Blackjack Casino House Edge

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Here are the different advantages for the casino using the blackjack house edge calculator from Wizard of Odds. Remember, the house edge is based on perfect basic strategy. Every misplayed hand increases the house edge for the casino. In the 3:2 blackjack game, the house edge, for player playing perfect basic strategy, is in the 0.5% range. That means for every $100 wagered, they take in, on average, $0.50. With 6:5 blackjack, that edge shoots up to almost 2%! So now you can expect to contribute upwards of $2 per $100 wagered to the house coffers.

The house always wins. But when it comes to real money blackjack, the way the house edge works is quite a bit different than in other games.

Before I dive into the topic, let’s make sure we’re all on the same page on this one—there’s not a game in existence where the house doesn’t have an edge.

That funny phrase about how “the house always wins” isn’t just a clever casino spiel, it’s reality. Casinos could not exist if they didn’t have an edge. It just wouldn’t make sense from a business standpoint.

Every game you play in a casino has a house edge. And how large that edge is depends on the rules the casino puts in place to some extent, and on you to some extent—your strategy, your tactics, your knowledge of the game, your decisions on how you play and why you make the plays that you do. All of these things affect how large the house’s edge truly is.

So, how does that house edge work for blackjack, anyway? Let’s take a look.

Start Thinking in Percentages

If you don’t like math, you’re probably not going to like gambling much. Or, at the very least, you’re not going to be very good at it.

House edges are usually expressed in percentages. Blackjack is well-known as being one of the few games where the house edge is low enough that you can potentially profit.

Now, as mentioned before, there are many factors that determine the house’s edge, but you’re looking at anything between 0.5% (if you’re implementing a good blackjack strategy) and a few percent (or even more).

There’s a reason so many gambling movies focus on blackjack. It’s one of the games where you can potentially come out on top if you know what you’re doing.

Why? Because the house edge only really means something for a statistically significant number of hands. What that little percentage up there means is that, on average, all players who are playing blackjack are going to lose about 0.5% of what they bet over time.

It’s clear right away why this only means something across a large number of bets. If you bet $100 and lose a hand, there’s no possible way to lose 50 cents. You either win some money, you lose some money, or you end up neutral.

But if you add up all the bets of all the players who are currently on the floor of a casino, and you start to measure the amount won and the amount lost over time, you’ll see that the house is going to be up about 50 cents a hand on average.

Casinos are profitable for precisely this reason. The rules are set up so that, statistically and over time, house losses are negated by house wins, and a slight profit is made. Slots tend to have the worst odds (and thus, are most profitable for the house), but the house holds an edge in almost every game available to you. But there are rare exceptions.

What Determines the House Edge

There are a number of factors that specifically determine the house edge. First and foremost is strategy. If you don’t know what you’re doing and don’t have a clear strategy, the house edge is going to be closer to 2% than 0.5%.

Other rules that can often feel completely strange or incalculable to new players also affect the house edge. For example, the amount you can win if you play a natural (blackjack—21) plays a big role in the house edge.

You’ll find that some casinos will pay you 3:2 on a natural (which means, for example, that you get $15 on a $10 bet), but many other casinos have moved to paying 6:5 (you get $12 if you get blackjack on a $10 bet). That greatly increases the house edge, so avoid it if you can.

Other rules play a factor—does the dealer hit or stand on a soft 17? Can you double after a split? Can you double on any first two cards? How many hands can you re-split to? Can you re-split aces? Can you hit on re-split aces? What about when a dealer gets a blackjack—do you only lose your original bet? What’s the surrender rule?

All of these seemingly insignificant rules play a huge role in the house’s edge, but remember—the house is winning over time over many different hands.

You don’t have to play a lot of different hands, you can come out on top.

Beat the House – Walk Away When You’re Winning

If you decide that the house edge in the casino you’re playing in is, say, 1%, that means you’re losing about 1% of whatever you’re betting over time.

But what happens when you win on the first hand? Let’s say you hit blackjack on your very first hand—lucky, but certainly not impossible.

Let’s further say that you bet $100 on that firsthand and the casino pays 3:2 on a natural, so you’re now up $50.

What happens when you walk away? You walk away with $50.

See, the house edge only means something over thousands of hands—tens of thousands, hundreds of thousands—all the hands that you play and that everyone else plays.

But if you only play a few hands (even a few dozen), you’re not in the realm of statistics anymore, you’re in the realm of randomness and luck.

If you’re following a decent blackjack strategy and you’ve practiced a lot, with a little luck, you might find yourself up by many hundreds or thousands of dollars over a short period of time.

If you walk away from the table before you start to lose (and you will start to lose if you play enough hands), then you’ve just beaten the odds.

The same can be said for losing, however, if you find yourself down, cutting your losses may be the best way to go. It’s certainly possible you can win your money back and get on top again, but on average, you are literally paying money to play, in the form of that 1% of your bet that the house is claiming on average.

The Solid Base of the House Edge That You Can Never Overcome

While we can talk all day long about blackjack strategy and how much money you make on a natural and all that jazz, I think it’s instructive to look at the origin of the house edge in the first place.

Every game you play in a casino has some simple rule that automatically guarantees the house and edge of some sort. Games of pure luck keep that house edge rigid, for example, there’s not much you can do to influence the odds of a roulette wheel. You place your bet, you let that sucker spin, and you either win or you lose. That’s that.

Blackjack’s house edge may be much more flexible given how you can apply strategy, but the foundation of the edge comes from the simple fact that you can bust before the dealer even has a chance to play their hand.

Think about it! If you bust, the dealer might have busted as well, but it still counts as a win for the dealer because you bust first. The dealer doesn’t have to reveal their hand until the end.

That translates into a huge advantage for the dealer. The house starts off with such an enormous advantage that all those other rules have to be put into effect just to get the darn thing down to something reasonable, and even then, you need a solid strategy if you’re going to beat the house.

What Is a Blackjack Strategy?

A blackjack strategy is essentially a set of rules that takes into account probabilities of cards turning up and then makes recommendations one what you should play based on your hand and the card the dealer has revealed.

While there are more than a few blackjack strategies out there, you’re going to need to do at least some studying if you want to understand how to reduce the house edge and get yourself to a place where you can at least have a chance of making some profit.

Remember, even with a strategy, the house still maintains that edge. There’s no way around it. So, on top of whatever strategy you come up with, it’s still a good idea to learn how to get out when the gettin’s good.

That means that sometimes, you’re going to have to eat a loss and come back another day (before your losses get too big).

Sometimes, you’re going to walk away when you feel like you’re on a winning streak. At the beginning, I say that you’re going to have a bad time if you don’t like math, and it’s true. Every hand you play is a complete tossup. There’s no such thing as having a hot or cold streak.

The only way you beat the house is to quit when you’re ahead.

Conclusion

The house edge works in blackjack in just about the same way it works in every other game, that is to say, it works for the house and against you. Learn some blackjack strategy, take free gambling lessons at some of the bigger casinos, learn what you can learn from watching the pros, but ultimately, if you want to beat the house edge, learn to walk away.

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.

Casino Blackjack House Advantage

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!