Casino Blackjack House Advantage

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  • The house advantage increases or decreases based on the rules set by the casino. For instance, a game with more decks in play will have a greater house advantage compared to one with less. Usually, players will opt for a casino offering the lowest house edge. The lowest house advantage in blackjack can go as low as 0.13%. Play Blackjack Online.
  • When it comes to understanding what the house advantage in blackjack is, it is common knowledge that in a casino online game of Blackjack, there is, in general, a lower House Advantage, as is compared with many other casino online game titles offered by various casino gambling sites. The House Advantage for a typical game of Blackjack has been.

By Hon. Ion Saliu, Founder of Blackjack Justice

In blackjack the house edge is the statistical advantage the casino has over the player. At any blackjack table the dealer is the casino representative. By acting last in a hand, the dealer gains the advantage over the players by seeing their cards, actions and potential mistakes.

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.
Casino

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!

Blackjack Casino House Edge

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.

Casino Blackjack House Advantage Rewards

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.

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House

Playing and mastering blackjack are two entirely different things. Mastery of blackjack starts with understanding the house edge and recognizing how it can impact your game. Understanding the house edge is vital for becoming a player that is capable of taking on the house. Without further ado, let’s delve into how to reduce the house edge!

This guide will also show you the ins and outs of the house advantage, blackjack odds and blackjack strategy. You’ll be ready to sit at the table and take on the dealer after you’ve read this!

What is the House Advantage?

The house edge is the mathematical advantage that a casino has over its players. This edge varies from game to game, and is normally represented as a percentage and denotes the amount of return that the house can expect to receive over time. It also represents the percentage of losses that the player will likely incur.

Let’s say that the house has an edge of 5% in a particular game. If a player bets €100, then the house will likely earn €5, while the player will likely lose €5. This does not mean that the player can’t win more or turn a profit – it merely means that the house will take some money at the end.

What Percentage is the House Edge in Blackjack?

The house edge in blackjack is low relative to other games, with it being as low as 1% when a basic blackjack strategy is implemented.

Casino Blackjack House Advantage Plan

In blackjack, the house edge comes from the dealer having a hidden card about which the player has to make assumptions. In addition, if the player busts, the dealer wins, even if they then bust in the same round. Learning blackjack odds and strategy makes this less of an issue.

Blackjack Odds

Admittedly, learning blackjack odds is a little more difficult than it is for other casino games. This is down to the randomness of the draw and the number of different combinations. Nevertheless, there are some ways of determining the odds of drawing specific cards. The initially probability of drawing a card of any value is 7.69%, based on there being 13 different possible options.

However, seeing as Jacks, Queens and Kings all have a value of 10 in blackjack, the odds of drawing a card valued at 10 is 4/13, which is a probability of 30.7% in percentage terms. As a result, the house edge can be reduced simply by having an idea of the odds of drawing certain cards. For example, if you happen to draw a Jack and a King, then you know that the odds of drawing yet another 10-value card are much reduced.

Reducing the House Edge in Blackjack

There are a variety of ways to reduce the house edge in blackjack. As previously mentioned, the simplest is to learn a basic blackjack strategy and commit it to memory before you play. A basic blackjack strategy is a set of rules, usually presented in a chart, which tells you how to play your hand after it is dealt. For example, if you are dealt a soft 17 (Ace, six), the chart compares it to the dealer’s upcard and informs you of how to act. In some cases, using a basic strategy can reduce the house edge to just 0.5%! If you want to lower the house advantage, studying the basics of blackjack strategies is a good place to start.

In addition to basic strategy charts, several strategies have been developed to reduce the house edge in blackjack even further. Unlike the basic charts, which only focus on the total value of your hand, these strategies look at what cards make up your hand and give specific actions depending on the cards – they’re called composition-dependent strategies.

Casino Edge In Blackjack

Here’s an example. If you have 16 and the dealer has 10, depending on the composition of your hand there are a number of different options. For instance, if you had three separate hands that all equaled 16, with the first comprised of a 10 and a six, the second of nine and seven, and the third of four, five, and seven. If you followed basic blackjack strategy, you’d hit on all these hands, but with a composition-dependent strategy, you don’t hit on the final hand. This is because it is made up of low-value cards that would otherwise be needed to make a pat hand (under 21) from 16. The blackjack odds of drawing a low-value card are much lower than with the other two hands.

In most cases, by using a composition-dependent strategy along with the existing basic strategy charts, it’s possible to reduce the house edge to as little as 0.18%, which is practically nothing!

Casino Blackjack Rules

Hopefully, you’re now fully informed of what the house advantage is, how it applies to blackjack, and the steps you can take to reduce it. If you think you’re ready to put the new knowledge to the test, why not play on one of our online blackjack tables!