There is only one correct blackjack basic strategy given a set of rules. Since all casinos don’t offer the same rules the strategy can be slightly different. Learn about the blackjack strategy guide with this in-depth analysis. This includes an introduction, the history and a break down of the rules and variations. Julian Braun was born in 1929 in Chicago which at that time had ill fame. Despite difficult childhood which happened to Julian during the years of theGreat.

1. Julian Braun - Blackjack
2. Julian Braun Blackjack

Blackjack is a slightly deceptive game. Its simple rules of play may fool you into believing it is easy to master but if you delve deeper, you will quickly find this is a purely mathematical game that is all about odds and probabilities. Blackjack Hall of Fame inductees Edward Thorp and Julian Braun were among the first people to come to this realization in the 1960s. They ran millions of simulations on old IBM computers to refine the basic blackjack strategy Ed Thorp published in his Beat the Dealer book, which is now a classic in the blackjack canon.

1. Bonus
   $300
2. Bonus
   ⋆80 Free Spins
3. Bonus
   $300

Julian Braun - Blackjack

If you truly want to win at this game, you need to gain a good understanding of what the odds and probabilities for every possible scenario at the table are and base your playing decisions on these odds. The following article aims at introducing you to the foundations of blackjack odds and probabilities. Toward the end, we have also included several charts that may prove to be useful.

Understanding Blackjack Probabilities

Many people use “probability” and “odds” as two interchangeable terms but in fact, there is a pronounced difference between the two. While inherent in gambling, probability is, first and foremost, a separate branch of mathematics that deals with the likelihood of different events occurring. Probability permeates all aspects of our lives, from weather reports to statistics and playing at your local casino.

Probability is calculated on the basis of known data but cannot be used to predict exact outcomes, like the outcome of a hand in the game of blackjack, for example. It simply shows you the likelihood of an event happening, based on the knowledge of the number of desired outcomes and the number of all possible outcomes. You can use this knowledge to execute the best play at the blackjack table but it alone does not show you with absolute certainty which card the dealer will pull out next.

Statisticians use what is known as a “probability line” to represent the probabilities of events, which can be classified as certain, likely, unlikely, and altogether impossible. The further to the left an event is positioned on the probability line, the more unlikely it is to take place. Conversely, when an event is positioned further to the right of the line’s center, it has a higher likelihood of occurrence.

The probability of a given outcome happening is quite simple to calculate. All you have to do is divide the number of desired outcomes by the number of all possible outcomes. In the context of gambling, this translates into dividing the number of ways to win by the number of all possible outcomes.

Independent vs. Dependent Trials

Before we proceed with concrete examples, we would like to make a distinction between independent and dependent events (or trials in statistics). An independent event has no impact on another event’s probability of occurring (or not occurring). Such is the case with the dice tosses in the game of craps and roulette spins, where previous outcomes have no influence on the results of the trials that are to follow.

Here is an example of determining the probability of rolling a 2 with a six-sided dice. There is only one possible way for you to roll a 2 out of 6 possible outcomes. It follows that the likelihood of a 2 being rolled is 1/6 = 1.166 * 100 = 16.66%.

The probability of rolling a deuce with two dices is even slimmer because there are more permutations (36 to be precise) but there is only one two-dice combination that results in a 2. Respectively, the likelihood of this independent event occurring is 1/36 = 0.027 * 100 = 2.77%. No matter how many times you toss the dice, the probabilities of the tosses, or trials, will always remain the same.

With dependent events, on the other hand, previous trials influence the probabilities of the trials that are to follow. Unlike roulette and dice games, blackjack is a game of dependent trials where each card dealt changes the composition of the remaining deck and therefore, influences the likelihood of forming specific hands on the next rounds of play.

This phenomenon is best explained through examples, so let’s calculate the probability of drawing an Ace from a single deck of cards. Single-deck blackjack utilizes a full deck of 52 cards without any jokers where we have 13 card denominations of 4 different suits each, which is to say there are only 4 Aces out of 52 cards. Therefore, the likelihood of you pulling an Ace at random is P(Ace) = 4/52 = 0.0769 * 100 = 7.69%.

Independent vs. Dependent Trials Additional TipsProvided that the Ace you have already drawn is discarded instead of being reintroduced back into the pack, the probability of pulling an Ace on the next trial will be slimmer. We have three Aces left and the number of cards in the deck has now dropped to 51. The calculations are as follows: P(Ace) = 3/51 = 0.0588 * 100 = 5.88%. The more cards of a given denomination have left the deck, the slimmer the likelihood of drawing a card of said denomination on your next try.

The only unknown factor in the game of blackjack is which card we will pull out next. We can determine the probability of drawing a specific card but cannot say with absolute certainty which card will leave the pack on the next draw.

The only random factor that impacts the draws is the reshuffle. If we place the Ace back into the deck and reshuffle after each trial, the probability of pulling it will remain the same as now you will be dealing with independent trials.

Another Example – Hard 16 vs. Dealer 10 (No Surrender)

Let’s demonstrate how probabilities in blackjack work when more cards have left the deck. We assume you start a fresh round in a no-hole-card game after the single deck has been reshuffled. You are dealt Q-6 against a dealer K but surrender is unavailable, in which case you are forced to hit your hard 16. What is the likelihood of improving your total on the next hit?

We are left with 49 cards since 3 cards have been removed from the deck already. The following cards can help you improve your 16: an Ace for a total of 17 (your Ace will be counted as 1 in this case since otherwise it will bust your hand), a deuce for a total of 18, a 3 for a total of 19, a 4 for a total of 20, and a 5 for the best possible outcome of 21.

Thus, you have 20 cards that can help you out of 49. The probability of drawing a “good” card is 20/49 = 0.408 * 100 = 40.8%. Conversely, the likelihood of you busting by pulling one of the 29 “bad” cardsis 29/49 = 0.591 * 100 = 59.1%.

The Probability of Obtaining a Blackjack

Naturals are the strongest hands you can obtain in the game of 21. Not only it is impossible to lose with a natural (in the worst-case scenario you will push with the dealer) but you get a little extra in terms of profits since blackjacks return 1.5 times your original bet (on condition you are not foolish enough to play 6-to-5 games). Because of this, it is important for you to gain a proper understanding of the probabilities of getting blackjacks.

Knowing the number of decks in play, you can easily determine the likelihood of receiving a natural after the reshuffle. For the purpose, you must multiply the probability of pulling an Ace by the probability of pulling ten-valued cards like 10, J, Q, and K (there are four of each in a single pack for a total of 16). It is also necessary to multiply the result by 2 because there are two possible permutations of cards in a hand of blackjack, for example A-Q and Q-A, K-A and A-K, and so on.

The probability of drawing an Ace is 4/52 while that of pulling one of the ten-value cards is 16/51. The number of cards has dropped to 51 in the second case to account for the Ace that has been removed from the deck. Therefore, we calculate the probability of getting dealt a blackjack in the following way: P (Ace) * P (Ten-Value Card) * 2 = (4/52) * (16/51) * 2 = 0.0482 * 100 = 4.82%.

The likelihood of getting naturals decreases as more decks are introduced into the game, which, inturn, slightly increases the advantage the casino has over you. This often sounds antithetical to inexperienced players who reason it should be the other way around because there are more Aces and ten-value cards when multiple decks are used.

The Probability of Obtaining a Blackjack Additional TipsThis line of reasoning is erroneous because the effect of the individual cards’ removal is not as pronounced in multiple deck games as it is in single or double deck variations. The probability formula we use is the same, however, no matter how many decks are in play.

Below are the probabilities of drawing a blackjack at the start of a fresh shoe with two, four and six decks. You will notice the difference becomes less pronounced the more decks are introduced into play. The difference in blackjack probabilities between six and eight decks is so minuscule, we did not bother including the calculations here.

• The probability of a blackjack with two decks is (8/104) * (32/103) * 2 = 0.0479 * 100 = 4.77%
• The probability of a blackjack with four decks is (16/208) * (64/207) * 2 = 0.0475 * 100 = 4.75%
• The probability of a blackjack with six decks is (24/312) * (96/311) * 2 = 0.0474 * 100 = 4.74%

Converting Probability into Odds

Odds are different than probability in that they show us the ratio between the number of desired outcomes occurring and the number of ways in which the desired outcome will not occur. In the context of gambling, this corresponds to the ratio between winning and losing outcomes. Unlike probability, the odds are normally expressed as fractions instead of as percentages.

Here are a couple of examples so you can get a firmer grasp on how odds work. Let’s suppose you are interested to know the odds of you hitting number 9 in single-zero roulette where there are 37 numbers on the wheel in total. There is only one number that wins, so it follows there are 36 ways for you to lose. Respectively, the odds for you succeeding are 1 to 36, or 1/36. This corresponds to implied probability of 2.70% which weirdly enough coincides with the advantage of the casino in this game.

Let’s use another example with a single-deck blackjack game. What are the odds of you pulling the Queen of Spades from the 52-card pack? There is only one Queen of Spades in the deck opposed to 51 cards of different suits and denominations, so the odds of you drawing this card are 1 to 51 or 1/51.

In gambling, odds are normally expressed in reverse showing you the chances “against” an outcome occurring, like so: 51 to 1 and 36 to 1. You can convert the implied probability into odds with the following formula: (100/P) – 1 where P stands for probability.

Converting Probability into Odds Additional TipsIn the example with you hitting number 9 on roulette, the calculations run as follows: (100/2.70) – 1 = 37.03 – 1 = 36.03, or roughly 36 to 1. In the one with the Queen of Spades, the implied probability of 7.69%, when converted into “odds against”, corresponds to (100/7.69) – 1 = 13 – 1 = 12, or 12 to 1.

The above calculations show us the actual, true odds of hitting a 9 and of drawing the Queen of Spades from a full 52-card deck on the first trial. The casino extracts its advantage (and profits) by ensuring it always retains a percentage of all players’ cumulative wagers.

In games like roulette and craps, this is achieved solely through payout reduction. The true odds of hitting an individual number on a single-zero wheel are roughly 36 to 1 whereas the casino pays you only 35 to 1.In blackjack, the house extracts its edge in a variety of ways including payout reduction for naturals (6 to 5 instead of 3 to 2), unfavorable rules, and increasing the number of decks in play.

The Probability of the Dealer Busting and the Effect of Cards’ Removal

In blackjack, the odds and probabilities fluctuate with each card that leaves the deck or shoe. This is so because small cards 2 through 6 favor the dealer, whereas high cards 10, J, Q, K, and A favor the player. Cards 7 through 9 are neutral because they favor neither the player nor the dealer.

The dealer has higher chances of exceeding 21 when they start their hand with small cards like 4, 5, and 6. The player’s advantage increases when the dealer exposes one of these cards. Respectively, the player’s advantage begins to drop when high cards are removed from the deck. Examine the table below for more information on the dealer’s probability of busting with individual upcards.

Blackjack is the only casino game where cards “have a memory” since your chances of winning change each time a card is removed from the deck. In fact, this is the basic premise of card counting which we discuss further on in this guide.

When the composition of the deck or shoe is such that ten-value cards and Aces outnumber small card, the player holds an advantage over the dealer. It is the other way around when there are more small cards left to be played. The table below shows you how the cards of different ranks impact your chances of winning:

Julian Braun is the author of How to Play Winning Blackjack. He refined Edward Thorp’s original blackjack strategies in the 1960’s using more advanced computer programming but he wasn’t the first blackjack author and he wasn’t the first computer programmer, so few people know his name. Sure, we all remember that Neil Armstrong was the first man to walk on the moon at 2:56 UTC July 21, 1969, but who remembers that second guy who set foot on the dusty terrain of the moon less than 20-minutes later? If you don’t know, it was Buzz Aldrin. And, if you don’t know who Julian Braun is, that’s alright too.

Braun was born in Chicago, September 25, 1929. He had a typical childhood in a middle-class neighborhood and graduated from the Illinois Institute of Technology with a dual degree in Mathematics and Physics. That tells you he was a bit of a nerd, and after spending time in the Marines he traveled to California and did his post-graduate degree at what was then San Diego State College, but he missed home.

He was a quiet, introverted person with a love of numbers that led him to IBM where he eventually became head of the company’s teaching program at their downtown Chicago research lab. As was befitting his personality he collected stamps and played chess for excitement. When Thorp’s book Beat the Dealer exposed the possibility that the casinos of Nevada might actually be beaten at the game of blackjack, Braun took note. He was intrigued by Thorp’s use of computers to arrive at his estimation of the best Basic Strategy to use and a card-numbering system that we now know as card counting to gage when the odds had swung form the house to the player.

Braun got in contact with Thorp about the computer program he used and Thorp never thought twice before sending his computer colleague a copy of the program, written in Fortan, that he had run at MIT. After scanning Thorp’s work, which arrived with no instructions or documentation, Braun realized how the algorithms worked and wrote a new program that he was able to run through a high speed (for those days) IBM 7044 Mainframe computer. It wasn’t a laptop, it was huge, filled with wires and tubes, and took up an entire room, but it was able to get the job done once Braun ran 9 million simulations. His work on the program was relentless and meticulous. He refused to quit until it was perfect.

The end result was in improved version of basic strategy and a program he used to develop data used by Lawrence Revere. Braun then shared his information with Thorp and an updated second edition of Beat the Dealer was published. Revere’s book, Playing Blackjack as a Business followed, with a tip of the hat to Braun.

Later, Lance Humble worked with Braun and the same program developed the Hi-opt strategies and card counting system. Braun wasn’t paid for his work as the blackjack world’s programing genius, but his name was certainly bandied about the publishing world. It always made authors sound both smart and connected to mention Braun’s name.

Braun as a Blackjack Player

As a loner and computer geek, Braun would seem perfect for a role as a blackjack card counter. He had a good job, time to travel to Las Vegas, and a brilliant mind. What more could you ask? After working with both Edward Thorp and Lawrence Revere, Braun did some gambling of his own. Yup, the wild gambler was even tossed out of a casino.

Being barred is a problem for all players, and the better your cover act and ability to avoid detection, the longer playing career you are likely to have. And then we have Braun. The computer guy. Quiet, introverted, and precise. He stuck out like a sore thumb.

Julian Braun Blackjack

In a rare bit of humor, Braun revealed later in life to Arnold Snyder, a fellow blackjack master and author, that he did play blackjack on a semi-regular basis. He also admitted that he was barred from playing while on a trip to Reno.

Braun said that during a trip to Reno in the early ‘70’s he found the best game in town at the Nevada Club. The casino was fairly small, with low-limit games that couldn’t compare to Harrah’s next door, so they offered a very good game with slightly better rules than their neighbor. And, Braun played nearly every day for two weeks. There’s your first hint.

The second hint is that the Nevada Club was owned by Lincoln Fitzgerald, a former Detroit casino operator (yes, they were illegal, but connected to the right people) of the 1940’s who was as obstinate and stingy as ever a casino owner could be. In fact, he refused to share his Reno profits with his old “friends” back home and they sent him a message in the form of a blast from a shotgun. He lived, but spent the rest of his life in a wheelchair.

As for Braun, he played his typical precise betting system and perfect basic strategy. His stakes? $1 to $10, with adherence to the numbers from the Hi-lo system. Eventually a Pit Boss stopped him as he walked in one day and said “The owner has observed you playing and he has decided that he doesn’t want your action anymore.” That’s the only barring I’ve ever heard of where the maximum wager was $10.

There’s a good lesson there, though. You have to fit in and have some casino comportment to get away with card counting, even if you are playing tiny stakes.

Braun the Author

Over the years, Braun gained popularity as a programmer, but not necessarily as a blackjack person. His own style wasn’t flashy. He certainly wasn’t Ken Uston with stories to fill books, but he was accurate and reliable. Eventually he convinced a publisher to cover his own work as a book.

Originally produced as a pamphlet for Lance Humble’s International Gaming, Inc. and entitled Braun on Blackjack, the work was expanded and published in 1980 as How To Play Winning Blackjack. In the introduction Braun admitted that his goal was to “correct, clarity, and the very least, to amplify my findings so as to clear up any misunderstandings….I shall attempt as logically as possible to trace for you my work over the past 18 years.”

Much of the book was edited and changed before publication, without input from Braun. What was never changed was his approach (or the exact numbers) for basic strategy or his counts. That’s a good thing. Unfortunately, Braun was disappointed with the overall content of the book and some of the advice provided by his publisher. Ah, welcome to publishing.

Unfortunately for Braun, although his book’s forward states his desire to clarify previous blackjack play decisions mentioned by others, sometimes in the same breath as his name, he also wanted the right to say he was more of a contributor to blackjack than just a computer programmer. And, he probably would have been happy to make some money from book sales, since his previous work was without pay.

As things worked out, Braun did increase his visibility, and the book sold well initially. It is still relevant, but the 170-pages are a bit dull. They read like a computer guy wrote much of it. There you have it.

Braun kept in touch with a few friends over the years, but as mentioned, he was a quiet guy. He was diagnosed with Parkinson’s disease in the early ‘90’s and that certainly slowed him down, but not completely. Unassuming till the end, he worked as a day trader from home for several years and never really retired. He passed away September 4, 2000.