Different Variations Of Blackjack

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  • Multi-hand blackjack is the most common variation that you’ll find in online casinos. In fact, it’s rare when an online casino doesn’t offer this game. Multi-hand blackjack is just like it sounds in that you can play multiple hands in the same round. All of the multi-hand games we’ve seen offer a maximum of 3-5 hands.
  • Blackjack actions is a parameter that counts everything: Busted hands, pat hands (17 to 21), blackjack hands, and draws or hits to the first 2-card hands (incomplete hands). The software does NOT print the incomplete bj hands.
  • Although there are different variations of blackjack, the main of the classic one is to get a score of 21 without exceeding it. After being dealt two cards and taking a look at the dealer’s face-up card, players must make a decision about the move they would like to make. In most cases, the deck is shuffled only once before the game begins.

Blackjack is an old game that today operates under fairly standardized rules. Sure, you might find games with different numbers of decks, different surrender rules, or different rules for how the dealer decides when to stand and when to hit.

By Ion Saliu, Founder of Blackjack Mathematics

I. Fundamental Probability Issue: True Odds at Blackjack, Software Calculator
II. Fundamental Myth of Blackjack Gambling: Counting Cards
III. Theory of Streaks: Foundation of Blackjack Gambling Strategy, Systems
IV. Blackjack Resources, Software, Systems, Basic Strategy Cards (Color Charts)

1. The Fundamental Probability Issue: True Blackjack Odds - New Software Calculator

First captured by the WayBack Machine (web.archive.org) on November 21, 2002.Different Variations Of Blackjack
  • They say roulette is the queen of casino games. Then, blackjack is the king of the casino. Many believe that Blackjack, or 21, or twenty-one is the most popular casino game in the world. Blackjack is also the most researched game ever. It is also the only casino game with fluctuating odds (or probability). The winning chance changes with the composition of the deck. This is more about blackjack mathematics than anything else.
  • For gambling is such a mathematical phenomenon that the casinos would do ... you know what to you ... if you knew well about it! This casino game is so easy to win ... but it is NOT about card counting! In truth, card counting at blackjack lopsidedly serves the greedy interests of the casinos.
  • The blackjack player is honestly served only by the Fundamental Formula of Gambling (FFG). And thus the casino henchmen will threaten you if you simply write down in a notebook what you lost and what you won. Hey, that's a tax requirement in any jurisdiction!

Let me start by saying that the game of blackjack has caused me the most serious problems with casinos and gambling developers/authors/system vendors. Blackjack or Twenty-one (seen the movie 21?) is the most popular casino game and the most researched one. There are plenty of books dedicated to the so-called mathematics of blackjack.

There is worthiness in a few of such books or eBooks. For the most part, however, there isn't much mathematics in all those blackjack studies. The heart of the matter is a worthless concept known as card counting.

I do have a strong interest in blackjack. It is well documented at my website. As a matter of fact, I consider myself the best blackjack player ever. As Muhammad Ali put: 'It ain't bragging if you back it!' So, I put the money where my mouth is: I issued a casino gambling challenge, especially at the blackjack tables. So far, nobody has dared to honor my challenge. The real casino challenge is open to any gambler, gambling author, or gambling system developer — card-counting or not.

I wrote a book about the true mathematics of blackjack, insofar as precise probability calculations are concerned. You might be shocked to hear, but the mathematical truth is that your knowledge of blackjack probabilities or odds is dead wrong. Everything you had known was based on guesswork, albeit it educated guesswork.

To this date, the blackjack odds are the same as John Scarne calculated them in the 1950s. The computers were not the commodity they are today. And John Scarne was not a computer programmer! The way he calculated the odds made sense for the first two and three blackjack cards in a round. I quote from his 'Scarne's New Complete Guide to Gambling' (pg. 363):

  • 'We find that the dealer's first two cards can produce the counts from 2 to 21 in 1,326 ways.'

Indeed, Combinations C (52, 2) = 1,326 two-card blackjack hands (combinations of 52 cards taken 2 at a time). That is the only thing... half-way mathematically correct! The truly correct method applies the mathematics of combinatorics alright. But instead of the numerical sets known as combinations, we must apply the mathematics of arrangements. The combinations represent boxed arrangements. In this case, C (52, 2) = (52 * 51) / 2 = 1,326. Arrangements A (52, 2) = (52 * 51) = 2,652 — or double the amount of combinations. Hence, we played cute and said half-true for the blackjack combinations case!

In the case of the first 2-card hands, the combinations-generating method greatly simplifies the problem at no additional cost. 10-7 is equivalent to 7-10. The problem comes to life beginning with 3-card hands. A hand like 10-6-7 is not equivalent to 10-7-6: Dealer must stop at 10-7.

  • 'We'll discover that we need to know, however, and avoid most of the fractions, if we multiply 1,326 x 169 to get a common multiple of 224,094.'

Now, that's a big mystery! How did Scarne come up with that 169 factor??? Well, that's what they call an educated guess, or guesstimation! John Scarne didn't have a clue, mathematically speaking. He has never explained how he came up with that 169, kind of a new number of the beast! (There are 13 cards in each of the 4 suits in blackjack; 13 to the power of 2 equals 169... what's the relation?!)

In order to calculate the probability precisely, we must generate all the elements (blackjack hands) in lexicographical order. Nobody even knows how many hands are possible, as their size varies widely: From two cards to 10 cards (for one deck)! When two or more decks are employed, the blackjack hands can go from two cards to 11 cards.

Of course, there is a lot of blackjack software out there! But all that software belongs to the simulation category! That is, the blackjack hands are dealt randomly. Based on the well-known-by-now Ion Saliu's Paradox, random generation does not generate all possible combinations, as some elements repeat. So, we can never calculate the probability precisely based on random generation. If there are 334,490,044 total possible complete hands in blackjack, only 63% will be unique and 37% will be repeats — if we randomly generate 334,490,044 hands.

I rolled up my sleeves again. I had started years ago a blackjack project to generate all possible hands. It was very difficult. I found the project in the year of grace 2009 and also the code to generate sets from a list (last update: 2014). In this case, the list is a 52-line text file with the values of the blackjack cards, from the four 2's to the 16 Tens, to the four Aces. That's a stringent mathematical requirement. The deck of cards must be also ordered lexicographically, if we want to correctly generate all qualified sets in lexicographical order.

Different variations of blackjack

I generated blackjack hands as both combinations and arrangements. Then, I opened the output files (text format) and checked as many hands as possible. Yes, computing things are so much better today than just 5 years ago. The generating process is significantly faster. Also, opening large files is much easier today. My text editor of choice is my own MDIEditor And Lotto WE. It opens reasonably fast text files of several megabytes in size. The editor also uses a fixed-width font, which makes reading blackjack hands easier.

I wrote a special Web page dedicated to the topic of calculating precisely mathematically the bust-odds at blackjack following the Dealer's rules. There are lots of details, plus screenshots of the probability programs:

  • Blackjack Dealer Bust: Software to Calculate Probability, Odds, House Edge, Advantage HA.

Keep this new figure in mind: The odds for a blackjack Dealer's bust are at least 33%. The bust probability is calculated by dividing the number of Dealer's busted hands to the total possible blackjack actions.Blackjack actions is a parameter that counts everything: Busted hands, pat hands (17 to 21), blackjack hands, and draws or hits to the first 2-card hands (incomplete hands). The software does NOT print the incomplete bj hands.

How can we apply the new programming to determine the bust odds for the blackjack Player? After heated debates in forums in 2014, I simply modified my software. The hit-stand limits can be set by the user. Initially, it was fixed — the ubiquitous hit all 16s and under, stand on all 17s or greater.

The software user can set the hit-limit to any value. The choices are, obviously, from 12 to 16. I tried, for example, the hit limit to 11 — that is, hit anything 11 or under, stand on anything 12 or higher. Evidently, there is no bust in such situations. That's another proof that my programming is 100% correct.

I believe that setting the hit limit to 14 or 13 reflects pretty closely the bust odds for the Player. That is, stand on 15 or greater (as arrangements):

Or, stand on 14 or greater (as arrangements):

Now, the house edge goes between something like .3355 * .2248 = 8.3% and something like .3355 * .1978 = 6.6%. It averages out to 7.5%. It is a far cry from the intentionally false house advantage (HA) of 1%, or even .5%! The overwhelming majority of blackjack players lose their bankrolls quickly, because this is NOT a 50-50 game or so much close to that margin! And always be mindful that blackjack is strongly sequential: The Dealer always plays the last hand. Otherwise, the casinos would go bankrupt!

I have seen lots of search strings in the statistics of my website related to the probability to get a blackjack (natural). This time the request was personal and directed to me:

Different Variations Of Blackjack
  • “In the game of blackjack determine the probability of dealing yourself a blackjack (ace face-card or ten) from a single deck. Show how you arrived at your answer. If you are not sure post an idea to get us started!”
  • Oh, yes, I am very sure! As specified in this eBook, the blackjack hands can be viewed as combinations or arrangements (the order of the elements counts; like in horse racing trifectas).

1) Let's take first the combinations. There are 52 cards in one deck. There are 4 Aces and 16 face-cards and 10s. The blackjack (or natural) can occur only in the first 2 cards. We calculate first all combinations of 52 elements taken 2 at a time: C(52, 2) = (52 * 51) / 2 = 1326.

We combine now each of the 4 Aces with each of the 16 ten-valued cards: 4 * 16 = 64.

The probability to get a blackjack (natural): 64 / 1326 = .0483 = 4.83%.

2) Let's do now the calculations for arrangements. (The combinations are also considered boxed arrangements; i.e. the order of the elements does not count).

We calculate total arrangements for 52 cards taken 2 at a time: A(52, 2) = 52 * 51 = 2652.

In arrangements, the order of the cards is essential: King + Ace is distinct from Ace + King. Thus, total arrangements of 4 Aces and 16 ten-valued cards: 4 * 16 * 2 = 128.

The odds to get a blackjack (natural) as arrangements: 128 / 2652 = .0483 = 4.83%.

The generalized formula is:

Probability of a natural blackjack = (A * T) / C(R, 2)

  • A = number of Aces remaining in the deck;
  • T = number of 10-valued cards remaining in the deck;
  • C = combination formula;
  • R = total cards Remaining in the deck.
  • Read a whole lot deeper analysis:
  • Calculate Probability (Odds) for a Blackjack or Natural.

2. The Fundamental Myth of Blackjack Gambling: Card Counting

You might have seen that movie 21. It had absolutely no success in theaters. A DVD was released in 2008 with much more success. The 21 DVD reopened the huge gambling appetite for the so-called sure-fire strategy of counting cards at blackjack. The movie also introduced a powerfully symbolic ghost: The MIT Blackjack Team.

If you watch all the features of the DVD, you will see the author of the original book that inspired the 21 movie. In his interview, the book author and the screenplay writer admitted that his book was the result of a rumor! How could people with the heads on their shoulders believe that an MIT blackjack team was even possible?! MIT (Massachusetts Institute of Technology), such a prestigious institution, would even accept the rumor of a gambling team on the premises? Let alone a real gambling team consisting of faculty and student body?! But adding MIT to a blackjack team did wonders!

The legend of card counting started with a well-written book: 'Beat the Dealer!' The author, Edward O. Thorp, was a mathematician working for IBM. He also learned computer programming in order to prove his theory on blackjack card counting.

If the player keeps track of the cards that were dealt, there will be variable situations for the player. Thorp speculated that the situations were favorable to the player when ten-valued cards and Aces (high cards) were predominant in the remainder of the card deck. Reversely, the situation was unfavorable to the player when there were more small cards (2 to 6) compared to high cards. The 7, 8, and 9-valued cards were considered neutral.

The same John Scarne we talked about before puts jokingly the advantage of card counting. Suppose there is a one-deck blackjack game with 100% penetration (i.e. all cards are dealt). The player tracked the entire deck absolutely precisely. There are 5 cards remaining in the deck: 3 eights and 2 sevens. The player would bet the maximum immediately (actually, millions if it were possible!) There is NO way the player can lose! The player would always stay on two cards (it doesn't matter if it is 7+7, or 7+8) or 8+8)! On the other hand, the dealer would always bust. It doesn't matter: 7+7 (under 17); draws an 8 and busts. Or, 8+8 (still under 17); draws a 7 and busts. Or, 7+8 = 15 (under 17); either 7 or 8 as the third card would bust the dealer's hand!

A situation like that would have occurred, but extremely rarely. To have 2 sevens and 3 eights at the bottom of a 52-card deck has a degree of certainty in the same category as the moon colliding with the earth! Keep in mind, total possible permutations of 52 cards is calculated by factorial of 52 (52! = 1 x 2 x 3 x 4 x 5 … x 50 x 51 x 52). Who can say that number?!

As a matter of fact, John Scarne challenged Edward O. Thorp to a real blackjack game in a casino. I quote from Scarne's New Complete Guide to Gambling (pg. 361):“In 1964, in an effort to test Professor Thorp's 'winning Black Jack' statements I challenged him to a $100,000 contest to be staged in Las Vegas. Thorp's reply was a big 'No'.”

This excerpt is from page 348:

  • '… if he [Thorp] would like to team up with me and my partner to beat the Nevada Black Jack tables by making use of his unbeatable system. Thorp agreed and after the first three days of play in Reno, Nevada, we realized that Thorp knew nothing about the science of Black Jack play, and his countdown system never seemed to work… Thorp later admitted to us that he never really gambled…”

There is one more notable name to be mentioned here: Ken Uston. He became really famous when he appeared on CBS's newsmagazine 60 Minutes. The curiosity of the TV news division was triggered by a successful lawsuit that Ken Uston had won. He charged that he was barred from playing blackjack because of his skills as a blackjack card counter. The court system decided that no player may be discriminated against based on the skills of the player.

The curious thing is that Ken Uston became a spokesperson for the casino he had filed lawsuit against: Resorts. He appeared in TV commercials aired in New York and other big cities of the eastern board of the U.S. Even more curiously, the 60 Minutes Ken Uston segment was shot inside the same casino! Moreover, Ken Uston was allowed to win big money, as if were a fictional movie! Meanwhile, if a regular casino patron tries to take a benign photo on the premises, he/she might as well be thrown in jail! Not to mention that doing card counting can result in harassment and eviction by force, sometimes!

Card counting, as devised by Edward E. Thorp is a footnote to gambling history now. It offered a slight advantage in one-deck games, and especially towards the end of the deck. Ideally, a player could destroy the blackjack game if knowing the composition of the deck and the sequence of the remaining cards in the deck. The latter part is the real problem: Nobody will ever be able to know the sequence of the remaining cards in the deck. The count may be +5, but often the sequence is Low card, High card, Low, Low, High, High, Low, Low, High, etc. The dealer has the same probability to get the high cards. It is even more complicated when one considers that there are several blackjack players at the table.

The cards, Low and High, will be distributed randomly among them. What makes a particular player believe he/she would be the one to get the High cards? In one-deck games, and only playing head-to-head against the dealer, there is a slightly higher chance for the player to get a blackjack. The dealer also has an equally higher chance to get a blackjack. The difference is the player is paid 150% for a blackjack, while the dealer always gets 1 to 1 for a natural. Let's say the player has a 2% higher probability to get a blackjack (for a positive count, including Aces).

Under normal circumstances (count = 0, neutral), the probability of a blackjack is just under 5%. What is 2% of 5%? 0.02 x 0.05 = 0.001; that is, 0.1% better probability! That is, a 4.78% chance to get a blackjack, compared to 4.77%. Applying the Fundamental Formula of Gambling to p=4.77% and p=4.78%, we get, approximately, the same median: 14.18 and 14.15 hands. On the average, there will be 14 or 15 hands between blackjacks, in neutral counts, as well as in positive counts.

I have one problem with the two blackjack authors and researchers, Edward E. Thorp and Ken Uston. They reached a point of worshipping the method/system of card counting. I am sure they did a large number of computer simulations. I am sure they noticed the negligible effect of the system. Yet, they continued to influence a large number of potential casino players that card counting represented the road to the riches.

I would like to present a few more excerpts on Thorp and Uston. Carl Sifakis writes in his 1990 Encyclopedia of Gambling (pg. 36-37):

  • “Dr. Thorp is still in computerized mathematical research, but he is now concerned with looking for values in stocks… The late Ken Uston, author of numerous books on counting, was at the end of his life involved in computer work in the Middle East, helping Kuwait track billions of dollars in investments. He was not playing blackjack in Atlantic City, although he had won a court case that barred casinos in New Jersey from refusing to let counters play. In fact, Uston, upon winning that case, didn't hit the blackjack tables in Atlantic City but signed up to do TV commercials for Resorts International, the very target of his suit… One long time gambler, Murray Friedkin, says of Thorp in 'Big Julie of Vegas' by Edward Linn: 'Thorp is the smartest man in the world; if you don't believe me, ask him…Whatever Thorp may say, I can tell you that if he has made any money on blackjack he made it by writing a book.”

Why this aura of legend surrounding card counting at blackjack? Even more mystique is added when considering that Las Vegas is still barring card counters from playing blackjack. Says Carl Sifakis:

  • “And what of the casinos today? Blackjack is a much bigger game today than it was before 'Beat the Dealer' appeared. More people than ever patronize the tables and casinos today make more money from the game than ever before. That's a significant bottom line.”
Roger Gros, senior editor of Casino Player magazine writes in his 1996 Casino Gambling the Ultimate Play-To-Win Guide:
  • “After all, casinos make most of the money they make at the table games via blackjack. It's great advertising when someone reports a big win at the blackjack tables. Players have been encouraged for many years to believe that blackjack can be beaten, and the casinos don't want to do anything to disrupt that message.” (page 30).

Indeed, the legend of blackjack card counting plays as the most successful means of advertising for the casinos. It certainly attracts a large number of players who believe counting at blackjack is a road to riches. There are also other ways that the card counting legend favors the casinos. Read any blackjack book on card counting and virtually all of them contain the same cliché. “If you are a card counter, make some bonehead plays so that the pit boss won't ban you!” I think many card counters take the advice seriously. They do make bonehead, stupid plays from time to time just to hide their card-counting skills. What a stupid strategy for the blackjack player! What a profitable play for the casino!

It is admitted that counting cards offers no more than a 2% advantage for the blackjack player. That's a slim margin by all standards. Making bonehead plays can easily wipe out the slim, potential 2% advantage. The casinos owe big time to all authors of card-counting books. Then, in places where it is legal to ban skilled players from the blackjack action, the casinos commit downright robbery.

From what I have read, the casinos show a strong bias towards barring a blackjack player when he/she is at a serious loss! I read once that a known card counter was losing some $14,000. Exactly at that point, the pit boss approached the counter and asked him to leave the blackjack game! Get it? The $14,000 went immediately to the casino bottom line. Meanwhile, the player was deprived of a reasonable chance to recuperate his loss. After all, they say, blackjack is almost an even-odds game for a player using the basic strategy. It is fair to expect swings in the winning and losing columns of the player.

Of course, the banned player is allowed to play blackjack again. The pit bosses pretend to have forgotten him/her, until another significant loss for the player. The player is thrown out again! If the known counter is winning, the rationale is that a swing in the fortune will follow. Sooner or later, the player will encounter a severe loss. That's when you ask a counter to get out! What casino would be happy if a winner takes the money and run... for real?

The 21 movie was about counting cards at blackjack. It glamorized the tactic by adding intelligence to the whole scheme: the MIT factor! The movie was shot inside the MGM Grand casino! Surprise, surprise! Would you read again the threatening message from the chairman of the same casino (2001)? He threatened my guests that the casinos would throw out casino patrons who would dare to write down roulette numbers! Yet, the same casino allowed a big movie production inside their building! A movie production worshipping card counting...

3. Theory of Streaks: Foundation of my Blackjack Gambling Strategy

Yes, I and casino blackjack have always had a glamorous affair. I admit, I was playing blackjack at the same tables with women who showed a strong interest in me at times. A lot of mathematics is involved and implied in this casino game. Everything that has mathematics and potential to find more about Truth attracts me as pollen attracts a hard-working bee.

I was a farm hand since my arrival to the United States in 1985. It was hard physical work. I always looked at the positive side as well. The physical work balanced my intense intellectual work, including computer programming. Unfortunately, hard physical work leads to physical pain more often than not. In early spring of 1996, unbearable back pain took me out of farm labor. I was unable to find employment until late summer of 1997.

One of the things I did was studying casino gambling. I used one of Thorp's terms: gambling mathematics. It was definitely mathematics. I saw also a means to make some money. I thought numerous times of turning into a professional gambler. There was a problem nonetheless: Bankroll. I barely had money just to survive. I am not ashamed of telling the truth. Besides, I made Nietzsche's philosophy come alive: ”What does not kill me makes me stronger.”

I did receive employment in the late summer of 1997. I worked mostly in temporary jobs. Good thing is I was paid. I was able to put food on the table and sleep under a roof. Additionally, I was able to save some money. I tried to build a bankroll for casino gambling.

Going to a casino was a freebie from where I live. The casinos offered free bus drives. Actually, you paid $20 and the casinos gave you your money back on arrival. They are good at mathematics, aren't they? Just about everybody loses that $20 minutes after entering the casino! Well, not me!

I hit the Atlantic City casinos a few times until the end of that year of grace 1997. I had a couple hundred dollars when I first started with blackjack. I returned home with more than the double of that amount. My window of opportunity was five hours. The bus trip would start early in the morning (Wednesday or Sunday). The trip to Atlantic City took around five hours. The trip back home would be five hours later.

The casino bosses were not mean during my first hits in 1997 - 1998. First of all, I was a small-timer: No more that 200-300 dollars per session in winnings. Besides, they might have tried to figure out my system. It was clear to them that I applied a form of Martingale betting. Most gamblers know that Martingale betting requires doubling up the bet after each loss. Well, it was a whole lot more than that and a whole lot more refined, in my case. The only negative reactions I recollect came from other gamblers.

Keep also in mind that my blackjack system was based on the wrong assumption that the dealer's bust at blackjack was 28%, as taken as a biblical figure in the gambling kingdom. As seen in another chapter, that figure is significantly higher. Therefore, the house advantage at blackjack is higher. Also importantly, the player's position at the table is relevant. At that time, I tried the middle position.

By contrast, most blackjack players prefer the last position at the table (just before the dealer). That is the best position at the blackjack table: The last seat or the third base. It is a mathematical law. The more players before me bust, the lower the degree of certainty that I will bust — the BJ dealer as well. It is worth repeating. The bust probability is constant, while the degree of certainty of serial busts decreases. It is similar to consecutive heads/tails in coin tossing. Nobody gets three or four heads in a row with the same frequency as just one heads followed by one tails.

And thusly we returned to the concept of streaks once more. As I said before, probability theory might as well be named the science of streaks. The core of my casino blackjack strategy was founded on the application of streaks. The method required reasonably accurate records of the hands I played as loss or win. When I applied my gambling strategy in writing, I noted a loss by – (a minus sign) and a win by +.

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. It is highly recommended to play blackjack more aggressively at the beginning of short sessions. Then, move on to another table, preferably another casino.

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. Please reopen his informative book, Lady Luck — the Theory of Probability at page 346. The streaks can be calculated precisely and real events concur with the formulas.

Warren Weaver does the calculations by brute force. He takes the simplest and most fair game of chance: Coin tossing. Let's say we consider a total of 1024 tosses (it 2 to the power of 10; easier to work with, as the probability is 1/2). How many 4 consecutive runs of heads (H) can we toss in 1024 trials? Evidently, 4 heads should appear exactly in this pattern: THHHHT (where T stands for tails). The combined probability of that pattern is: 1/2 x {1/2 x 1/2 x 1/2 x 1/2} x 1/2 = 1/64. If we multiply 1/64 by the total number of tosses, the result is:1/64 x 1024 = 16 runs of 4 consecutive heads (or tails, for that matter).

I wrote software to calculate the number of streaks (or runs of consecutive outcomes) of various lengths for any given probability and number of trials. The program: Streaks.

My presentation here starts with the old blackjack figure of a dealer bust equal to 28%. Many blackjack players will still believe in that predicament for some time to come. 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 to play: 1000 (or changing blackjack tables around 5 times a day).

Following is the total streaks for the Dealer and the Player in 1000 hands, from single streaks (1) and 2 to 8 multiple like-streaks.

The 20 extra blackjack 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.

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%, 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 executives 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!

Now, the more pessimistic reality in blackjack, from the player's perspective. I am a strong believer in the validation of any idea or theory. My latest blackjack software (2009) undeniably proves that the percentage of the bust hands is, at least, 33%. The bust hands were generated following the dealer's rule: Hit all hands under 16 and stand on all hands 17 or higher. In this case, the house advantage (HA) at blackjack becomes: 33.6% x 33.6% = 11.5%. That HA figure is valid only for one player against the dealer. If we deduct the traditional 4% gained by the basic strategy player, we reach a 7.5% house advantage at blackjack.

The streaks will be worse for the player under these new circumstances (which I believe to be the correct ones). No wonder so many blackjack players are dismayed to hear that blackjack is almost a 50-50 game, if playing basic strategy! The players lose far more than the so-called mathematical expectation. I did hear casino players at the blackjack tables expressing anger after quickly losing all their chips. ”It was better to play roulette,” some said. I certainly agree with them right now. The house edge at roulette is better than in blackjack! Yes, some will always stigmatize you: 'Roulette is a sucker's game!'

The 33.6%-dealer-bust approach considers the blackjack probabilities as follows:

~ Dealer: p = 57% (or 0.575);
~ Player: p = 43% (or 0.425).

The number of hands to play is the same: 1000 (or changing blackjack tables around 5 times a day).

~ Dealer: 105 single-win streaks and 139 multi-win streaks;
~ Player: 140 single-win streaks and 105 multi-win streaks.

The 19 extra hands are most mathematically likely allocated as 11 (57%) to the dealer and 9 (43%) 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.

There is a significant difference that favors the blackjack dealer — that is, the casinos. A number of gamblers cautioned me with regards to John Scarne. Indeed, he helped the U.S. government with gambling matters, and especially defense against cheating the U.S. troops by gambling providers. On the other hand, he had a serious financial interest in the gambling industry. He was friends with Frank Sinatra, who, as loudly rumored, had friendship in the mob world. Perhaps John Scarne intentionally published wrong calculations pertinent to the house advantage at blackjack! The real odds would have scared away players from the most attractive and most popular casino game! Who knows?!

Noticeable differences, if playing 1000 hands continuously. My software Streaks and Blackjack always enforce the rule of playing fewer hands at the same table.

I was like most gamblers. I suspected dealer cheating quite a few times. Why does that dealer win so many hands in a row, while my wins come in single streaks that frequently? Believe me, I looked at dealers' hands so intensely sometimes that I risked being treated as hostile! I have never observed foul play, however. I played for fun in a Detroit casino in the summer of 2009. I spent some time with my daughter. One of my main points was the length of the streaks. Why did the dealer have so many long winning streaks (against me), while my winnings came mostly in the meager one hand a time? I remember asking my daughter if she remembered my streaks of 5 or longer winning hands? She was keeping track as well. I did not have a 5-streak in about 100 hands! As you see in the table above, a 5-streak of consecutive winning hands occurs 5 times in 1000 hands. That is, less than one occurrence (.5) in 100 hands.

  • The blackjack dealer has undoubtedly the best position at the table. No blackjack player can ever take the dealer's position. The best position for a player is just before the dealer (the last seat or the third base). The more players at the table, the better for the player in the last seat. The more players busted before the third base, the lower the bust probability for the blackjack player in the last position. The reverse is also true: No busts by the players before you, in the last position, your bust probability is higher — the blackjack dealer's, too!
  • If you play blackjack, be sure to sit in last chair, just before the dealer. The more players at the blackjack table, the better you are. And be sure to chip in with at least the table's maximum limit (to withstand long losing streaks). Try to play no more than 100 hands at the same table (higher probability for shorter losing streaks). You can play much more aggressively within the first 50-100 blackjack hands. If you and I happen to be at the same table, be grateful and let me sit at the third base! You can still learn a blackjack trick or two by watching me...
  • Hear now another new bold statement: Blackjack is a positional game of chance. The position of the players, dealer included, is of the essence. The position is next organically linked to the sequence of the cards being dealt, and therefore the blackjack hands. The degree of certainty for a busted hand depends, indirectly proportionately, to the position of the player (the lexicographic index of the sequence). That's the main reason why the blackjack dealer has the best position at the table (lexicographic sequence).
  • One cannot apply here the probability of the binomial distribution because of the fixed direction of the card dealing. The game would be a lot fairer if the dealing of the cards would be like in holdem poker. In poker, every player will be the first, the second, ..., the last hand, ..., and again ..., hand. The blackjack player, unfortunately, can't change the hand position or sequence... other than moving to another table...

The following passages show how I applied my streak strategy at the time when I thought the dealer bust was 28%. I also considered that player's probability was 48%, while dealer's was set to 52%. In the light of the new blackjack odds, the situation is worse for the player: 42.5% to 57.5%. In hindsight, my previous blackjack strategy was more aggressive than mathematically advised.

Yet, I was able to win consistently, up to 2003 when I reached a serious bump on the road. The floor manager of an Atlantic City casino prevented me from playing blackjack. I had been impeded to play roulette the same day, in the same casino. I did carry a pocket notebook (pencil-and-paper) and wrote down my losing and winning streaks. It was not a cheating device, by any stretch of imagination! A pencil is not an electronic device, like a miniature camera to peek at the cards in the deck! I never touched a deck of cards or a roulette wheel. I documented thoroughly the incidents and published several pages at my website especially Casinos Bar, Ban Winning Gamblers, Skilled Players.

You will find exact times and badge numbers and even names of the casino personnel involved. I didn't use a notebook in my previous casino outings. I memorized my streaks in the manner presented in detail here: The Best Casino Gambling Systems: Blackjack, Roulette, Limited Martingale Betting, Progressions.

I martingale more aggressively at the beginning of the blackjack game. I martingale the first count when it reaches 4. Since the second parameter is more consistent, I martingale it after it reaches 3. I go up to 7 in both cases (2-4-8 and 2-4-8-18). I stop at 7. My probability software Streaks proves the more aggressive betting at the beginning of a blackjack (or gambling) session. The degree of certainty DC for long streaks (losing or winning streaks) is lower.

I become more cautious after 100 blackjack hands or so. I martingale the first count after it reaches 6 (or 5 earlier in the game) and the second count after it reaches 5 (or 4 earlier in the game). I go as much as I can or allowed. If I sense that the streak is real bad, especially inside the same shoe, I stop the Martingale after 7, and start another one with 3 units after the previous streak ends.

My full system, as used with a notebook, keeps track of several streaks: Win (W), Loss (L), Dealer Bust (DB), Player Bust (PB), Dealer Blackjack (DJ), Player BJ (PJ). In my trimmed down version, without the notebook, I only keep track of two streaks: Win (W+), Loss (L-).

I recreate here a fragment with my real play at Trump Plaza Casino, July 21, 2003, beginning 5:30 PM; blackjack dealer: Ginny.

The interpretation.

As you can see, I did not go for the kill: My maximum bet was $50. The minimum bet was $10, the maximum limit at that blackjack table was $500. The 1 to 100 ratio of the bet spread is the minimum I accept. The + sign means I won; e.g. 40+ B (line #10) means I bet and won $40; the dealer busted that hand. The minus sign means I lost that hand; e.g. 25- b (line #14) means I bet and lost $25, while busting. I always differentiate between a dealer bust (B) and my busted hand (b). The j means a blackjack or natural (both for dealer or player). The session was short (under 100 blackjack hands). My longest losing streak was 5 consecutive hands. My longest winning streak was 4 consecutive hands (two occurrences). I won over $300, not counting my generous tips.

Yes, things can go wrong even in short sessions. A blackjack player might encounter a really long losing streak. As a matter of fact, that's the mantra of all casino executives or gambling gurus who have a strong financial interest (selling non-mathematical systems). They will tell you that you are going to lose in very long streaks. But they never mention the opposite: The gambler can win in very long streaks. I call that the gambler's fallacy in reverse. Things happen both ways: They are mathematical, but they represent the rare exception, not the norm. If you experience a long winning streak, my advice is to leave that blackjack table as soon as the hot streak ends.

  • Axiomatic one, you can watch my streak-gambling system beating an impartial blackjack computer program simulating a continuous shuffling machine (CSM).

The casinos react with hostility to the new blackjack dealer's bust odds, probability calculations by Ion Saliu in 2009. Blackjack is a casino game far worse than assumed by most gamblers.

No, the casinos couldn't resist reacting... once again! They should know by now that I don't get intimidated. Yet, they keep reacting every time I publish something of great importance. No doubt, my new research in calculating the blackjack odds of busting is ground-breaking. The new figures will surely have an impact on the game of blackjack. They even make me a criminal by association! They compare me to the criminals who become their own lawyers! Please read an hostile email I suspect originated in a casino highly paid office: Hostile Reaction by Casinos to the New Blackjack Dealer Bust Odds, Probability Calculations.

Blackjack: Software, Content, Resources, Systems, Basic Strategy, Card Counting

See above: The comprehensive directory of the pages and materials on the subject of blackjack, baccarat, software, systems, and basic strategy.

For the best mathematical casino gambling strategy (approach) for non-system players, read:

  • Casinos, Gambling, Win in Casino with Mathematical Systems.
  • The Best Strategy for Lottery, Gambling, Sports Betting, Horse Racing, Blackjack, Roulette.
  • The Best Blackjack Basic Strategy: Free Cards, Charts.
    All three color-coded charts in one file, in the best decision-making sequence: Split Pairs, to Double Down, to Hit or Stand.
  • Gambling Mathematics in Blackjack Proves Deception of Card-Counting Systems.
  • Calculate Blackjack Probability, Odds: Natural 21, Insurance, Double-Down Hands, Pairs.
  • New Casino Games by Ion Saliu:Parpaluck Blackjack.
  • ABC: The Best Blackjack Card-Counting System by Ion Saliu — the only system founded on mathematics and formulas.
  • Reality Blackjack: Real, Fake Odds, House Advantage, Edge.
    • DownloadSoftware: Casino Gambling, Roulette, Blackjack, Baccarat, Craps.
    • Specific software for blackjack, BJ
      ~ BJAQK and Blackjack: Probability and statistical analyses of thousands of blackjack hands from the perspective of a strict blackjack old basic strategy (OBS) player.

Read Ion Saliu's first book in print: Probability Theory, Live!
~ Founded on valuable mathematical discoveries with a wide range of scientific applications, including probability theory applied to blackjack gambling, software, systems, new odds.

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Blackjack’s biggest allure lies in its simplicity. The rules of this classic casino staple are easy to comprehend, or at least if one is playing the game in its purest form. You play against the house and your purpose is to get a hand total that is as close to 21 as possible without exceeding it. If your total is higher than the dealer’s, you receive a payout, if not, you lose. It really is as simple as this.

The enormous popularity this casino mainstay enjoys worldwide has caused dozens of blackjack variations to pop up over the years. Some of those have only minor rule deviations while others are so odd that it almost feels like you are playing an entirely different game, so much so that at BlackjackExpert.com we have dedicated separate pages to some of these variations.

Rule deviations make the game all the more exciting, presenting players with more winning opportunities but it is also important to recognize that some adjustments are there for the simple purpose of giving the house a higher edge. Because of this, it is important to differentiate between the variations that work to your advantage and those that are in the casino’s favor. Continue reading to learn all the fine points of blackjack rule variations and why do they matter.

Common Rule Variations

The thing about casino games, including blackjack, is that they are always slightly rigged against the player so that the house can extract advantage and profit from its tables. This is not to say the casino is cheating you out of your money. There are various legal ways for the house to gain an edge over players and the simplest of them is by enforcing various adjustments to the rules that have a direct effect on the odds. Some of these adjustments actually work in your favor improving your odds while others are designed to hurt your long-term chances of winning.

For those of you who are not familiar with what the term “house edge” refers to, this is the built-in percentage the house collects from each bet made at its tables in the long run. The house edge in blackjack fluctuates wildly but it is safe to say it generally ranges between 0.50% and 1.00% when you follow basic strategy to the tee, making 21 one of the games with the lowest casino advantage.

So for example, if you join a blackjack table with a 1.00% house edge, bet $10 per hand, and play about 60 hands per hour, your action would amount to $600 per hour. Respectively, you are expected to lose $6 on average to the house over the course of time. This is not to say you will not turn a profit over the short term but the more hands you play, the closer you will inch to these expected results.

The house can improve its long-term edge by adjusting some of the basic rules of play at the blackjack tables. The most common rule deviations pertain to the number of decks in play, the dealers’ standing totals, the payouts on naturals, to splitting pairs, and doubling down. We cover all these rule variations in further depth below.

Number of Decks in Play

Blackjack usually plays with one to eight full decks of cards, but deck penetration and the depth of dealing also do matter, especially if one is counting cards. There is a general consensus among skilled blackjack players that fewer decks give the house the lowest advantage. The casino edge increases proportionately to the number of decks in play. From this, it follows that the most profitable tables are the ones using a single deck of cards.

The reason for this is quite simple – the number of decks affects your opportunities to profit from double downs as well as your odds of getting dealt blackjacks. You can easily figure out the probability of obtaining naturals when you know the number of cards in play.

For the purpose, you multiply the odds of receiving an ace by the odds of being dealt a ten-value card. A full deck contains 52 cards and respectively, there are only 4 aces and 16 cards that are assigned a value of ten.

We use the following formula: Pb = n(ace) x n(ten-value cards) x 2 where n indicates the number of aces and ten-value cards, and Pb corresponds to the probability of being dealt a blackjack. The result is then multiplied by 2 as we also take into account the order in which the cards are dealt, which can be either ace/ten or ten/ace.

Therefore, the calculations for a single-deck game run in the following manner: Pb = (4/52) x (16/51) x 2 = 0.04826 x 100 = 4.82%. We multiply by 100 to obtain the figure in the form of a percentage. Also, the overall number of cards in the second brackets is reduced to 51 instead of remaining 52 because you have supposedly already drawn one card, the ace.

We can use the same formula to calculate the probability of receiving a blackjack when multiple decks are in use. Respectively, the likelihood of getting naturals in a six-deck game will be Pb = (24/312) x (96/311) x 2 = 0.04748 x 100 = 4.74%. The difference of 0.08% appears minuscule but when it comes to gambling, things unfortunately do add up in the long run.

The smaller your chances of receiving blackjacks at a given table, the more the house edge increases because it is the naturals that give players the best value in this fascinating game. In a single-deck game where you use perfect basic strategy, the house edge is -0.013% whereas eight decks give the casino an advantage of 0.57%

Dealer Standing Rules

If you are reading this, you probably already know that blackjack dealers make no decisions whatsoever when playing their hands because they need to abide by fixed rules. The house gains an edge over players by forcing them to act on their hand before the dealer acts on theirs. However, the rules the dealer follows also bear consideration because can vary, sometimes even from table to table in the very same casino.

The general consensus in the blackjack community is that tables where the dealers stand on all totals of 17 are the best ones to play at. You may come across blackjack tables whose dealers are required to hit soft totals of 17. This gives the casino an extra 0.22% edge over you. Dealers who hit soft 17s have a higher probability of improving their totals to 18, 19, 20, or 21 as opposed to their colleagues who stand on all 17s. Luckily, the dealers’ standing rules are clearly written on the baize of the tables, making it easy to figure out which games to avoid.

Payout Variations

We already talked about how blackjacks are the most valuable hands in this game. This is so because naturals pay out at higher odds than regular winning hands which only offer you even money. So instead of profiting from a hand that occurs more rarely, you are paid the same amount you would receive for any other winning total.

Any table with a reduction in the casino odds of blackjacks is not worth your time and especially, your money. Always shoot for the games where naturals return at a rate of 3 to 2 and your net profits amount to one and a half times your original stake. A blackjack payout of 6 to 5 is a no go.

Beware of variations like Blackjack Switch, for example, where the dealer pushes with you on totals of 22 instead of going bust. There is no need to clarify that the tables where the dealers take all ties are also to be avoided.

Pair Splitting and Doubling Rule Variations

Doubling down and splitting are two of the most important betting actions at the blackjack table for the simple reason they help you to extract more value in favorable situations. Casinos would often resort to rule modifications to prevent this from happening. You may come across tables where doubling down is restricted only to some totals, usually, 9, 10, and 11. This cripples your chances of increasing your profits, boosting the odds in favor of the house by 0.20%. Being able to double on any total gives you more flexibility in making the right decisions should you detect a favorable situation.

The same applies to splitting pairs of equal cards. It is in players’ best interest to be able to resplit to up to four hands. Just imagine the following hypothetical situation where you get a pair of aces, which you are advised to always split. If you are dealt one more ace on each split card, you have four hands starting with an ace and this improves your chances of obtaining a winning hand total. One such thing would occur on rare occasions, which is why it improves the house’s odds with 0.05% only but it still counts.

However, there are tables where the players are permitted to split pairs of ten-value cards only if they are of the same kind, two queens, for example. Remember these restrictions are detrimental to your long-term expected value.

The optimal rules would allow you to double down following a split. You pour more money into the action but this also increases the amounts you win. For instance, you start with a $10 bet and get dealt a pair of kings. You split those placing an additional wager of $10. You double down on both cards and receive aces on each king, winning a total of four hands for an overall profit of $50. This certainly is a satisfactory result for a wager that started off at $10.

Early vs. Late Surrender

The ability to be able to surrender potentially losing hands and forfeit half of your initial stake is of essential importance for your expected return. There is even a separate variation called Blackjack Surrender and it is the game of choice of many expert blackjack players. However, there is a clear distinction between early and late surrender, and it is the former that gives you better odds.

Simply put, early surrender enables you to admit defeat before your dealer has peeked for a natural. Needless to say, this saves you money. When late surrender is in force, you still can give up on your hand at the cost of half of your original wager, but you can do so only after the dealer has checked for a blackjack when showing an ace.

Of course, if the dealer indeed has a natural, you do not get to surrender anything because you lose right away. Hunt for tables with early surrender since this improves your edge by 0.39%. Let us warn you in advance, though – these variations are as rare as hen’s teeth, even more so if you play online.

Charlie Rules

The Charlie rules are great for blackjack players because they stipulate that once you draw a given number of cards without going bust, your hand is an automatic winner no matter what total the dealer obtains after you have acted. When playing live, you should feel free to inquire whether or not a Charlie rule applies at the table and if yes, for what number of cards. In randomly generated games, this is clearly written in the respective variations’ rules, which, it goes without saying, you must always go through in advance.

The reduction of the house edge in the presence of a Charlie rule is minuscule but as a blackjack player, you should learn to never look away from favorable rule variations. Casinos offer even-money payouts on seven-card Charlies which reduces the house advantage by 0.01%. On rare occasions, you will encounter tables with the six-card or five-card Charlies in force, which take away 0.16% and 1.46% from the house’s edge.

Why Rule Variations Affect Decision Making in Blackjack

Blackjack is one of the select few games where players can gain the upper hand through optimal decision making. The most common way to achieve this is either through advanced techniques like card counting or through using a basic strategy. The latter relies on the knowledge of your starting hand and the one card your dealer is showing. It helps you make optimal decisions under the assumption these three cards have already been dealt out from the shoe or deck and therefore, will not make another appearance before the reshuffle.

If you want to improve your chances of winning at blackjack, you should start with mastering basic strategy. That being said, you should not be too quick to memorize the first basic strategy chart you come across over the internet and follow it to the tee because the different rules also lead to variations in basic strategy. Some of the things you need to take into account include the rules on surrendering, splitting, and doubling, the deviations in dealers’ fixed rules, and the number of decks the game is played with.

Following a basic strategy designed for multiple-deck play at a single-deck blackjack table takes away some of your edge. Even a fraction of a percent matters in the long term so the best way to start would be to master basic strategy and then vary it in accordance with the rules that apply to the particular blackjack game you are playing. Once you put in a sufficient amount of practice, it would be much easier to vary your basic strategy depending on rule modifications.

Common Blackjack Variations at Online Casinos

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Now that we explained the most typical rule variations and why do they matter, we believe it is time to acquaint you with some of the most common blackjack variations you can find online or offline. Some of these improve your odds of winning, others reduce them but all are equally enticing.

Atlantic City Blackjack

When the first casinos in Atlantic City opened doors, they attracted the action of thousands of advantage players with the flexible rules at their blackjack tables. Card counters thrived in Atlantic City whose casinos did not persecute them as severely as their Sin City counterparts. Since gambling is regulated by the local New Jersey Casino Control Commission, all casinos in Atlantic City would offer the same rules at their blackjack tables, hence the name of this variation.

Atlantic City Blackjack is a multiple-deck game which uses eight full packs of 52 cards each. The dealers must stand on all totals of 17, soft or not, and peek for naturals on both aces and ten-value cards. Doubling down is possible on all totals, with players having the option to split to a total of four hands. One card is dealt on split aces and you have the option to double down after a pair is split. Naturals offer the standard payout of 3 to 2 but most importantly, you can surrender after the dealer has checked for a blackjack.

Vegas Strip Blackjack

Vegas Strip Blackjack ranks as one of the most favorable variations of 21. It typically plays with four full decks of cards. The objective of the player remains the same but some of the rules that distinguish it from other blackjack varieties are that the dealers are required to peek for naturals and must stand on soft totals of 17. A natural would usually offer the best payout of 3 to 2 although some venues at the Strip would host tables with a decreased payout of 6 to 5 on blackjack hands.

You can double down on any total your heart desires, even after you have split pairs. While we are on the topic of pairs, Vegas Strip Blackjack enables you to split to up to four hands, unless the pair consists of aces which cannot be resplit. You can receive only one card per split ace. You can split even pairs of ten-value cards that are unlike, like queen-jack, for example. This variation should not be mistaken for Vegas Downtown Blackjack which uses only two full decks and requires the dealer to hit soft totals of 17.

European Blackjack

Different Variations Of Poker Games

European Blackjack dominates gambling establishments across the Old Continent and is easy to distinguish since it does not use hole cards. This is actually rather detrimental to players because it eliminates both the necessity of a peek rule and the insurance side bet. Both of these protect you against the dealer’s potential naturals, so you get the picture.

Unlike the previous two variations, European Blackjack plays with two full decks and the dealer initially gets only one face-up card. Once all participants in the coup have made their decisions on how to play their hands, the dealer draws more cards to complete theirs for a total that should be no less than 17.

Things tend to get downhill from this moment on, with very rigid doubling and splitting rules. Doubling down is possible but only on two-hand totals of 9, 10, and 11. Only one split per pair is allowed, but if you get dealt unlike ten-value cards you can forget about splitting. Blackjack awards you a payout of 3 to 2.

Double Exposure

Double Exposure appeared for the first time in Sin City’s Vegas World casino back in October 1979. The game was originally named Zweikartenspiel but everyone called it Double Exposure. The name caught up and this is how the game is known to this day. You have probably guessed where the name originated from – in this variation the dealer has both their cards exposed, which helps with decision making and is especially great for advantage players.

This may come off as a major surprise but Double Exposure is actually one of the variations to give the house the biggest edge in blackjack. The rules have been modified unfavorably, of course, as a means of counterbalancing the edge you get by seeing both cards of the dealer. The games utilizes six regular decks and the dealer takes all ties with the exception of those with naturals, in which case you two would push. Double after splitting is out of the question at these tables and you have the option to split a single time only. But it actually gets worse – you receive even money for your naturals.

Perfect Pairs

Perfect Pairs is one of those blackjack variations you must try at least once in a lifetime, especially if you are seeking to profit from your side bets. The rules coincide with those in classic blackjack, as in fact the only difference here is the option to place a side wager on the proposition that your starting hand will consist of specific pairs. The more “perfect” the pair is, the bigger the payout you are entitled to. Do have in mind the house holds a ghastly advantage on these side bets that reaches 11% so you only stand a chance of profiting from those if you are counting cards or shuffle tracking.

Other than that, the game is usually played with four decks but the number may vary. Doubling down is permitted on all totals but on the downside, you are prohibited from splitting pairs consisting of aces. When a side bet is made, the dealer would pay out if it wins at the very start of the coup. There are three pairs that pay when a side bet is in place. Mixed pairs are of the smallest value and are likely to occur more often so they pay out 5 to 1. Colored pairs are rarer and return a payout of 10 to 1 whereas the perfect pairs (two suited cards of equal numerical value) offer the highest payout of 30 to 1.

Pontoon

Pontoon is easily one of the most fascinating blackjack variations out there. We will explain about the variation that plays in accordance with the British rules, where no cards are removed from the deck.

Here one full deck is normally in use. The betting actions are largely the same as those in classic blackjack but are given different names. You “stick” to your original hand total which means to decline additional cards. Requesting more cards is called “twisting”. Also, you can pay extra to draw more cards to improve four-card totals, with the option to buy up to three times but never after twisting. In Pontoon, the players are required to twist until they obtain a total of 15 or above.

Different Variations Of Poker

One of the biggest allures of the game is the increased payout of 2 to 1 for naturals, which are pretty much the same as blackjacks but are called pontoons in this instance. Do not be too quick to rejoice, however, since here no hole cards are in play and the dealer receives both their cards facing down. Respectively, there is no way for you to insure your hands against pontoons.

The second best hand in Pontoon is the five-card trick which is pretty much a five-card Charlie with a fancy name that pays out 2 to 1. Next in line is the regular 21 consisting of three or four cards giving you this total for an even-money payout. In you break 21, you bust, similarly to regular blackjack. Note that here the dealer takes all ties, including those with pontoons.

All Blackjack Variations

Blackjack Games with Progressive Jackpots

Different Variations Of Blackjack

More and more players are turning to online blackjack and the reason is not only to avoid heat on behalf of landbased casino personnel. They also do it because online they have the wonderful opportunity to play progressive blackjack variations. The more players wager on the progressive variation, the higher the jackpot becomes. Certain conditions must be met to become eligible for winning the pot, though, starting with the optional side bet you need to make. This is like an ante that is immediately added to the pools.

In one of the most common progressive variations, the one designed by Microgaming, you are awarded additional payouts for hands consisting of sevens, with cards of the same suits offering you some of the largest prizes. However, the largest prize of all is the progressive pot which is awarded for obtaining hands consisting of three sevens of diamonds.

Different Variations Of Black

To conclude it all, we would like to warn you that the house edge on progressive games is typically increased to counterbalance their massive winning potential, so the pot would have to escalate to a specific amount before one such game can give you a positive expected value.