Blackjack House Edge With Basic Strategy
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.
Typical blackjack players give about a 1.5% advantage to the house due to the mistakes they make playing their hands. But even those who get their entire basic strategy down cold still have a 0.5% disadvantage in the typical multi-deck game. So then, is a perfect basic strategy player doomed to end up a loser if he doesn't become a card counter? Suggesting all games are played with six decks - which is a common size for a blackjack shoe - Spanish 21 has the best house edge for the player according to the blackjack house edge table on top of this page. Standard 21 Blackjack is good too since you can actually have the edge by playing perfect basic strategy with a single deck.
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.
Blackjack House Edge With Basic Strategy For Beginners
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Blackjack is well-known as one of the best games for the player in the casino. Not everyone understands exactly what this means, though.
When someone who knows what he’s talking about says that blackjack is the best game in the casino, he usually means that it has the lowest “house edge.”
That’s a number that represents the casino’s mathematical advantage over the player. It’s expressed as a percentage, and the higher that percentage is, the more of an advantage the casino has.
Games like slot machines generally have a house edge of 6% or higher, and roulette has a house edge of 5.26%.
Blackjack, when played with perfect basic strategy, has a house edge of less than 1%.
But not every strategy works when it comes to winning at blackjack.
This post – the first in a series – looks at some of the good and bad strategies for winning at blackjack.
Using Basic Strategy Is a Good Approach to Winning at Blackjack
Casino games can be categorized in different ways, but one of my favorite ways to categorize these games is by whether your decisions matter.
When you’re playing roulette or a slot machine, you don’t make any playing decisions that matter. You place your bet and hope for the best.
But, in real money blackjack, you have to decide how to play your hand. You decide whether to hit, stand, double down, split, and/or surrender.
You might not believe this, but there’s a mathematically optimal decision for every situation in blackjack.
And it’s not a matter of intuition or premonitions, either. It’s solely a matter of probability.
Basic strategy lists the mathematically optimal moves for every possible situation in blackjack.
There’s a Mathematically Optimal Move in Every Blackjack Situation
Think about this:
Let’s say you’re playing blackjack with someone who believes in premonitions and hunches. And let’s also say that this player has the same hunch every time he gets a specific hand.
Every time he has a hand with a total of 19, he has a hunch that the next card will be a 2, giving him a 21, so he always hits in that situation.
Here’s the deal, though.
You have the following possible values for the cards in the deck:
- 2
- 3
- 4
- 5
- 6
- 7
- 8
- 9
- 10
You only have 4 cards that are worth 2 points. Every other card – all 48 of them – will bust your hand.
Of course, you know which 2 cards you have showing, and you also know one of the dealer’s cards.
This still means that you have 45 possible cards that will hurt you and 4 possible cards that will help you.
The right play is evident here.
And if that’s true, then it’s obvious that there’s a mathematically optimal play for every other situation in blackjack, too.
The Bottom Line Regarding Basic Strategy in Blackjack
The bottom line is that you should always use basic strategy in blackjack. Most players don’t know basic strategy entirely, and even some of the players who do will deviate from it based on a hunch.
What does this mean to the casino and to the player?
If you’re an average basic strategy player betting $10 per hand and playing 100 hands per hour, you’re putting $1000 per hour into action.
If you’re playing with perfect basic strategy, and the game conditions are such that basic strategy provides the house with an edge of 0.5%, you’re going to average losing $5 per hour.
The average blackjack player, though, deviates from basic strategy so much that the house has an effective edge of 4%. That’s still better than roulette, but compared to the house edge you face when using perfect basic strategy, it’s terrible.
Instead of averaging a $5 loss per hour, you’re now facing an average loss of $40 per hour.
Winning gamblers are those who buck statistical trends, but ask yourself this:
Is it easier to buck a $5 per hour losing trend or a $40 per hour losing trend?
Money Management Techniques Are a Bad Strategy
A money management technique doesn’t have anything to do with how you decide to play the cards in blackjack. It only concerns itself with how much money you have budgeted to play with, how much you’re willing to lose before calling it quits, and how much of a win is big enough to call it a day.
These aren’t bad things. They’re just not going to help you win.
The first factor of a money management strategy is deciding on the size of your bankroll for the session. This is essentially just an amount of money you’ve set aside for gambling during that session. You should always set this budget based on how much money you can afford to lose.
The other 2 factors in a money management strategy are stop-loss limits and win goals. A stop-loss limit is an amount that, once you’ve lost it, signifies that it’s time to quit your session. A win goal is just the opposite. It’s an amount that, once you’ve won it, signifies that it’s time to quit.
Most money management gamblers set their win goals and stop-loss limits based on a percentage of their session bankroll.
They might have a 20% win goal and a 40% loss limit, for example. A player with a $100 bankroll and those limits would quit once he got up to $120 or once he got down to $60.
The reason these money management techniques don’t change the odds is because they’re just arbitrary stopping points in the lifelong gambling session that they’re engaged in.
The law of large numbers still applies, no matter when you stop – unless you stop forever.
Most blackjack players don’t stop gambling forever just because they won $20.
Counting Cards Is a Good Blackjack Strategy
The only time you should deviate from basic strategy is when you’re counting cards, and the count is such that deviating from basic strategy is the mathematically correct move.
And, unlike many people think, you don’t have to memorize the deck to count cards (although you can.)
Counting cards has more to do with keeping a general accounting of how many low cards have been played versus how many high cards have been played.
Having low cards in the deck is bad for the player, but having high cards in the deck is good for the player.
Here’s why:
The high cards are the aces and 10s. These are the only cards that can result in a blackjack (a “natural.”) While most blackjack hands pay off at even money when you win, a blackjack pays off at 3 to 2 odds.
Bet $10 on a hand of blackjack and get a 2-card total of 21, and you’ll win $15 instead of $10.
If the deck has a higher proportion of 10s and aces in it than low cards, your probability of getting a bigger payout increases. If you bet more when you’re more likely to get a bigger payout, you’ll get a mathematical edge over the casino.
Don’t believe me?
Think about it from this perspective:
Suppose you took every card out of the deck beside the aces and 10s.
Would you be more likely or less likely to get a blackjack in that situation?
To keep up with that total, you assign values to the cards based on how high or low they are.
The most basic counting system, the Hi-Lo System, uses values of +1 and -1, so it’s easy to use.
The low cards are good to see come out of the deck, so you count each of those as +1.
The high cards are bad to see come out of the deck, so those count as -1.
When the count is positive, you raise the size of your bets. The higher the count, the bigger your wagers should be.
Is Cheating at Blackjack an Effective Strategy?
Casinos will love it if you believe that counting cards is cheating.
But think about that for a minute.
Why would anyone think that thinking about the game you’re playing – even if you’re thinking about it intently – is cheating?
You wouldn’t accuse an expert chess player of cheating just because he was thinking about the game he was playing, would you?
Blackjack House Edge With Basic Strategy Builder
The truth is that counting cards isn’t cheating, but casinos will back you off from the blackjack tables if they think you’re counting.
But enlisting the help of the dealer by paying them to signal you about their hole card gives you information the other players at the table don’t have. This is really cheating, and it’s illegal. You can your blackjack dealer buddy face possible jail time with this strategy.
That’s a bad strategy.
Basic Strategy Blackjack Trainer
You’d have to win a lot more money at the blackjack table than you probably will to make it worth spending any time at all in jail.
Conclusion
When writing about good and bad gambling strategies, blackjack is one of the best games to discuss. It’s a game where your decisions matter so much that you can even get a mathematical edge over the casino if you make enough good decisions.