Introduction to Blackjack

Blackjack is one of the most played casino games of all times and it’s also known as twenty one due to the fact that this particular number plays a crucial role for the game’s objective. It is offered by almost every casino all around the world which makes it extremely convenient for the players as they can enjoy it everywhere they go. So far, the game’s origin remains unknown and the first written evidence of it was found in the 17th century.

Blackjack grew in popularity so much because unlike many other casino games, it can be won with the right strategy and skills. It is true that it requires the most preparation and knowledge of all games but players can be sure that all of their efforts and time will be worthwhile. The more they practise this game, the better chances they have of gaining advantage over the opponent which in this case is the casino. This is the reason why there are a number of different strategies, they can learn and try which makes the whole game extremely interesting and challenging.


Even though many people are familiar with the basic rules of the game, only few know what it takes to win. Lacking the right strategy and knowledge, many players fail to understand how Blackjack actually works. Despite being one of the hardest casino games of all times, it is also one of the most popular ones. The reason behind this is quite simple, as already mentioned, Blackjack is so much more than just basic rules and card decks. What also contributed to its great popularity in the past was the fact that the public sector drew a lot of attention to it by publishing a number of interesting stories and news which attracted a lot of players.

Blackjack Is the Only Mathematically Beatable Casino Game

Blackjack is unlike any of the other games available on the casino floor because, contrary to popular belief, it requires a good deal of decision-making. Players’ decisions have a direct impact on their long-term odds of winning. Good decisions increase players’ long-term chances of turning a profit and vice versa, bad decision-making inevitably leads to greater losses in the long run.

Blackjack stands out from other games because it is mathematically beatable. In fact, this is the only gambling game, along with full-pay video poker, where players can gain an edge over the house through strategy play. But why can a gambler prevail in blackjack while having zero chances at beating games like roulette or craps in the long run? It all boils down to two mathematical concepts – dependent trials and independent trials.

The vast majority of casino games, including craps, slots, roulette, keno, and stud poker, are games of independent trials. Even if a craps player throws a 7 on five straight rolls, their chances of winning or losing on the sixth dice roll inevitably remain the same.

A craps shooter cannot obtain any viable information to improve their winning odds by examining the results of previous trials. All possible outcomes in chance games of independent trials share the same odds of occurring. An outcome can occur a hundred times in a row but it still stands the same chances of occurring on the 101st trial.

With independent trials, the probability of all possible outcomes happening is a product of the individual probabilities of the outcomes. An independent trial has no impact whatsoever on the probabilities of occurrence of the rest of the trials. Moreover, as these results are entirely random, no strategy can help you to predict what outcome will occur next.

Dependent Trials in Blackjack

This is not the case with blackjack, though, which is a game of dependent trials. Here the collective probability of all outcomes occurring is a result of their conditional probabilities. In blackjack, the conditional probability of an outcome is affected by the outcomes that occurred before it.

People frequently say the cards have no memory but this aphorism does not apply fully to the game of blackjack. Cards that have already been dealt impact the remaining deck’s composition. In turn, this influences the players’ winning chances in the future. Let’s consider the following example.

You take a deck of 52 cards and shuffle in up with your friends John and George. You receive a pair of aces on the first round of play while John and George both get blackjacks (an ace next to a 10 or a face card).

The cards that have just left the deck give you very valuable information about what is likely to happen next. In one such scenario, you can easily deduce no blackjacks can possibly occur during the second round of play unless you return the discards to the deck and reshuffle. All four aces have left the deck so blackjacks are impossible.

A Parallel with Another Casino Card Game

This partial predictability is exactly what makes blackjack a mathematically beatable game as long as one uses an adequate strategy. It is worth mentioning the casino card game baccarat is also based on dependent trials although it is significantly less exploitable than blackjack.

The main difference here is that the edge baccarat players can gain through card tracking is very minuscule. This stems from the fact the player and the banker hands are played under a fixed rule set each and every time.

Furthermore, the set of drawing rules for the player hand is similar to that for drawing to the banker hand. There is absolutely no decision-making, whatsoever, on behalf of the player or the dealer. The bottom line is in baccarat, there are no cards that strongly tip the odds either in favour of the house or the players.

The Origin of Blackjack Strategies

The stage for beatable blackjack was set in the 1950s with the discovery of basic strategy. But perhaps more interesting is the fact that said strategy was invented by four men who had nothing to do with blackjack, or gambling for that matter. Herbert Maisel, Wilbert Cantey, Roger Baldwin, and James McDermott were all US Army engineers with a background in mathematics.

It occurred to them that blackjack is based on dependent trials and players could gain an edge by keeping track of the dealt cards. The four men subsequently devised a mathematically optimal strategy for each possible player hand against each possible dealer card by using desk calculators.

It told players what the optimal playing decisions were in every possible situation they might encounter at the blackjack tables. The strategy they birthed first appeared in 1956 in the Journal of the American Statistical Association.

Casinos paid no mind to this publication at the time but it captured the attention of another numbers man, Professor Edward O. Thorp, who tested the strategy using early computers at the MIT University. Thorp ran a number of simulations to arrive at the discovery the playing decisions suggested by the four engineers were accurate almost to the tee.

Advanced Play

Thorp proceeded with more simulations to perfect the strategy and subsequently came up with a clever way to gain an advantage over the house in blackjack. Thorp also invented the first system for card counting and published it in his book Beat the Dealer. Note that all this occurred at a time when blackjack was still played with a single deck of cards.

Thorp’s book became a big hit, which eventually led to casinos tweaking the rules of the game in an attempt to offset the advantage basic strategy and card counting gave to players. Playing conditions became less favourable and more decks were introduced into play. The irony lies in the fact this only resulted in the invention of newer, simpler, and more effective strategies and card counting systems.

Also ironic is that Beat the Dealer led to greater profits for casinos from their blackjack tables. Many people read the book and arrived on the gaming floor with the intention to beat the house at its own game. Few actually succeeded.

Most laymen lacked the patience, time, and inclination to learn basic strategy, let alone to master advanced techniques like card counting. Casinos around the world had a field day as unskilled recreational players crowded at their blackjack tables.

Further Refinements of Blackjack Strategy Play

Then another mathematician arrived on the scene to drive blackjack strategy and advantage play to further heights. Harvey Dubner was also somewhat of a computer expert so it did not take him long to come up with a newer card counting system that was much simpler than Thorp’s.

Basic Strategy

Mr Dubner gave the blackjack community a very precious gift in the form of the High Low Count system. It was originally presented at a Las Vegas conference during a panel called “Using Computers in Games of Chance and Skill”.

The High Low Count remains the most popular and widely used counting system by advantage players to this day. The system was later refined by a computer programmer named Julian Braun. The improved version was then published in the 1966 edition of Thorp’s now-legendary Beat the Dealer book.

The Work of Julian Braun and John Scarne

Among the people who saw a deeper meaning in blackjack were the mathematicians Julian Braun and John Scarne who dedicated a considerable amount of time to study how the game actually works. They took into account even the smallest details of the game and observed in what way every different move changed the course of the game.

As a result, they created many strategies and theories which allowed them to predict to some extent how the game would unveil further. Even though Mr Braun and Mr Scarne were not gamblers, they managed to make a number of findings which greatly contributed to what we know today about blackjack.

Their theories were proof that the game follows a particular pattern and therefore, it can be guided and influenced using an appropriate strategy. This is one of the reasons why the decks in the game were increased a few times as many of the casinos started losing money due to these findings and this was an attempt on their side to prevent strong players from beating the game.

The secret that lies behind every useful strategy that has ever been developed is in the odds and probabilities of the cards. In order to be able to apply any of these strategies correctly, it is essential to understand its principles and know it inside out. The work of Mr Braun, in particular, was so important that it earned him a spot in the Blackjack Hall of Fame in Las Vegas. He was inducted in 2005 for his contribution to blackjack statistics analysis.

Counting Cards in Blackjack

Basic blackjack strategy tells you how to optimally play your hands against different dealer upcards. While this reduces the house edge to under .5%, it cannot help you win in the long term. The strategy is based only on the knowledge of three cards and does not account for the changing deck composition.

The silver lining is that blackjack players can tilt the odds in their favour and turn a long-term profit by mastering card counting. Unlike baccarat where no cards favour considerably the player or the dealer, in blackjack, the excess of high cards remaining to be dealt works to the advantage of players. And the opposite – when low cards outnumber high cards, the advantage switches in favour of the dealer.

A card counter can turn a long-term profit by betting more during advantageous high counts where their winning chances are greater. And vice versa, the size of wagers decreases as the deck is depleted of high cards.

Some players prefer to not place bets at all when at disadvantage and wait it out until the composition of the deck(s) changes, a practice known as wonging out. For more information on card counting and basic strategy, you can check Casino Guardian’s articles on these topics.

What It Takes To Win

In Blackjack every decision matters greatly because every move players make affects the game in such a way that it can change its course completely and lead to a different ending. The possibilities of the card combinations are just endless and if players want to win they need to think ahead to the next turn of their opponent. In order to become winners, they need to be extremely prepared and take into account the following things prior to entering the game: their bankroll, money management skills and acquired knowledge. Of course, Blackjack is a casino game and as such, there isn’t any universal formula that will inevitably guarantee the desired success.

Also players need to bear in mind that in order to accomplish their goal, they need to have a decent bankroll. A lot of people view Blackjack just as the rest of the casino games – a chance to win big if they get lucky and thus, there is no need to have a decent bankroll beforehand. Unfortunately, this game doesn’t work like that and many people find this out at worst by losing a substantial amount of money.

However, it is worth noting that having a decent bankroll doesn’t determine whether players will win or lose but it simply indicates what amount of money they have the chance to win. Moreover, discipline and money management skills always play a crucial role for the players’ performance and shouldn’t be underestimated in any case.

Important Things to Consider Before Playing Blackjack

Relying completely on luck while playing blackjack is not only a waste of time but also of money. Players are highly recommended to set win goals and loss limits before they join the game. By doing so, they do not risk surpassing them which can also help them develop better discipline and learn how to resist the temptation to continue. It is indisputable that blackjack requires a solid bankroll. However, the amount players can start with is not strictly set but it directly reflects every decision they make throughout the game.


Players need to remember that there are a few things that are essential and must be considered prior to playing if they want to win in the long term. In order to do so, they need to know the rules by heart, have a good bankroll, and learn basic strategy.

It is highly advisable to acquire all the needed knowledge and know a strategy backwards and forwards as this is the only way to win in the long term. Blackjack is the perfect casino game for adventurous players who like to challenge themselves by putting their skills and knowledge to the test and at the same time they have the chance to make a profit while having fun.