understand, the dealer always waits for the player to finish playing before continuing to play. That means that if the player goes over 21, he loses his bet regardless of what the dealer does. So if the dealer beats 21, the player loses anyway since he was previously eliminated. This results in the house winning the case, which is actually a tie and this happens 7.9% of the time you play. This represents approximately an 8% advantage over the player, which is ultimately reduced to 5.6% if we consider that blackjacks pay 3 to 2, instead of 2 to 1 capital. That is the main advantage of the casino.
To combat this, the player has options that allow him to have a flexible strategy. He can double when he is interested, split hands, fold, etc. But the most important thing is that he knows the dealer’s card that will make him make those decisions (instead of just hitting or standing) with that card in mind and this is where the math comes into play again.
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In the 1950s, a group of mathematicians led by Roger Baldwin developed the Basic Strategy. This is based on optimizing the player’s decisions so that the action he chooses is the most profitable of all the actions he can perform. This first gives us the greatest possible profit in the long term.
And it is achieved by developing a probability model that calculates based on the player’s hand adapted to the dealer’s card when the decision to stand, hit, double, split or bet is best for hard hands that are inflexible like your soft one (where the Ace is and the sum can be changed).
In mathematical language we can say, through a recursive function with defined final values, and a table that contains all the probabilities of the dealer’s sum, the maximum between the expected profit if it is maintained and the
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