House Odds In Blackjack

House Odds In Blackjack 5,7/10 7540 reviews

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’s say the house edge is half of one percent like it is on most blackjack games. If you were betting 100 dollars on each round and you played 100 rounds an hour, you would be betting a total amount of $10,000 worth of individual bets every hour. 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. Let’s say the house edge is half of one percent like it is on most blackjack games. If you were betting 100 dollars on each round and you played 100 rounds an hour, you would be betting a total amount of $10,000 worth of individual bets every hour.

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

Many people will be visiting a casino this summer, whether on a trip to Vegas, on a cruise ship, or just at a local casino during a 'staycation.'

But before you go, you may want to know which games give you the best chance of winning.

So we went behind the scene at two casinos, and spoke with the game managers, to find out which games give you an edge.

Table Games Your Best Bet

Jay Bean, a Caesar's floor manager, agreed to sit down with us and talk about the games with the best odds.

He said many people don't realize that table games have much better odds than slots. They are intimidated by thoughts of card sharks taking their money, with images of an intense Texas Hold 'Em tournament in their minds, and so they stick with the safe games: the slots.

But they are doing themselves a disservice, he said.

Bean's advice? After you've spent some time on the slot machines, move on to the Blackjack table, and start by just observing.

1. Blackjack

Blackjack has the best odds of winning, with a house edge of just 1 percent in most casinos, Bean said.

Plus, you are playing against only the dealer, not hooded poker champions.

'Blackjack is one of our easiest games to play,' Bean said. 'You're just looking for a number that beats the dealer's number without going over 21.'

If you're a novice, Bean said to sit down during a less busy time, such as the afternoon, and the dealer will walk you through the game.

But the same is not true with poker: You should practice the game with your friends first, at home, Bean said, until you are comfortable with it. Bean said novices are best off passing on the poker tables, where yes, the competition can be tough.

You can find out more information about the game of blackjack at the following link:
http://wizardofodds.com/games/blackjack/

2. Craps

So from the Blackjack table, he suggests moving on to the dice game Craps, the game with the second best odds, also nearly 50-50.

The Craps table can be a bit intimidating for the beginner with all the boxes on the table, Bean admitted. But it's really not tough, and it has one of your best chances of winning. In the end, all you are really doing is betting on a dice roll.

For more information on craps, visit:
http://wizardofodds.com/games/craps/

3. Roulette

Bean said your next stop should be the Roulette wheel. It's simple, and pays fairly well.

'So you bet on your favorite numbers,' Bean said. 'The dealer spins, and if your number comes in you win.'

What Are The House Odds In Blackjack

If you stick to betting on just Reds or Blacks, you have nearly a 50-50 chance of walking away a winner. If it lands on red when you choose red, you will double your bet, Bean explained.

While it may seem you have an even chance of winning by simply choosing a color, there is one catch that gives the house its edge: the extra green 0 and 00 position on the wheel. It's on all American roulette wheels.

Or, if you feel lucky, play just one number. It's hard to win, but if you do it pays out 36 to 1.

For more information on roulette, visit:
http://wizardofodds.com/games/roulette/

Worst Odds

Your worst odds? The casinos, understandably, did not want to talk about games with poor odds.

So we turned to Forbes Magazine, which in a report about Best Bets at the Casino, said two popular games -- the Wheel of Fortune and the ever-popular slot machines -- have the lowest odds of winning, with a house edge of 10 percent or more.

The Experts Agree

Professor of Analytics Michael Magazine has crunched the numbers, and agreed that blackjack is the best way to go home with money in your pockets. He said if you take a little time to learn the game, you have the best odds of winning.

'You are somewhere between 44 percent to 48 percent in every single hand of winning,' he said, noting that no other casino game gives you odds that good.

But Magazine cautioned that he's not promoting gambling, because he said even games with the best odds still favor the house.

'Play it long enough and you will lose. In the long term the house doesn't lose,' Magazine said.

Odds Of House Winning In Blackjack

If You Love The Slots....

Finally, if you really enjoy playing the slots, here is some good information to know, from state casino reports we examined.

With slots, the more money you put in per bet, the higher your chance of winning. If you put the max in a penny machine, which is usually around 50 cents, you have much better odds than if you put in 2 cents.

In addition, penny slots have the lowest odds, with $1 and $5 slots paying much better.

Always gamble responsibly, and don't waste your money.
__________________________