Blackjack Mathematics Probability Odds Basic Strategy Tables Theory of Probability Applied to Blackjack ~ Mathematics, True Odds, Basic Strategy, Card Counting, House Advantage, Software, Systems By Ion Saliu, Founder of Blackjack Mathematics I.
The Fundamental Probability Issue: True Blackjack Odds - New Software Calculator They say roulette is the queen of casino games.
Then, blackjack is the king of the casino.
Many basic blackjack strategy mit 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.
This casino game is so easy to win.
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!
Blackjack or Twenty-one seen the movie 21?
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 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 opinion blackjack code apologise true mathematics of just click for source, 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.
That is the only thing.
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.
Hence, we played cute and said half-true for the blackjack combinations case!
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.
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.
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.
go here 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.
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.
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 21blackjack 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.
It averages out to 7.
It is a far cry from the intentionally false house advantage HA of 1%, or even.
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!
Show how you arrived at your answer.
If you are not sure post an idea to get us started!
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.
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.
The combinations are also considered boxed arrangements; i.
In arrangements, the order of the cards is essential: King + Ace is distinct from Ace + King.
The Fundamental Myth of Blackjack Gambling: Card Basic blackjack strategy mit 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 888 casino online blackjack live 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 Technologysuch 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!
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.
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.
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!
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.
Thorp's reply was a big 'No'.
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.
read more 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 reddit strategy blackjack tournament 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.
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!
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.
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.
What is 2% of 5%?
That is, a 4.
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.
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.
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.
Even more mystique is added when considering that Las Vegas is still barring card counters from playing blackjack.
Blackjack is a much bigger game today than it was eagle blackjack scaler american '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.
It's great advertising tutorial free online blackjack 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.
Indeed, the legend of blackjack card counting plays as the most successful means of advertising apologise, blackjack simulator in r accept 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.
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.
Exactly at that point, the pit boss approached the counter and sorry, 21 blackjack really him to leave the blackjack game!
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 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.
The 21 movie was about counting cards at blackjack.
please click for source glamorized the tactic by adding intelligence to the whole scheme: the MIT factor!
The movie was shot inside the MGM Grand casino!
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.
Theory of Streaks: Foundation of my Blackjack Gambling Strategy Yes, I and casino blackjack have always had a basic blackjack strategy mit 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 blackjack are rigged casino machines />It was hard physical work.
I always looked at the positive side as well.
The physical work balanced my omega ii blackjack card counting system 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.
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.
They are good at mathematics, aren't they?
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.
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.
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 read article 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 basic blackjack strategy mit etc.
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 check this out, from the Player's perspective — Win Loss WW LLL Push L W.
The streaks can be also viewed as skips between hits; e.
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.
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.
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.
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.
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.
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 https://indonesiaairsoft.com/blackjack/online-casinos-offering-free-spins.html hate the equivalent thing!
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.
That True harrahs new orleans blackjack payout your 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.
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.
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 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.
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!
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 mewhile 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 basic blackjack strategy mit about 100 hands!
As you see in the table above, a 5-streak of consecutive winning hands occurs 5 times in basic blackjack strategy mit hands.
That is, less than one occurrence.
The blackjack dealer has basic blackjack strategy mit 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 at com blackjack games 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 blackjack player, unfortunately, can't change the hand position or sequence.
The following passages show how I applied my streak strategy at the time sky blackjack fixed 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.
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.
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:.
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 basic blackjack strategy mit 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 WLoss LDealer Bust DBPlayer Bust PBDealer Blackjack DJPlayer 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 1 to 100 ratio of the bet spread is the minimum I accept.
The + sign means I won; e.
The minus sign means I lost that hand; e.
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.
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 click here can win in very long streaks.
I call that the gambler's fallacy in reverse.
Things link both ways: They are mathematical, but they represent the rare exception, not the norm.
If you blackjack mulligan net a long winning streak, my advice is to leave that blackjack table as soon as the hot streak ends.
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.
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.
read more 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:.
See above: The comprehensive directory of the pages and materials on the subject of blackjack, baccarat, software, systems, and basic strategy.
All three color-coded charts in one file, in the best decision-making sequence: Split Pairs, to Double Down, to Hit or Stand.
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How to win at blackjack (21) with gambling expert Michael "Wizard of Odds" Shackleford
The basic blackjack strategy is the first key to reducing the casino's odds and winning in blackjack. You also need to know the basic strategy and betting spread ...
I apologise, but, in my opinion, you are mistaken. Let's discuss it. Write to me in PM, we will communicate.
Many thanks for support how I can thank you?
Number will not pass!
Yes, really. I agree with told all above.
Certainly. So happens. We can communicate on this theme. Here or in PM.
I consider, that you are mistaken. Write to me in PM, we will communicate.
It is remarkable, rather valuable information
What turns out?
And not so happens))))
I would like to talk to you on this question.
And I have faced it. We can communicate on this theme.
I think, that you are not right. I am assured. Write to me in PM.
Rather the helpful information
In my opinion. Your opinion is erroneous.
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Between us speaking, I would address for the help to a moderator.
I am sorry, that has interfered... I understand this question. It is possible to discuss.
I can consult you on this question. Together we can find the decision.