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BOP (Blackjack Of Probability)Blackjack is the most popular game in casinos.All most player say dealer's 5 & 6 is bust card.But, Do you know�...

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Type Name Latest commit message Commit time Blackjack probability software to load latest commit information.

Jan 7, 2016 Apr 6, 2013 Apr 6, 2013 Dec 21, 2015 Jan 7, 2016 Blackjack odds calculator See --help for an overview of options.

When printing strategy tables, the columns blackjack probability software the dealer's first card and go 2-9,J,A.

I may fix this in the future, or at least give the user an option to sacrifice speed for correctness.

Red Stand Green Hit Yellow Split Cyan Double double your bet, hit exactly once then stand Purple Surrender lose half your bet Note that in some games, not all of these actions are allowed, and so won't show up in the final table.

Accuracy This program will undoubtably generate tables that differ from other strategy-tables you might find online.

Disclaimer Should you wish blackjack probability software use this program for something stupid such as trying to win any actual games of blackjack, please see LICENSE for a full legal disclaimer.

You signed in with another tab or blackjack probability software />You signed out in another tab or window.

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Hit or Stand is a Blackjack game that trains you. how to play Casino Blackjack with the highest. probability of success. Your score will be. determined by the�...

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Valid for casinos

The Odds of Winning a Blackjack Game The Odds of Winning a Blackjack Game The Odds of Winning a Blackjack Game Definition of the Casino House Edge https://artwinajans.com/blackjack/bellagio-blackjack-decks.html the Game of Blackjack The casino house edge is a theoretical number.It is calculated blackjack probability software taking all the bets made at the blackjack tables, multiplied by what percentage the casino blackjack probability software keep.

The calculations assume that player decisions will be statistically correct when playing blackjack.

Another theoretical number is the return percentage or pay out percentage.

This is how much the blackjack player's get to keep of their own bets.

Simply put, the return percentage is the percentage of the bet that would be returned to the players if every blackjack play decision were statistically correct.

In other words, a 95% payout rate means 100 minus 95, or a 5% house edge.

For the blackjack player, this means a loss of 5% of their blackjack bets.

You keep 95% of the money you walk into the casino with, and the casino keeps 5%.

The game of blackjack offers the best odds of winning for the players, but only if you are aware of the variables that affect the odds.

The variables are cumulative.

You also need to take into consideration a number of criteria when evaluating a casino, the most important of which is that the gaming house uses accredited software guaranteeing randomness rather than tampering with the odds, if you can't physically watch the blackjack dealer shuffle the cards.

Blackjack Strategies and Their Affect on the Casino House Edge Blackjack players who use Basic Strategy can affect the blackjack odds to the point where they are playing almost even with the casino.

It's possible to find a blackjack game with a house edge of 0.

If you don't use a specific strategy and just play on impulse, your house edge will be in the range of 2-5% in favor of the casino.

If you play Basic Strategy, the house edge is approximately 0.

That blackjack probability software one half of one percent.

The term Blackjack Conditions or House Rules refer to the specific rules in effect at a blackjack table.

One casino might have several different sets of blackjack rules, depending on the blackjack table you play at.

There is a wide variety of blackjack rules, and these rules absolutely affect your Odds of Winning a game of blackjack.

Some casinos have more player friendly rules than others.

If you study the blackjack rules that different casinos offer, often the more out of the way casinos will offer better odds to the player.

For example in Las Vegas, the casinos that are https://artwinajans.com/blackjack/odds-of-winning-money-at-blackjack.html accessible to tourists are not as generous in their rules as the casinos at the edge of town where most of the locals play blackjack.

In the blackjack strategy chart below, odds with a plus are in your favor, odds with a minus favor the casino.

The following odds are based on blackjack conditions using 8 decks of cards, double down allowed on the initial 2 cards dealt only, double down allowed on any total, double down after splitting allowed, and resplitting allowed up to a total of 4 hands.

Possible blackjack rules include: Blackjack Rule Description Effect on Odds Remember: Pluses increase YOUR odds of winning, minuses decrease them.

Double Exposure The cards are dealt face up, including the dealer's cards.

Suited blackjack means of the blackjack probability software suit.

You lose half of your bet.

You lose half of your bet.

Usually split Aces are allowed only one card.

Allowing blackjacks the full payout after splitting is a rare, but good rule.

RSA - Resplitting Aces Allowed The option to split Aces on a hand that has already split on gotten another pair of Aces.

You lose half of your bet.

You lose half of your bet.

This means you might double down or split, effectively betting more, and losing more.

Double After Split Allowed EXCEPT on Aces You can double down after splitting, except when you've split Aces.

H17 - Dealer Hits on Soft 17 Normally the dealer stands on 17.

But with this rule the dealer will hit on a Soft 17 A-6.

If the player and dealer both have 17, the player loses.

Player Loses 17-18 Ties Yes, this rule exists.

If the player and dealer both have 17 or 18, the player loses.

This is NOT considered to be a good blackjack strategy.

If the player and dealer both have 17, 18 or 19, the player loses.

This is NOT considered to be a good blackjack strategy.

This happens only blackjack probability software the dealer checks for blackjack.

Your odds are better to actually play out your hand, so this rule is in the casino's favor.

If the player and dealer both have 17, 18, 19 or 20, the player loses.

Player Loses 17-21 Ties Yes, this with partycasino/win 1000 theme exists.

If the player and dealer both have 17, 18, 19, 20 or 21, the player loses.

This is NOT considered to be a good blackjack strategy.

Double Down Rescue The option to surrender after doubling down.

Redoubling Allowed The player may redouble his bet.

Double Down on Initial 2 Cards Only This is the standard double down rule.

Double Down on 2-3 Cards Only The option to double down even after taking one hit.

Some tables allow doubling on any number of cards, or 2 cards only, or 2-3 cards.

Develop your winning strategy and test it using this customizable blackjack simulation software.

Peek Ace The dealer checks for blackjack if they have an Ace showing.

Peek Ace or Ten The dealer checks for blackjack if they have an Ace or a Ten showing.

Insurance Insurance is a side bet made when the dealer has an Ace showing, usually totaling half of your regular bet, where you are betting that the dealer has a blackjack.

See Insurance Table Below As you can see, a blackjack game that pays 2:1 on a regular blackjack will increase your odds of winning by 2.

This demonstrates how important small rule variations become on your overall odds of winning.

House Edge on Insurance The first rule is never buy insurance even if you have a blackjack.

The ONLY exception is when you are card counting.

Card counters can make insurance bets when the deck is rich in tens but if you do not count cards, don't buy insurance.

The house edge for insurance favors the casino, and it is cumulative.

The following chart shows the house edge on the insurance bet depending on the number of decks used, and this is in addition to the standard house edge, so you would subtract this from your odds percentage.

The advantage can shift from player to house depending on which cards check this out been played and the skill in which you play your cards.

The more decks, the better the odds for the casino.

The following chart shows the house edge depending on the number of decks used, and this is in addition to the standard house edge, so you would subtract this from your odds percentage.

This is actually to the player's advantage unless you are counting cards.

The house makes up for the lost advantage blackjack probability software the fact that the dealer can deal about 20% more hands per hour.

This means that the house's advantage is increased by sheer volume of hands dealt.

For the player, this means that your losses will be greater.

If you are playing 20% more hands per hour, your losses will increase accordingly.

Remember that you are unlikely to see millions of rounds of blackjack 21 basic strategy />A Harvard Mathematician concluded that it takes 7 shuffles to randomize a single deck of cards.

Multiply that by 8 decks and you can be sure that 8 decks will not be shuffled until they are totally randomized.

This changes the dealer break ratio, bringing it to a much lower percentage than computer simulations calculate.

The difference between seat 6 and 7 is about.

You will lose blackjack probability software />The difference between seat 1 and 2 however, is.

Counting cards will increase your odds of winning.

However, casinos routinely ban card counters, even though it is not illegal.

There are three parts to blackjack money management:. Our risk of ruin (the odds of losing our entire blackjack bankroll) would give most card counters (not�...

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I am looking for software that bets using perfect blackjack frequencies. For example, with a spread of $5-$50 on a single deck game, betting�...

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This software can be used to prove that by playing Blackjack, it is possible to beat the dealer on the long term under certain conditions.

As far as I know, Blackjack blackjack probability software the only game offered by casinos, where this has been mathematically proven.

This software was written in in 1992 during my studies of physics for a seminar about probability calculations.

Download the sources from.

These executables have a very simple UNIX-like command line user interface.

Disclaimer This software may be used to understand and to learn the strategies of how to beat the dealer.

This program is blackjack probability software in the hope that it will be useful, but WITHOUT ANY Blackjack probability software without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.

See the for more details.

This software should work on every computer younger than myself.

The only tools you require are a C compiler.

The probability calculator has no dependencies, not even to the standard C library.

Minor modifications to the Makefile may be necessary.

If you are able to compile a simple Hello World program, you are able to compile this software on your computer.

I will not answer any questions about how to build it on your architecture.

Bugs This program has been released to public in 1998.

Since then it has been downloaded a few times daily.

Nobody ever reported a bug, except for the unser interface.

I therefore assume that the mathematical engine of the program is bug free.

Guarantee I will pay 100 US Dollars to the first person showing a bug in the mathematical engine of this software, namely probability.

This offer is voluntary and no legal claims can be derived from this guarantee, therefore no law is applicable.

The alternative solution must show a considerabely higher total gain than this Blackjack simulator after at least 10 million simulated games with exactely the same content in the shoe.

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So then, I decided to get a little more complex, and set up a test in Python that would simulate a game of blackjack. Now, I didn't program both a dealer and�...

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Find out the winning blackjack odds and blackjack probabilities of losing and look for ways to change them!

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Blackjack odds calculator.. is home to over 40 million developers working together to host and review code, manage projects, and build software together.

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However; the Blackjack software programs that online casinos use include all of the cards in every new round of play. The analysis will apply to�...

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Calculate your odds of winning a blackjack game. Odds chart, definitions and explanations. Blackjack download let's you fine tune your strategies and test your�...

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Basic strategy was created by blackjack probability software a computer simulation of millions of blackjack hands.

One of the first blackjack simulations was done by Julian Braun of IBM.

Basically, these computer simulations showed the mathematical probability of improving the blackjack hand or beating the dealer, by a certain playing strategy.

In other words, telling the blackjack player what action he or she should take hit, split, double-down, etc.

The important thing to remember is that nearly all basic strategy rules are indisputable in the long run, the finite nature of mathematical science dictates that a particular playing decision, based on the player's cards and the dealer's exposed card, will yield a predictable outcome after millions of hands of play.

It is imperative as a blackjack player to learn this basic strategy, because by using it, you will eliminate the normal 5 or so percent advantage the casino has over the unskilled player.

With basic strategy the house advantage is only about 0.

That is less than a 1 percent disadvantage to the player.

This is why blackjack can be one of the most profitable games to play in a casino.

Basic strategy varies according to the type of playing conditions that you are exposed to.

Namely, how many decks that are in the shoe you are playing.

Below I have listed the basic strategy rules for single deck blackjack probability software and for multiple deck shoes.

Another fact that I must stress is to play exactly the way listed below.

Do NOT alter your play see more on some hunch that you have, or by a perceived idea that you always lose when you split eights for example.

You may think that you lose more often than you win in certain basic strategy situations, but this is NOT the case over the long run.

The only time you should vary from basic strategy is under certain circumstances where you are counting cards.

I will explain this in more detail under the card counting section of this web site.

But always remember, even the most skilled card counter will still use basic strategy for the vast majority of continue reading or her playing decisions.

So I urge you to study the rules below and practice them until they do not require any thought on your part.

There are many inexpensive blackjack games which you can buy for your PC, and several shareware ones which you can easily obtain off of the internet.

The best commercial version that I have found is called "Play to Win" by Wizard Works, and it is available now in any major computer software supply store.

This game also has a coaching option where it will tell you what como ganar en electronico to make based on basic strategy.

In fact, if you attempt to make a wrong decision a dialog box will pop up and suggest to you the proper playing decision to make.

You can also play online for free here on Blackjack Center via the link found above.

Since it opens a new window you can ALT-TAB back to Blackjack Center whenever you want to review the blackjack probability software strategy rules listed below.

Regardless on what you use to practice, whether it be a computer blackjack game or simply a deck of cards, you MUST learn basic strategy to have any hope of being a consistent winner at the blackjack tables.

The charts below should be self explanatory.

On the blackjack probability software hand column is the total of the cards you have in your hand and the proper playing strategy based link the dealers up card.

SINGLE DECK - BASIC STRATEGY Your Hand vs Dealer's Upcard 8 Double on 5 to 6.

A,2 to A,5 Double on 4 to 6.

A,6 Double on 2 to 6.

A,7 Double on 3 to 6.

Stand on 2,7,8 or A.

Hit on 9 or 10.

A,8 Double on 6.

Stand on 7,10 or A.

The above chart assumes the casino doesn't allow doubling down after pair splitting.

If the casino allows doubling down after pair splitting then blackjack probability software the following pair splitting rules.

Your Hand vs Dealer's Upcard 2,2 Split on 2 to 7.

FOUR, SIX, EIGHT DECK - BASIC STRATEGY Your Hand vs Dealer's Upcard 5 to 8 Always Hit.

Hit on 10, A.

A,2 Double on 5,6.

A,3 Double on 5,6.

A,4 Double on 4 to 6.

A,5 Understand winning money in blackjack rather on 4 to 6.

A,6 Double on 3 to 6.

A,7 Double on 3 to 6.

Stand on 2,7 or 8.

Hit on 9,10 or A.

A,8 to A,10 Always stand.

Treat as 10 above.

Stand on 7,10, or A.

The above multiple deck basic strategy is valid if the players are allowed to double down after pair splitting.

If doubling down is not allowed after pair splitting, then use the following pair splitting rules.

Your Hand vs Dealer's Upcard 2,2 Split on 4 to 7.

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So I wrote a minimal program that simulates gameplay with card counting.. the number of unused aces if it can be split, and if it is a blackjack.

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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.

The 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, 20, 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 16 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 the 13 cards of one suit in a blackjack deck!

He did it without 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 only 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 blackjack probability software />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 blackjack probability software 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 situation 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 verification 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 the 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 blackjack probability software 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 see more 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 of 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 https://artwinajans.com/blackjack/potawatomi-blackjack-table-limits.html 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.

go here 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 the BjDeck1-11.

TXT source files of incomplete decks of cards.

The output files are also available absolutely freely as downloads: learn more here />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 the bottom of BjAllHands1Combos.

TXT, you see that the bust percentage is 33.

Keep this new figure in when hit 16 on to blackjack 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 blackjack probability software 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 order for multiple decks.

John Scarne tried to figure out the Dealer's bust odds https://artwinajans.com/blackjack/winning-money-in-blackjack.html 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 blackjack probability software 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 blackjack probability software 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 Moliere.

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 1 hit or stand blackjack, Dealer 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: 26 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 from 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 that 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 free 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 phrase blackjack and tilt side bar have 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 https://artwinajans.com/blackjack/blackjack-hit-or-stand-on-16.html 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 now that I don't get intimidated.

Yet, they keep reacting every time I publish something of great importance.

No doubt, my new research in calculating the blackjack odds of busting is ground-breaking.

The new figures will surely have an impact on the game of blackjack.

They even make me a criminal by association!

They compare me to the inmates who become their own lawyers!!