💰 Blackjack Odds and Probability – Explanation and Calculations

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He s always preaching to me that blackjack players "don t want to know how the. Because the dealer s chance of busting is higher when she shows a small ...


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Blackjack – Dealer probabilities
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The Odds of the Dealer Busting in Blackjack
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I'm writing a java project for the university where am I exploring blackjack from the math point of view.
Right now I've stumbled upon the probability of dealer busting depending on the up card for 8 decks in a shoe.
So I got those results through the millions of this web page each time deck is different, full probability of busting in blackjack reshuffled.
As you can see, the odds that I've acquired with my application and the correct ones from the website are quite similar from TWO to NINE.
But there's something wrong about TEN and ACE.
The difference is just too much to be ignored.
So can somebody please explain to me what am I missing?
Below I've attached necessary source codes for this issue I've excluded a lot of other methods from classes that are not related.
Would appreciate any help so much.
Thank you in advance for reading this.
With 8 packs, there are 32 10s and Aces; If the first card is a 10 or Ace, there should be 31 left fewer than the undrawn valuesbut isBusted starts with all 32.
I was thinking about this too.
But when I've tried to draw the card from the deck and calculate it accordingly, the odds got even worse.
click I decided to not include this until I come up with the solution for Aces and Tens.
more info most tables the dealer also hits on a "soft" 17, i.
Because you always stop on every 17, you will have lower odds of busting.
So may not be the only issue.
Thank you very much for your answer.
You're totally right, but, unfortunately, that's not the case, because this is for "Dealer Stands On Soft 17" case only.
There are two tables probability of busting in blackjack the and I've chosen the correct one.
Seems that everything is correct.
I was just looking at the weird table with odds.
Not sure anymore what isbut comparing to the it looks pretty fine.
Thanks to everyone who tried to help me.
Thanks for contributing an answer to Stack Overflow!
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It's very important to know the probability of your hand busting when you are holding any total in the game of blackjack. The following odds chart shows the ...


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Blackjack Statistics: Play Your Hands Properly | 888 casino NJ
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Blackjack odds – Blackjack Life
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The odds involved in blackjack are whether a player will bust or win his bet.
You need to first understand, what hands favor a dealer or the house, a phenomenon probability of busting in blackjack as house edge.
This amount is calculated by multiplying the total bets by the amount the casino keeps.
Another reason why the advantage lies with the casino is because the player probability of busting in blackjack first and if he busts, he loses visit web page the dealer continues to play.
Standing on 17 or higher and hitting on 16 and less gives a chance for both player and dealer to bust at an even rate.
This reduces the house edge from a 8% to even 6%.
However using basic blackjack strategy reduces the house edge to 0.
A player should always look for games that have better odds for him and be aware of the variables that affect the odds of blackjack.
For example, if a player is dealt with a total of 16, the probability of busting is 0.
Knowing when to stand or hit is also vital for blackjack.
According to probability of busting in blackjack table above, a player has a higher chance of busting if he hits on any number higher than 12.
Standing on 17 is always wiser for the player while hitting on any number less than 12 also reduces the chance of busting.
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Jump to Odds and Probabilities - Blackjack Odds and Probability. Players' Hand, Chances to bust on a hit. 11 or less, 0%. 12, 31%. 13, 38%. 14, 46%.


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Blackjack odds – Blackjack Life
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probability of busting in blackjack

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Consulting a blackjack odd chart can show the probability of busting a hand based on the current hand value of the player. Basic blackjack rule will tell that a ...


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Blackjack Odds Charts - Black Jack Probability Winning Odds
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Blackjack Strategy: The 3 most misplayed hands in Blackjack

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Here Are Blackjack Dealer Bust Probabilities. February 16, 2018 by Marc Meltzer. The dealer has a 2 of hearts showing. The person at third base says “you.


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The Maths Behind Blackjack

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Blackjack probabilities for the dealers final score. If the Blackjack dealers first card is low, say 2 through 6, his probability for busting is high. In these situations ...


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Blackjack Dealer Bust Software to Calculate Odds Probability
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Universal Strategy for Blackjack
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Blackjack Dealer Bust Software to Calculate Odds Probability Blackjack Dealer Bust: New Software to Calculate Odds, House Edge ~ The Only True Bible of Blackjack Mathematics and Probability By Ion Saliu, Founder of True Mathematics of Blackjack Verse One: Two: Three: Four: Harrahs blackjack rules atlantic Six: Seven: I.
History or How the Blackjack Odds Were Calculated — John Scarne First capture by the WayBack Machine web.
It is well documented on this site.
Matter of fact, I consider myself the best blackjack player ever.
As Muhammad Ali, the greatest of them all, 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.
You might be shocked, but the mathematical truth is that your knowledge of blackjack probabilities or odds is wrong.
Everything you had known was based on guesswork, albeit it educated guesswork.
link software generates every possible blackjack hand based on the BJ Dealer's rule: Draw to 16, Stand on 17.
The algorithms do not skip any configuration, such as four consecutive Aces.
As rare as such a configuration might be, it must be taken into consideration as it is an element of the total number of possibilities.
The probability is founded on number of favorable cases and number of total possible cases.
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!
Two-card counts of 17, 18, 19, this web page, and 21 will show up 462 times of 1,326.
The Black Jack rules demand that the dealer must stay on all those hands, so he cannot bust on any of them.
Two-card counts of 12, 13, 14, 15, and 16 will be held by the dealer 514 times out of 1,326.
Since the rules demand that the dealer must draw to a count of read more or less, he will bust.
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 never explained how he came up with that 169, kind of a new number of the beast!
But that relation has absolutely no mathematical rationale in Scarne's calculations… except for continue reading 13 cards of one suit in a blackjack deck!
He did it comps blackjack the help of computers — and he came pretty close to what good computer programming achieves.
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!
True Mathematics, Combinatorics, Probability Applied to Blackjack 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.
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 put it aside and forgot about it, as other projects felt more compelling to me.
I found the project and also the code to generate sets from a list.
In this case, the list is 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.
Let's make this analogy to lotto combinations.
Generating lotto combinations in lexicographic order is far easier than generating blackjack hands.
The lotto combinations have a fixed length.
There are 13983816 total possible elements for this type of lotto game.
Incidentally, I released my lotto software in 1988.
At that time, I was the visit web page one who knew how to generate lotto combinations in lexicographical order.
A few others were able to generate lotto combinations only in random manner.
It took other programmers several years before they discovered the trick of lexicographical lotto generation.
History always keeps accurate and unbiased records!
The lotto combination generation in lexicographical order is very simple today.
The lotto generation in lexicographical order as arrangements is also very simple.
Blackjack lexicographic hands can be only generated from a list, such as a deck of cards.
Lotto combinations can be generated from a list as well.
The list, however, must be ordered lexicographically; e.
Blackjack hand generating face a tremendous obstacle of its own.
The number of elements per combination or per arrangement varies widely: From two cards to 10 or 11 cards per hand.
That was the challenge that kept gambling programmers paralyzed up until now.
It is so much easier to say simulation!
That is, generate blackjack hands randomly!
Random-generating or so-called simulation does not satisfy the condition of accuracy.
The undeniable Ion Saliu's Paradox proves that only around 63% of all possible sets will be generated.
In roulette, it is around 65%.
In 38 American roulette spins, only 24-25 numbers will be unique.
The year of grace 2009 has proven to be augural to me.
I was able to successfully finalize the software to generate all possible blackjack hands in lexicographical order.
It is not easy and it wasn't easy, ever.
I went through various methods and algorithms.
Verification is the hardest part, as there are NO mathematical formulas regarding blackjack combinatorics and probabilities.
I played blackjack in Detroit in the year of grace 2009.
I visited with my daughter after many painful years of separation.
She is an adult now, although they always check her ID before entering a casino.
The first time, in June 2009, I and she too were shocked how easy it is to lose playing those CSM blackjack tables.
CSM stands for continuous shuffling machines.
I make the same statement I made about the blackjack slot machines.
They are deceptive devices: The devices are programmed to beat the player far worse than the cheat blackjack red dead redemption of games with normal blackjack shoes.
I stand by my statement even if corrupt judges might be attracted by the smell of my blood I always wear nice deodorants!
I visited my daughter and Detroit again in August.
We only checked the so-called high-limit gambling room.
The maximum-to-minimum ratio of the table limits was worse than on the casino floor.
We also did an experiment playing slot blackjack.
I left the area after a couple of hours by winning just one dollar!
Nobody is supposed to win the blackjack slots!
Nobody can beat the devilishly programmed chips!
My strongest impression was related to betrayal of the basic strategy BS it is!
My daughter almost always advised me to stand on 15 or 16 even 14 against Dealer's high cards.
That made the difference against the masked bandit inside the programmed chip.
Breakthrough Software to Generate All Blackjack Hands and Calculate the Odds Accurately As I said, the hardest part of my blackjack software development was the probability of busting in blackjack phase.
I generated blackjack hands as combinations or 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 started by creating one deck of cards.
That is, write a simple text file with 52 lines, consisting of one card number per line, from the four 2's to go here four Aces written as 11.
The file name is and is absolutely free to download.
From that pivotal layout file deck of cardsI deleted 4 of the 10's to get the deck used in the Double Attack Blackjack game.
The new text file has only 48 entries 12 Ten-value cards, instead of 16.
The file name is and is absolutely free to download.
The output files for the arrangements generation are gigantic!
Thus I needed to create smaller deck files.
The reduced deck files helped me tremendously with the verification process.
One deck, had only one suit of the 13 cards one 2, one 3, …, to 4 Tens, one Ace.
The fourth deck, had only one suit of the 13 cards one 2, one 3, …, to 4 Tensexcept for Aces.
All four suites of the Ace are in that layout file 16 entries in the file.
I created two more deck layout files also completely free to download.
One file was the result read article shuffling randomizing the regular 52-line BjDeck1.
The other file was the result of reversing the order in the deck.
The composition is from the four Aces to the four deuces:.
These two BJ deck files prove that the arrangements method of generating hands is the most precise.
All three layout files generate the same amount of hands and the same bust percentage: BjDeck1, BjDeck1Shuf, BjDeck1Rev.
By contrast, the combinations method of generating hands leads to three different result files.
It generates all possible blackjack hands as arrangements.
That is, the order of the cards is of the essence.
Total number of qualified completed BJ hands is staggering for all one-deck regular files: 334,490,044.
As of the Double Attack Blackjack game: 302,394,480 total possible completed hands.
I only calculated the hands, but did not generate them.
I simply commented out the statements for printing to an output file.
I did generate, however, the arrangements for probability of busting in blackjack BjDeck1-11.
TXT source files of incomplete decks of cards.
The output files are also available absolutely freely as downloads: and.
Those two output files for incomplete decks played a role of biblical importance, as it were.
They helped me discover the most subtle errors of generating blackjack hands of variable size length.
Generating hard-count hands was as easy as a breeze.
The big problem came from the Aces, as they are counted either 1 or 11.
Blackjack hands such as 2+A+2+A must be hit by the Dealer; hands such as 2+A+3+A are mandatory stand.
I perfected my blackjack probability software due in great part to those two output files.
One can easily check the error-free files in MDIEditor And Lotto WEor potent free editor.
I have checked several times: Each and every hand is absolutely correct and no hand is missing.
Of course, we follow the rules for the blackjack casino Dealer.
Yes, some casinos rule now that hit soft 17 e.
A+6 is mandatory for the Dealer.
First off, that's a bad rule for the blackjack player; avoid such tables at all costs.
Secondly, my software can be easily adapted to accommodate the hit soft 17 rule.
It generates all possible blackjack hands as combinations.
That is, the order of the cards is not important.
Hands such as 2+A+2+A or A+A+2+2 are always written as 2+2+A+A.
Total number of qualified completed BJ hands is far-cry lower for all one-deck regular files: 297,615 for 52 cards.
As of the Double Attack Blackjack game: 257,877 total possible completed hands.
I calculated the hands and also generated them.
If you click on a text file, it opens directly in your browser; if you right-click, you can choose to download Save as to your computer.
History in the Making — Shocking but True New Odds of Blackjack Dealer Bust NO LONGER APPLICABLE AD LITERAM!
You, Player, try to avoid busting!
Let them Dealers bust more than you, especially when FEW or NO Players before you and Dealer busted!
Mathematical tip: If a majority of Players before you busted, expect a lower bust DC degree of certainty for Dealer — You gotta play more aggressively!
If you go all the way down to can pch blackjack tournament something bottom of BjAllHands1Combos.
TXT, you see that the bust percentage is 33.
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 hands.
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!
Programming BJ software for more decks is severely limited by today's computers I have access to.
For one, the size limit of an object e.
The speed of today's computers will also make virtually impossible to generate all possible blackjack hands in lexicographic probability of busting in blackjack for multiple decks.
John Scarne tried to figure out the Dealer's bust odds by just using 13 blackjack cards from 2 to Ace — one suit only!
Using various partial decks, I noticed that the bust odds grow with an increase in the number of cards, therefore the bust odds grow with an increase in the number of decks of cards.
That is valid for both Dealer and Player.
It also means that the house edge also increases better for the casinos, worse for the gamblers.
Just about everything I write about generates strong reaction.
I do not talk about the positives regarding my ideas — they are clearly in the majority.
I am referring here only to the negative reactions.
There is honest criticism, especially rooted in less knowledge on the subject.
There are also objections in the manner of common sense.
There are probability purists who will fight the blackjack figures my new blackjack software reveals.
They will argue against a number of blackjack hands generated by the BJ odds programs: 2 2 2 2 3 3 3 or 3 3 3 2 2 2 2 or 2 2 2 2 3 3 11 11 11, or 2 2 2 2 3 11 11 11 11 3, etc.
Such hands will never come out, they scream!
But, hey, who decides what hands come out and what hands will never come out?
Is there a god of blackjack who makes such decisions?
The purist argument resembles the older heated debate regarding the.
Indeed, lotto combination 1 2 3 4 5 6 does come out so rarely that it has not been drawn in our lifetime!
The standard deviation plays a hostility-causing crucial role.
The same should be true about another random phenomenon as the game of blackjack.
There are some issues here that we must address.
Calculating the standard deviation for lotto is as easy as it can be just use my SUMS standard deviation software.
It is extremely hard to calculate standard deviation for blackjack output files.
Think of those huge 10 GB files!
We must have a 64-bit operating system and 64-bit compilers to create adequate software to handle that size.
Here is the most important issue.
We know exactly how to calculate the probability of any lotto combination.
There is no other way in mathematics - only mathematics counts here!
The most vociferous reaction against my ideas comes from a minority who deeply hates me, no matter what I do and what I say.
Most of them are jealous and resentful authors of gambling systems.
There are also casino representatives executives, agents, or moles as I also call them.
The casinos have a vested interest in aggressively.
There is deception and conspiracy to commit deception as regards the game of blackjack.
They've heard continuously players complaining that they lose too much and too fast at blackjack.
Some players believe the BJ dealers cheat sleight of hand.
I remember, a few years ago, a player shot dead a floor manager in Atlantic City.
The player claimed, under arrest, that he committed the crime because he was cheated!
My opinion is mathematical-based.
The blackjack HA is higher than that unreal 0.
Has anyone seen a situation like this in 100 bets?
Actually, I was generous and set HA to 2%, as you won't have 50.
As per my example above, I challenged self-proclaimed blackjack players to a challenge.
Let's see if they can resist 1000 hands playing strict basic strategy!
Their only response to my challenge was in the form of cursing me!
My blackjack challenge to prove the house edge is detailed further on Facebook by applying the test of the binomial distribution and the normal probability rule: by.
Possible Bust Situations; Comparative Analysis of New Bust Probability Versus Old 28% Bust Odds Axiomatic ones, "The style is the man," said that witty writer Molière.
I do have my own style.
Sometimes it brings out the worst in the creatures of smallness!
This very topic attracted a lot of virulent reactions from half-dozen or so lowlifes should I "forgive" them?
Basically, they started a war against my new figures for the Dealer bust at blackjack!
As coolheadedly as only me can be kidding!
We'll analyze the easiest case here, although it is NOT common by any stretch.
Expect the situation to be worse for Players in the most common casino situations: multiple decks and several players at the same table.
There are 2 two elements: Dealer and Player.
There are 2 two bust situations: well, Bust and No-bust.
That's the way I explained in a gambling forum, as my way to "lighten up" virulent lowlifes… innocuous fun!
We count blackjack hands only, not bets.
In 3 and 4 we must make adjustments, as the Player can bust less if applying basic strategy.
In situation probability of busting in blackjackDealer and Player have an equal opportunity to win, lose, or tie.
Let's divide the 44 out of 100 hands equally: 22 favorable to Dealer, 22 in favor of Player.
We notice now only 92 hands out of 100.
The 8 missing hands are those 8 cases when the Dealer does NOT even play her hands out — the simultaneous bust cases!
We count blackjack hands only, not bets.
In 3 and 4 we must make adjustments, as the Player can bust less if applying basic strategy.
In situation 1Dealer and Player have an equal opportunity to win, lose, or tie.
Let's divide the 52 out of 100 hands equally: go here favorable to Dealer, 26 in favor of Player.
We notice now only 92 hands out of 100.
Now, this is a mystery!
The 8 missing blackjack hands are NOT covered by those 4 cases when the Dealer does NOT even play her hands out — the simultaneous bust cases!
The most disturbing fact in Bhowever, is the equality of number of hands won by Dealer and Player!
That can never — ever — be true!
Blackjack is far, far just click for source being a 50—50 game!
Remember, I am talking here only about number of hands, not bets!
The Player gets a 2% advantage if the BJ natural is paid 3 to 2.
That is an affront to the intellect and sanity.
It is also crass casino deception — they know probability of busting in blackjack 9 out of 10 blackjack players lose their bankrolls quickly.
IF the game was truly 50—50, then an equal number of blackjack players will win an amount of money double to their bankrolls.
Again, that never — ever — happens.
The casinos know that reality very, very well.
Casino reports show intakes of 20% — 25% for the blackjack games.
The casinos justify there are many idiotic blackjack players.
Yet, the truth is the vast majority of the players know basic strategy.
In fact, even the casino dealers offer classic blackjack rules advice to less knowledgeable players.
Something like: "The book says to take that action in your situation.
The 28% bust odds figure leads to the misconception that blackjack is, in the worst-case scenario for Player, a 50—50 game.
Blackjack is NOT better than coin-tossing.
Conclusions Regarding the Greatest Breakthrough in Blackjack History — New Strategy I got my conclusions, of course.
And I do have a new blackjack strategy.
For starters, figure out the BJ Dealer bust probabilities this way.
Getting a second bust hand, with only one Player at the table, is 0.
The simultaneous bust is what creates the house advantage in the game of blackjack.
This is the new and most accurate figure representing the blackjack house edge or advantage.
How about three busted hands in the same round 2 Players, one Dealer?
Granted, the busted hands may not be exactly in consecutive fashion.
We will be in a probability situation known as the odds of M successes in N trials.
You can perform such calculations easily with my mathematical software SuperFormula.
But please be always mindful that the blackjack players get their bust hands before the Dealer; the busted players will lose their bets immediately, before the Dealer even plays her hand!
The more Players at the table, the lower the bust chance for the Dealer goes.
See how well placed the blackjack Dealer is?
I may not place myself as well as the BJ Dealer.
I can only place myself as well as the next position before the casino Dealer.
I don't know why they call it the third base.
How many players busted before me?
The more of them busted, the happier I would be!
It took me a while to reach this moment in my activity.
I am highly conscious of validity and validation.
There is no doubt in my mind now that this new blackjack theory of mine is valid.
I verified many times.
I finally decided that my theory was validated beyond reasonable doubt.
The registered members of my website have access to additional files that validate my algorithms and theory.
How about the software?
The offer was withdrawn for patenting reasons — the source code was outrageously cheap.
You can get the programme for free from the aforementioned Web page.
It shows every 2-card hand perfectly, plus 100% accurate statistics, such as PAT hands, STIFF hands, PAIRS, DOUBLE DOWNS, BJ NATURALS.
Don't mention it, axiomatic one!
I am one of the very best humans who ever was, despite rough edges… especially when I harangue down aggressors… VII.
Additional Resources in Blackjack See a comprehensive directory of the pages and materials on the subject of blackjack, baccarat, software, systems, and basic strategy.
The program calculates the number of streaks of losing exactly N consecutive blackjack hands from the Player's perspective.
We symbolize a Dealer's win by L and a player's win by W.
They should know by more info that I don't get intimidated.
Yet, they keep reacting every time I publish something of great importance.
No doubt, my https://chakefashion.com/blackjack/average-dealer-hand-in-blackjack.html 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 inmates who become their own lawyers!!

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Blackjack Odds and Probability – Explanation and Calculations
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Max cash out:
$ 200

But a number of blackjack odds and probabilities are important to. The probability of busting in this situation is 29/49, which amounts to ...


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Blackjack Dealer Bust Software to Calculate Odds Probability
Valid for casinos
Blackjack Dealer Bust Software to Calculate Odds Probability
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