Extra Rules Affecting Blackjack Odds European No-Hole-Card Rule. Some blackjack variations are played with a hole card that is dealt to the dealer only after all the players have played their hands. This rule affects player strategy when playing against dealer up 10 or an Ace. The Dealer’s Odds of Having a Blackjack The probability of a dealer hitting a blackjack when she’s holding an ace is nearly one in three. For instance, in a game with one deck, where the dealer stands on a soft 17 (not a common occurrence), the odds of hitting blackjack are 31.37%.

By Hon. Ion Saliu, Founder of Blackjack Justice

First capture by the WayBack Machine (web.archive.org) May 21, 2020.

Your Honor, I hereby accuse the Order of Casino Sycophants of damaging public deception. They make-believe that the glamorous game of blackjack has a frivolous house edge. Said game with its odds is so attractive to the masses that we can treat it equally to tossing a golden coin.
Our complaint shall prove that the real conditions of the game are far worse than the fake-news promoted, indeed imposed, by the Order of Casinos and their Sycophants.

Let me just say that benign ignorance has been at the heart of the matter. Nobody really knew what the real odds (probability) of blackjack were. Analysts lacked the fundamental elements required by the fundamental formula of probability: favorable cases (over) total possible cases.

Calculating the odds is the sine qua non condition of calculating the house advantage or the edge the casinos have in the game of blackjack. No casino offers a game where they don't have an edge or advantage. It's their bloodline — a legal requirement, as a matter of fact.

The first attempt at calculating the house advantage in blackjack is granted to John Scarne, a non-mathematical man who had the ambition of being the greatest gambling writer in history. Personally, I grant such honor to Blaise Pascal who analyzed a backgammon game. The historical event is known as de Méré Case and it founded a branch of mathematics hence known as theory of probability.

John Scarne rightly figured out that the casino gains an edge in blackjack because of the simultaneous bust — the dealer and the player bust at the same time. However, when the player busts, he/she loses the bet immediately as he/she always plays first. It is possible that the dealer can bust his/her hand (in the same round), but it is too late for the player; they already lost their bet.

John Scarne calculated the odds of dealer's bust to be 28%. If the player played by the same rules as the dealer, the simultaneous bust would be: 0.28 * 0.28 = 7.8%. But since the player is allowed to stand on 16 or less under certain circumstances, our 'mafia' man calculated that the final odds would be around 5.9%. That's the 'physical probability' of casino winning at blackjack.

The casino offers bonuses to the player, however. They pay 3 to 2 for a natural 21 (Ace+Ten in the first 2 hands of the player). They also allow double-down and splitting pairs. At the end of the day, the bj house advantage goes all the way down to that glamorous figure of 0.5%.

Right now, we focus our attention on the raw figure of 5.9%. Based on that figure (and so-called simulations), everybody agreed that the results of blackjack were:

• 48% winning hands for the dealer
• 44% winning hands for the player
• 8% hands end up as pushes (ties).
• 44/92 = 47.8% winning probability for the player

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 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). In 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 a decade ago. The generating process is significantly faster.

I wrote a special Web page dedicated to the topic of calculating precisely mathematically the bust-odds at blackjack following the Dealer's rules. There are lots of details, plus screenshots of the probability programs:

• Blackjack Dealer Bust: Software to Calculate Probability, Odds, House Edge, Advantage HA.

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 21), blackjack 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 16 and under, stand on all 17 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. That is, stand on 15 or greater (as arrangements):

Or, stand on 14 or greater (as arrangements):

• Now, the house edge goes between something like .3355 * .2248 = 8.3% and something like .3355 * .1978 = 6.6%. It averages out to 7.5%. It is a far cry from the intentionally false house advantage (HA) of .5%, or even .17% (promoted by several crooks)!
• 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.

Recalculating the raw figures for winning/losing hands, my theory shows:

• 50% winning hands for the dealer
• 41% winning hands for the player
• 9% hands end up as pushes (ties).
• 41/91 = 45% winning probability for the player

Axiomatic ones, who's right and who's wrong? If you have been a frequent visitor of my website, you already know how many hits I've been taken from casino executives, agents, moles, other gambling authors, system developers, vendors, gurus, bishops, saints, etc. Granted, the attacks against yours truly were far more intense earlier (beginning 1998 and ending early 2000's). They realized I wouldn't get intimidated, so they have given up, by and large.

In this year of grace 2019, I came up with a new idea: Let's set at the same table mathematics and reality. The first attacks aginst me went along the lines: 'Mathematics, specifically formulae, have no place in gambling — as it is totally random.' And I've always counterattacked: 'But what is not random, crooked idiots? The entire Universe is ruled by Almighty Randomness, as voided of consciousness as it might be!'

Standard deviation is the watchdog of randomness. Let's see what figures of blackjack odds are right by employing the binomial standard deviation. Then, compare the results to casino gambling reality.

It is time now to apply the most important bonuses the casinos grant to the blackjack players:

• natural 21 pays 3-to-2
• double down pays 2-to-1 (if successful)
• splitting pairs pays 2-to-1 (if successful).

We ignore the current tendency in the gambling industry to pay a natural bj 6-to-5.

The double down success is closely around 60%. The same success rate of 60% occurs in the pair splitting situations.

Next, it is very important to know the probability/odds of appearance for the 3 bonuses above.

• natural 21 occurs in 4.8% of cases, but only when dealing 2 cards to oneself at the beginning of a 52-card deck. We average the odds to 4% for multiple players (4 players and a bj dealer is an average situation in my book). Refresh your memory by reading this popular resource:
  • Calculate Blackjack Probability, Odds: Natural 21, Insurance, Double-Down Hands, Pairs.
• double down hands have an appearance rate of 8%, as first calculated by yours truly. Please read this very popular resource:
  • Calculate Probability of Double-Down Hands.
• splitting pairs hands have an appearance rate of 3%, as first calculated by yours truly. Please read this very popular resource:
  • Calculate Probability of Split Pair Hands.

Axiomatics, we run my probability software widely known as SuperFormula.exe, the function D: Standard Deviation. We run the function twice: First, for the traditional black jack parameters (5.9% odds, 48% winning probability for the player); secondly, for what I consider closer-to-reality blackjack parameters.

We take a common case of playing 100 hands. That is, the blackjack player must cash in the amount needed to play 100 hands at the minimum bet. For example, in the rare case of $10 minimum bet, the player must chip in at least $1000. I can't stress enough the stupidity of players who start with $100... they lose quickly... then leave the table... go to another table and cash in $100... etc. Vae victis! Poor victims!

WHOA! ON AVERAGE, THE PLAYER WINS 52 BET UNITS AFTER PLAYING 100 HANDS!!! That's a flagrant impossibility in 99.7% to all blackjack players, in all casino situations. You and I will never, ever, see a basic strategy player be ahead $52 after playing 100 hands, at $10 table minimum!

We come back to earth by going with my fundamental blackjack parameter: 45% winning odds for the player.

You, the player, do lose. Still, this is the happiest case calculated by my blackjack-odds software: One deck of cards. Today's PCs are still incapable (at least in the case of this programmer) to calculate for two or more decks of cards. But I experimented with calculable amounts of cards. The rule is very clear: The more cards, the worst the odds get for the player. In other words, the more decks, the worse conditions for the blackjack hopeful! And even worse with multiple players at the table (the common reality)!

Haven't you witnessed this in any casino, at any blackjack table? The overwhelmingly vast majority of players lose their bankroll quickly. They leave the venues almost on their knees. 'How the hell is this possible,' they ask themselves (sometimes loudly). 'Blackjack is supposed to be a 50-50 game... damn it!'

It ain't such a golden coin game, kokodrilo (royalty-name for big-time gambler)! I'm afraid you were misguided big-time... you still are. You are mostly cheated by the card-counting crooks, the bedfellows of the casinos in that gambling bedlam! You go by their insane odds and you are guaranteed to win as a matter of fact. Play 100 hands and win $52 at $10 minimum bet. Well, then, ask for a $100 table minimum and make a $500 net. This is the average, but it will be confirmed in any reasonable long run. Not the billions of hands long-run prophesized by the crooks!

Blackjack: Software, Content, Resources, Systems, Basic Strategy, Card Counting

See above: The comprehensive directory of the pages and materials on the subject of blackjack, baccarat, software, systems, and basic strategy.

• Blackjack: Basic Strategy, Card Counting, Charts, Tables, Probability, Odds, Software.
• The Best Blackjack Basic Strategy: Free Cards, Charts.
  All three color-coded charts in one file, in the best decision-making sequence: Split Pairs, to Double Down, to Hit or Stand.
• Gambling Mathematics in Blackjack Proves Deception of Card-Counting Systems.
• Probability Software to Analyze Blackjack Streaks: Wins (W+), Losses (L-), Busts, Pushes.
• Best Card Counting Blackjack Systems, Casino Marketing, Gambling Deception, Fraud.
• The Best Blackjack Strategy, System Tested with the Best Blackjack Software.
• Blackjack Insurance Bet Favorable to All Players.
• DownloadSoftware: Casino Gambling, Roulette, Blackjack, Baccarat, Craps.
• Specific software for blackjack, BJ
  ~ BJAQK and Blackjack: Probability and statistical analyses of thousands of blackjack hands from the perspective of a strict blackjack old basic strategy (OBS) player.

Home Search New Writings Odds, Generator Contents Forums Sitemap

Table Of Contents

• American Blackjack is a variant of the classic game of Blackjack
• It has better odds than European Blackjack

Blackjack, respectably being the most popular card game at Casinos, has plenty of variants for you to choose from.

Whether you play online or visit the brick-and-mortar Casinos, you’ll come across American Blackjack tables.

How does American Blackjack differ from other variants? Is it worth your time and money? Find out once and for all in this article.

Know all about American Blackjack but looking for free/real money American Blackjack games to play?Head to this online Casino and play at 5+ different American Blackjack tables!

Before we start…

Let’s get one thing straight. Many online Casinos don't call American Blackjack tables 'American Blackjack'.

But you can find American Blackjack tables by other names, for example, Atlantic City Blackjack or Vegas Strip / Vegas Downtown / Vegas Single Hand Blackjack.

The biggest difference between American Blackjack rules and other variants is how the cards are dealt for the dealer. And all of the mentioned games are dealt the same way as American Blackjack is.

American Blackjack vs European Blackjack

In European Blackjack, the dealer gets only one card and the second one comes only after the players make their moves.

In American Blackjack, the dealer gets both cards right away: one card face up and one (hole card) face down.

Let’s be honest now.

It seems like a minor thing to consider in the game of Blackjack. You may not even notice the dealing unless you really pay attention to it.

But it makes a difference in the house edge and the rules.

American Blackjack House Edge

Many things affect the Blackjack odds. It starts with the number of decks used, blackjack (a combination of + , or aka a natural) payouts, specific rules of when the dealer stands, and more.

The card dealing also makes a difference.

When the dealer gets an Ace or 10-value card as a face-up card, they can peek at their second card to see if it makes a natural (a two-card hand of 21 points in value).

If it does, unless you have a natural blackjack, too, you lose your wager before you decide whether to hit or stand on your dealt cards.

If it doesn’t, the game goes on as usual.

However, when it comes to the European Blackjack table, the dealer wouldn’t have a card to peek at.

So, you would make your move, perhaps double down and increase your wager, just to end up losing anyway against the dealer’s natural.

This small difference - option to avoid increasing wager in case of the dealer having a natural - counts for the 0.05 percent lower house edge in American Blackjack games.

While the house edge still depends on other factors, American Blackjack tables therefore usually have only 0.31-0.35 percent edge.

How to Play American Blackjack

One thing that doesn’t change much among Blackjack games is the basic rules.

No matter which variant of Blackjack you play, your goal is to beat the dealer. You can do so by having a higher-in-value hand while not going over 21.

You start American Blackjack game by making your bets. Like with most table games, they usually start at $1.

Both you and the dealer get two cards each.

You see your hand and its value. Also, one of the dealer’s cards. Based on this information you need to make your move:

Possible Move	Meaning
Hit	To ask for one more card. The total bet stays the same
Stand	To play with the current hand without asking for more cards. The total bet stays the same
Double Down	To ask for one more but last card. The total bet is doubled
Split	To split cards of the same value into two hands. The total bet is doubled
Take Insurance	In case the dealer has an Ace, to place a side bet which is won if the dealer has a natural. The total bet is increased by 0.5 of the original wager
Surrender	To give up before seeing how the game plays out. The total bet is reduced by 0.5 of the original wager

Unless you surrender, after you make your last move, you see the dealer’s hole card. Then the dealer plays out their hand.

There are three outcomes of the game:

Odds Of Getting Blackjack

Possible Outcome	Meaning
Your hand beats the dealer’s	You win and get the payout
The dealer’s hand beats yours	You lose your wager
Both you and the dealer has the same value hand	It's a push. In this case, you may get your wager back or lose it nevertheless (specific tables may have different rules regarding the push)

American Blackjack Payouts

There are three types of Blackjack payouts: a natural win payout, other wins payouts, and insurance payout.

The same ones are available at American Blackjack tables, too:

• a natural (blackjack) pays 3 to 2
• insurance pays 2 to 1
• beating the dealer other way pays 1 to 1

How to Win at American Blackjack

I've written it many times before and I’ll write it many times again: following the basic strategy is the best way to play Blackjack.

American Blackjack is no exception.

Whether you play American or European Blackjack, you see your cards and you see the dealer’s face-up card.

It’s enough to base your moves according to the basic strategy. Read more about the basic strategy here or download a pdf of printable basic strategy chart here.

Another thing that increases your chances of winning at Blackjack is card counting.

It’s a lot easier to learn than it sounds and you can use this card counting guide to do it like a pro.

However, card counters may find different Blackjack variants more convenient.

In American Blackjack online, the dealer uses up to eight decks of cards at the same time. In European Blackjack often only two while you can find Classic Blackjack games where only one deck of cards is used.

With fewer decks, it's easier to count cards. Especially when you’re a beginner.

American Blackjack Games Online

Now that you know how to play American Blackjack and how to beat the dealer at the game, are you ready to play?

If so, online Casinos are heaven for American Blackjack players.

As mentioned before, don’t look for games called exactly American Blackjack.

The developers tend to give Blackjack games various names but you’ll be able to recognize Blackjack that follows American Blackjack rules from the very beginning.

Read the info section of the game or place your first bet to see how the cards are dealt.

Odds Of Winning Blackjack Against Dealer

At many online Casinos (e.g. here) you can do it completely for free.

Odds Of Winning At Blackjack

Of course, when you play for free you can’t win real money. But it’s a great way to practice online Blackjack basic strategy or the art of card counting.

Odds Of Matching The Dealer In Blackjack

Once you’re ready to play for real money (and win real money, obviously), top up your Casino account and place real money wagers.

After all, Blackjack is the best game you can play for real money. And once you’ll start playing American Blackjack, it won’t be long until you see why.

Spoiler alert: It has everything to do with Blackjack odds.

Good luck!

The promotion presented on this page was available at the time of writing. With some Casino promotions changing on daily basis, we suggest you to check on the site if it still available. Also, please do not forget to read the terms and conditions in full before you accept a bonus.