In order to understand how the best strategy is computed, lets have a look at the Blackjack rules. Blackjack is played with 1 to 9 decks of 52 cards each. The values of the cards correspond to their numerical value from 2-10. All face cards (Jack, Queen, King) count 10 and the Ace either 1 or 11, as the holders desires. A score with an ace valued as 11 is named soft-hand. A soft-hand score of 17 is denoted as 7/17.
The color of the cards does not have any effect.
The goal of the game is to reach a score (=sum of the cards) as high as possible but not more than 21. A Blackjack (Ace and a card whose value is 10) beats all other combination of cards. If the final sum is higher than the sum of the dealer, the player gets a play-off of 1:1 of his initial stake. If the players combination is Blackjack, the play-off is 3:2 of the initial stake. If the sum of the dealer is higher, the player loses his bet. If the sum is equal, then nobody wins. If the player holds a score of 22 or more, he busted and thus he loses his bet immediately. If the dealer busts, the players wins independently of his final score.
An Ace will have a value of 11 unless that would give a player or the dealer a score in excess of 21; in which case, it has a value of 1. The dealer starts the game. Every player gets 2 cards, face up. The Dealer's first ace counts as 11 unless it busts the hand. Blackjack Strategy. When the value of dealer's revealed card is 4,5 or 6, it may be fruitful to double your bet with an Ace and 4 in hand. You may want to surrender if you have 16 in your hand while the dealer has a 9,10 or A. You should always split if you have a pair of Aces. If you get a pair of 7s, only press hit if the dealer. A 'blackjack' is a term used when a player scores the highest possible points using only two cards, which would be a ten and an ace. This is why blackjack is sometimes known as the game 'twenty one (21)'. An ace can either be worth 1 point or 11 points. This card is almost like a wild card, the player gets to choose what the point value is. Standard values in a game of Blackjack are: Face cards of the Jack, Queen and King are worth ten; Cards two through ten are worth their face value; The Ace has two possible values of either one or eleven depending upon the effect it will have on the player’s hand; Each player begins a hand of Blackjack by receiving two cards. Blackjack Card Values. Blackjack is a game in which precise values are assigned to each card in the deck. These blackjack card values never change no matter where you play. They remain true for online blackjack and they are also true in a live casino. The blackjack card values are: Ace = 1 or 11; 2-9 = Face Value; 10, J, Q, K = 10.
Blackjack can be played from one to seven players against one dealer. The dealer shuffles the cards. Now all the players must place their bets. Then each player and the dealer receives one card. The cards all lie face up. Thereafter the player receive a second card. The player now can continue to buy further cards, one by one, until he believes that he is near enough to 21. If the player believes to have reached a score high enough he must signalize the dealer to stay, which means not to ask for any further card.
The player has some more possibility's other than buy and stay. If he reached a score of nine, ten or eleven with his first two cards, he can double his bet. However if he does so, he will be dealt only one more card.
If the first two cards are of the same value, the player has the possibility to split his hand, which means that each of the cards are used to start with a separate bet. For each split hand, an additional bet equal to the first is required. There is one exception: If the player splits two Aces, he receives only one more card and in such a case a score of 21 is not considered as Blackjack.
Once the last player has decided to stay with his score, the dealer starts to draw a second card. If his result is reaching a score of 17 or more, he will deal himself no further cards. If the dealer has a score of 16 or less, he must draw until he has reached 17 or more. If the dealer exceeds 21, he busts. This is the basic knowledge You have: The dealer can not split nor double; he must play according to strict rules: Dealer must stand on all 17. That's the players advantage! On the other side, if both the player and the dealer busts, these scores are not considered as equal and the player looses his stake. That's the dealers advantage!
How to compute the correct strategy
The analyst sees the shoe as black box which computes him a probability for drawing a card of a certain value. Say we have 6 decks of 52 cards, so the probability of drawing an Ace is 6*4/6*52 = 24/312 = 7.7%. The probability of drawing a second Ace without reshuffle is 23/311 = 7.4% and so on. As the game goes on without reshuffle, the probabilities to draw certain cards will raise or decline, depending on which cards have gone in the past. From our point of view the shoe behaves like a wheel of fortune with varying distances between the nails.
The first thing to do, is to calculate the probabilities of the dealers last hand. This computation is straight forward as the dealer has no way of doing any decision. So it is quit easy to find out the probabilities of his final score.
The next thing is to find out the probabilities of what would be if .. . If the players score is 16, what's the probability of achieving 17, 18, 19, 20, 21 or busting. Probabilities also have to be calculated for splitting and doubling.
Nfl betting lines season wins against. Because the player knows the dealers first hand before deciding what to do, he can compare the probabilities of the dealers last hand against the probabilities of possible final scores for each intermediate score he has. With this comparison, winning expectations can be calculated, gaining information about the best playing strategy.
Knowing the best playing strategy and knowing the probabilities for each final score, the dealer and the player will reach, the total expectation can be calculated. The total expectation is the magic number playing Blackjack. If it is below zero the player has to place minimum bets as with this card distribution he will lose on the long term. If however the total expectation is above zero (unfortunately thats quite rare) the player has to place high bets.
Interpret the strategy tables
For each decision a player can do the best strategy can be computed. There are 20 possible conditions where the player has to take decisions. These are:
- Buy or stay if the score is 12, 13, 14, 15, 16, 7/17 or 8/18.
- Double or buy, if the sum of the first two cards is 9, 10 or 11.
- Split, buy or stay, if the first two cards have the same value.
All these decisions depend upon the dealers first card, making a total of 200. There are some fundamental rules, which never change and must always be obeyed:
- Alway buy if the score is below 12.
- Always buy if the score is below or equal to 7/17. With a soft hand You can't bust, so there is no reason to stay if the score is 17 or less.
- Never buy if the score is 17 or higher.
- Never split 5-5. A score of 10 is a good point to start with, so use it.
- Never split X-X. A score of 20 is too good, to take any further risks.
- Never ever double a Blackjack.
For other decisions consult the expectation and probability tables computed on the Blackjack strategy pages.
Blackjack King Value
The stake has to be placed before the player can see the dealers first card. So during that decision, very little information is available. The only information the player here, is the total expectation for the current card distribution in the shoe. If this is above zero, he shall place high bets.