1. Introductory notes to blackjack (or black jack)
Help other people find this worthy resource in blackjack, basic strategy, card counting, charts, probability, odds....and thusly return a favor to yours truly!The cards two to 9 have a numerical value equal to the number printed on the card. Tens also have a numerical value equal to the number printed on the card (10, of course). All face cards (Jack, Queen and King) have the value of 10. Aces (A) may be counted as either 11 or 1.
The rules of blackjack are relatively simple to learn. This page is not meant, however, to be a blackjack tutorial. A dealer plays against a number of players, from one to seven. Every player and the dealer receive initially two cards each, dealt by the dealer. Each player's hand is played against the dealer's hand only. If a player's hand has a value closer to 21 (without going over) than the dealer's hand, the player wins. The best possible hand is known as a blackjack (twenty-one in the first two cards). This hand consists of an A (ace) and a ten-valued card (10, J, Q, K). The payout for a blackjack is 3-to-2: the player is paid three chips for every two chips bet. When both the player and the dealer have blackjacks, it is a normal tie (push) situation; the player retains the initial bet.
The player has several choices after receiving the first two cards.
1) Hit or draw: take one or more cards to add-up to a better hand
2) Stand: stop taking more cards
3) Double down: double the initial amount (in cases considered more favorable)
4) Split pairs: if the two cards are equal in value they may be played in two separate hands.
The dealer has limited choices. The dealer must draw until dealer's hand adds-up to 17 or more. The dealer is not allowed to stand on 16 or less. The dealer is not allowed to draw to a hand summing up to 17 or more.
It is also important to know how to hand signal player's actions.
- Hit: tapping the table next to your cards with your finger tips or by placing your hand near your cards and moving your finger tips toward you (somehow like a gesture of grabbing)
- Stand: moving your hand left to right, in a flat, palm down position about two inches over your cards (like waving off)
- Split: place another bet, equal to your initial bet, alongside your initial bet; do not touch your cards, the dealer will split your cards
- Double down: you ante up another bet equal to and alongside your first bet; the dealer will deal you one more card (only one), across the first two cards.
Both the player and the dealer can go over 21. The situation is known as bust. The player loses the bet immediately. The dealer plays his/her hand last, after all the players at the table. This rule creates the so called house advantage or house edge or percentage advantage. John Scarne was the first to calculate the house advantage at blackjack: 5.9%. The only advantage the dealer (casino) has is provided by the simultaneous busts. The dealer busts 28% of the time (odds: 1 in 3.57). If the player mimics the dealer (draw to 16 or less, stand on 17 or higher), the player will bust 28% of the time. The odds (probability) for the dealer and the player to bust at the same time: .28 x .28 = 7.84%. But the player is paid 3 to 2 for a natural (blackjack), whereas the dealer is paid still 1 to 1 for a blackjack. Therefore, the house edge will go down to around 5.9%.
The player can learn and play the basic strategy. Thus, the player will reduce the number of busts. The bust probability for the basic strategy player is reduced to 17% (odds: 1 in 5.88). Therefore, the basic strategy player faces a disadvantage of .17 x .28 = 4.76%. But because the player gets paid 3 to 2 for a natural, and because the player can double down or split pairs, the house edge goes all the way down to 1%.
There are several bonehead plays, however. Such foolish plays can increase the house advantage at blackjack to 10%-15%. Example of such a play: hitting a hand of 19 or 20! Some look intrigued at me, but I split a pair of 10-cards. I only do that when there is a high probability I am in a clump of high cards and the dealer face card is 4, or 5, or 6.
2. Gambling mathematics, theory of probability applied to blackjack (or black jack)
The house edge can be diminished to only around 1% if the player follows certain rules. The set of rules known as basic strategy make blackjack one of the fairest games of any kind, almost as fair as coin tossing. I strongly recommend that you do not attempt to play blackjack before you learn basic strategy.
An IBM computer scientist, Edward O. Thorp, published “Beat the Dealer” in 1962. The book introduced a winning method known as card counting (also counting cards). The method considered the ten-valued cards and the Aces as “positive”, and the cards 2 to 6 as “negative”. If the net result in the remaining deck was positive, the player must increase the bet accordingly. The method had visible results when only one deck was used and very few cards remained in the deck. The casinos modified the rules dramatically. The “penetration” was introduced: not all the cards in the deck are played. Shuffling is done unexpectedly. Also, most casinos introduced the multiple deck blackjack. Card counting is now very similar to cult believing, like religious fundamentalism or UFO believing. I can only recommend you read my message
My recommendation is to learn basic strategy and the Fundamental Formula of Gambling (FFG). I created several pages to help you learn basic strategy. Color-coding is the key. Learning blackjack basic from spreadsheet-like tables is much harder. Only a few blackjack players have mastered the basic strategy. The rest can learn a lot easier if follow color-coded charts first. Then, they can look up tables for reinforcing and perfecting. I compiled all the color-coded charts and the basic strategy table in one page. Then I created one page for each color-coded basic strategy and one page for the summarizing strategy table.
The links are located at the end of this primer. The color-coded charts are created around the main actions a blackjack player can take. Thus, there is a split pairs chart; there is a double down chart; and there is a color-coded hit or stand chart. The action is colored red. For example, if the recommended action is split pairs, the corresponding situation is colored in the highly visible and memorable red colour. Your first two cards are shown in the left column. The dealer's up-card (face card) is shown in the top row. Let's say, your first hands are 7, 4. The dealer face card is 6. Look first at the split pairs chart; it does not apply, you don't have a pair. Look next at the double down chart. Your cards add up to 11. There is an entry in the left column. The intersection (cell) of row 11 and column 6 is colored red. The recommended action is therefore double down.
You will notice that dealer's card 6 represents an important demarcation (frontier) line. Most player's actions are dramatically different for dealer's cards 2 through 6 compared to dealer's cards 7 through A. If the dealer shows a face card of 4 or 5 or 6, the blackjack player will double down or split pairs more often; the blackjack player will stand on lower counts, starting at 12. That's the key to learning basic strategy. The color red of the actions makes learning even easier.
I do not present any of my blackjack strategies here. (But read how I apply Martingale to blackjack.) Keep in mind that the cards have streaks as any other gambling phenomenon analyzed by FFG. The decks have a high degree of clumpness at the beginning of the game. It is difficult to shuffle the new card decks to a high degree of randomness in a minute or so. Therefore long streaks of like-cards come out after the initial shuffle. The clumpness diminishes after several shuffles. Try to get a seat in the first position (next to dealer's left hand side). If you track the streaks of cards (how many highs and how many lows) you can make changes to the basic strategy. Try to get a seat in the last position (next to dealer's right hand side). That way you can see everybody's cards. Perhaps a high card is more likely; stand on 16 against dealer's 10, even if the basic strategy requires a hit (draw). You know you'll bust anyway, why not get an extra chance…
3. Essential resources in blackjack (or black jack)
Finally, my recommendations. Software: Masque Blackjack. Books: New Complete Guide to Gambling by John Scarne; Best Blackjack by Frank Scoblete.
• I released in April 2005 a great blackjack software analyzer: BJAQK.EXE. BJAQK.EXE stands for: Best on Jack Ace Queen King – and all other cards. We might as well call this game BLACK JAQK, or BlackJaqk, or BlaqkJaqk, or Blaqk Jaqk! The free program is available from the FTP Download Site, software category 5.5. The freeware is a probability and statistical analyzer of thousands of Black Jack hands from the perspective of a strict blackjack basic strategy player. This program is a great complement to the free blackjack strategy presented on the page: "The Occult Science of Gambling — Limited-Step Martingale".
The software generates truly random blackjack hands based on the probability of winning/losing/pushing from the standpoint of applying strict basic strategy rules. The software user can choose to generate and automatically analyze any number of hands, from dozens to millions (even billions, if the PC is out of this world!) The analysis is saved to a text file that can be viewed in any text editor. The report is so logically organized that even a modest blackjack player will comprehend it.
No further support is available for free. Big-time casino gamblers, who want much more, can't have it both ways: for free and also win big. More formidably powerful systems, strategies, software from Ion Saliu are available for a minimum license fee of US $10,000 (ten thousand US dollars). There must be a reliable way to put the money upfront. No promises, no oaths — just show me the money! There is a strong tendency from most gamblers or lottery players to attempt to cheat this great guy named Ion Saliu (aka JAQK Fowuru). Even persons who appear to be reliable, honest, and intelligent attempt first to cheat JAQK Fowuru out of his ideas, systems, theories, software and other fruits of creativity.
• Always check out the What's New page for the latest and current blackjack systems licensing availability.
• For the best mathematical casino gambling strategy for big–time gamblers read:
Super Roulette Strategy Systems Now Free (applicable to blackjack as well).
4. Ion Saliu's Gambling Theory of Streaks Compared to Other Gambling Methods
My gambling theory, including blackjack, is founded on mathematics, specifically the Fundamental Formula of Gambling (FFG). Also, everything I set out in my software must be validated mathematically to the best of my knowledge.
In all honesty, I don't see anything out there that offers better ways to winning at gambling or blackjack. I wish there was something easier and more efficient than my approach. Ain't nothing, honestly. IF my casino gambling methodology doesn't win the — there is absolutely nothing to accomplish such daunting tasks. Never will be, if my research has been futile. Never mind that they will continue to put huge efforts in playing the stock market or predicting the weather. The latter two phenomena are equally random to blackjack gambling or casino gambling. They have some advantages, but casino gambling has its advantages as well. In the end, it's all about streaks and skips, no matter what the phenomenon is. The skips (misses) are shorter and the streaks are longer if the probability is higher; and vice versa.
The rest of the blackjack gambling theory is nothing more than counting cards. Card counting in blackjack has virtually NO mathematical validity. The number of card permutations is staggering (even with one deck of cards). Besides, there is more than just one blackjack player at the table. The cards are distributed among several players, plus the blackjack dealer. High (positive) counts that consider the Tens and Aces might extremely lightly increase the chance to get a blackjack (natural) when the dealer doesn't. That probability is negligible (virtually equal to zero) if there are several players at the blackjack table! How about the contradiction regarding the negative counts in a remaining deck of cards? They are bad at blackjack! Yet, the double down situations in blackjack require a negative count! Six plus four, five plus five, seven plus four, etc. They must be in a negative run!
So, right now, I cannot see any casino gambling approach better than mine. That's the only way, like my gambling theory and software do: Track the winning and the losing streaks and their corresponding skips (misses). There are some no playing moments (or play the minimum bet); other situations demand a higher bet. It is hard work, but nothing else works better.
In fact, the science of gambling is the science of the streaks. Theory of probability, in general, is the science of the streaks and skips. A statement such as "This event will always have the probability equal to zero point zero zero three four etc." is virtually meaningless. The probability represents the ratio of the favorable cases over total possible cases. So, it works with integers. In real-life we deal with integers (discrete values) such as numbers of elements and numbers of trials. The events will hit, or miss, in streaks pretty clearly predicted by rules and formulas of probability theory. If you play longer sessions at the blackjack table, for example, you will face a higher probability of some very long losing streaks. But play shorter blackjack sessions, and there is a far better chance that you'll escape with shorter losing streaks. Recommended to play blackjack more aggressively at the beginning of short sessions.
A session at the blackjack table can be recorded as a succession of streaks. For example, from the Player's perspective –
Win|Loss|WW|LLL|Push|L|W...etc.
The streaks can be also viewed as skips between hits; e.g. how many hands the Player skipped between two hits (wins). The underpinning of the streaks is undeniably mathematical. If you don't believe me, take Warren Weaver's word on it. The title of the book is: "Lady Luck — The Theory of Probability". The streaks can be calculated precisely and real events concur with the formulas.
I present here only the result of discarding the pushes. The approach considers the blackjack probabilities as follows:
~ Dealer: p = 52% (or 0.52);
~ Player: p = 48% (or 0.48).
Number of hands: 1000 (or changing blackjack tables around 5 times a day).
~ Dealer: 120 single-win streaks and 128 multi-win streaks;
~ Player: 130 single-win streaks and 118 multi-win streaks.
Noticeable differences, if playing 1000 hands CONTINUOUSLY. Streaks.exe and Blackjack.EXE always enforce the rule of playing fewer hands at the same table.
Following is the total number of streaks for the Dealer and the Player in 1000 hands, from single streaks and 2 to 8 multiple like-streaks.
~ Dealer: 120, 62, 32, 17, 9, 5, 2, 1: A total of 505 winning hands;
~ Player: 130, 62, 30, 14, 7, 3, 2, .8: A total of 475 winning hands.
The 20 extra hands are most mathematically likely allocated as 11 (52%) to the Dealer and 9 (48%) to the Player. Thus, the Dealer can expect up to 11 consecutive wins in 1000 hands – one time; the Player can expect up to 9 consecutive wins in 1000 blackjack hands - once.
The probability for dealer to bust: 28%. In a majority of cases, the blackjack dealer busts in two consecutive hands, or skipping one hand, or skipping two hands. The same is NOT true for the player. The basic strategy blackjack player busts 17% of the time. Therefore, the streaks of the player's bust are longer.
True formulae are always simplicity itself. Simple is the most powerful demonstrative element of Truth. “It is so simple! It is undeniable”, good people say.
Let's calculate the number of streaks of losing exactly four consecutive blackjack hands (from the Player's perspective). We symbolize a Dealer's win by L and a player's win by W. We can calculate the number of the streaks consisting of exactly four consecutive losses for the Player.
That is, calculate the number of the streaks in the format WLLLLW. If probability for W = .48 and the probability for L = 52% (give to Caesar what belongs to Caesar...not that Palace...), then the combined probability is: .48 * (.52 * .52 * .52 * .52) * .48 = .016845963 or '1 in 59 or 60' hands. Mathematics of gambling expects such a streak once every 60 hands, or twice in 120 blackjack hands. Or, 17 times in 1000 continuous blackjack hands.Yes, it is possible, albeit mathematically rarely, that the blackjack player can experience 3+ such streaks in 100 hands. Equivalently, however (casino fat-cats hate the equivalent thing!), the blackjack player could experience 100-hand sessions with all losing streaks shorter than four (3-)! Those are likely sessions with longer player's win-streaks, usually with more frequent dealer's busts!
You might really want to run those two great pieces of software: Streaks.exe and Blackjack.exe. You can view here a report generated by Blackjack.exe for 100 hands. I wrote also more extensively on the mathematics of streaks (the essence of gambling). My writings on gambling streaks (beginning late September 2008) triggered even more intense hatred from casino fat-cats. I am blamed for not keeping all that math to myself. But why didn't they let me gamble in their casinos, in the first place? Just a couple thousand dollars a day winning at blackjack and roulette would have done it! If they had let me play, I might have been more secretive for longer! For, in the end, Truth must always come to life! Truth is always above anybody and anything.
This is the only valid mathematics regarding the game of blackjack. Other things, such as card counting, are all but cuckoo speak or cult following. Beware: The casinos do encourage the cult of counting cards at blackjack. It's all about money the easy way for the casinos!
5. Blackjack Links and Resources at This Web Site, Including Color-Coded Charts For Basic Strategy
The footer of this page shows the most significant pages of this web site. The links that follow are just a few. They detail more the mathematics of blackjack, plus blackjack systems and software. Copy and paste and build your best blackjack strategy manual! But keep in mind that I am the true copyright owner, no matter how you edit the material!
For the best mathematical casino gambling strategy (approach) for non-system players, read:
• Casino, Casinos: Gambling, Gamble, Win, Winning in Casino.
• The Occult Science Of Gambling:
~ The Fundamental Formula of Gambling and Limited-Step Martingale.
• It presents also Double-Attack Blackjack, a new game played in Atlantic City.
Blackjack: Software, Content, Resources, Systems, Basic Strategy And Card Counting.
See a comprehensive directory of the pages and materials on the subject of blackjack, baccarat, software, systems, and basic strategy.
Doctor in Occult Science of Blackjackology
Important Odds (Probabilities) in Blackjack
Probability Odds Probability Odds
to bust to bust to win to win
Dealer (in general) 28% 1 in 3.57 52.95% 1 in 1.88
Player (in general) 28% 1 in 3.57 47.05% 1 in 2.13
Basic strategy player 17% 1 in 5.88 49.5% 1 in 2.02
Dealer's face card: 5 42% 1 in 2.38 up to 58% -
Dealer's face card: 6 42% 1 in 2.38 up to 58% -
Dealer's face card: 7 26% 1 in 3.85 up to 74% -
Dealer's face card: 10 23% 1 in 4.35 up to 77% -
Dealer's face card: A 17% 1 in 5.88 up to 83% -
Color-coded chart to learn the best Split Pairs strategy. When you get your first two cards, look at this table first. The pairs occur the least in a blackjack game. If your hand is not a pair, move to the next chart: Double Down.
Color-coded chart to learn the best Double Down strategy. After consulting the Split Pairs table, look next at this table. The Double Down situations occur more often than pairs at blackjack. If your hand is not a Double Down situation, move to the next chart: Hit or Stand.
Color-coded chart to learn the best Hit or Stand strategy. After consulting the Double Down table, finally look at this table. The Hit or Stand decisions are by far the most frequent and important situations in blackjack.
All three color-coded charts in one file, in the best decision-making sequence: Split Pairs, to Double Down, to Hit or Stand.
The traditional method of learning the Basic Strategy: all decisions in a table. The dealer up card is listed across (horizontally), while the player's first two cards are listed vertically in the leftmost column. For example, dealer's up card is 5. Player's first two cards: A+4; the right move: D (Double Down). It makes it somehow more difficult to learn the best decisions.
Remember to check the free software downloads site:
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