Standard Blackjack Odds
The house edge is a statistical way of measuring the casino’s advantage over the player. The standard payout for winning with a blackjack is 3 to 2, which may not seem that much better than the even money payout on normal wins, but you'll be cheating yourself if you believe that. Some blackjack tables pay 6:5 on winning naturals, and sometimes just even money. The Fundamental Probability Issue: True Blackjack Odds - New Software Calculator First captured by the WayBack Machine (web.archive.org) on November 21, 2002. They say roulette is the queen of casino games. Then, blackjack is the king of the casino. Many believe that Blackjack, or 21, or twenty-one is the most popular casino game in the.
- Blackjack Odds Explained
- House Odds For Blackjack
- Standard Blackjack Strategy Card
- Odds Of Winning Blackjack
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Blackjack Probability and Blackjack Odds
To fully understand the game of blackjack, you must understand and master blackjack odds. It's crucial to know how the casino gains its edge and how it helps them win. It's also important to understand blackjack odds such as the odds of hitting a 10 or the odds of being dealt a blackjack. You can read over these blackjack odds charts to help understand the logistics behind blackjack.
Casino and Dealer Advantage in Blackjack
In most casino games of blackjack, the house advantage (the dealer advantage) is ~ 8%. The house gets this advantage by the dealer being the last player to act. By acting last, all other players have already made their decisions and could quite possibly bust before the dealer has his turn.
By using correct blackjack basic strategy, you can turn the casino edge in blackjack from 7%-8% down to 0.5%. If you correctly use advanced card counting techniques, you can often change blackjack odds and give yourself the advantage over the casino. Manipulating the house odds to your favor is the reason most casinos don't allow card counters to play blackjack.
Probability of Busting on a Hit
It's very important to know the probability of your hand busting when you are holding any total in the game of blackjack. The following odds chart shows the blackjack odds of busting, depending on your current hand value:
Blackjack Odds Explained
| Hand Value | % Bust If You Hit |
|---|---|
| 21 | 100% |
| 20 | 92% |
| 19 | 85% |
| 18 | 77% |
| 17 | 69% |
| 16 | 62% |
| 15 | 58% |
| 14 | 56% |
| 13 | 39% |
| 12 | 31% |
| 11 or Less | 0% |
Two-Card Count Frequencies
This interesting blackjack odds chart is the two card count frequency chart. This chart shows the percentage chance that you will be dealt a hand in each given value range. The most important frequencey to note is the chance of being dealt a natural blackjack (natural 21 value. The odds of being dealt a natural blackjack are merely 4.8%. Following this chart you will see that the most common two card hand, at 38.7%, is a hand totaling 1-16, which is considered a decision hand.
| Two Card Count | % Frequency |
|---|---|
| Natural 21 | 4.8% |
| Hard Standing (17-20) | 30.0 % |
| Decision Hands (1-16) | 38.7% |
| No Bust | 26.5% |
| TOTAL | 100.0% |
Dealer Final Hand Probabilities
This blackjack odds chart shows the dealer final hand probability. These are the percentages that the dealer will end up with a hand totaling each corresponding value (up to 16). Read over this chart to understand the odds that the dealer has to make his final hand.
| Dealer Final Hand Value | % | Cumulative % Total |
|---|---|---|
| Natural 21 | 4.82% | 4.83% |
| 21 (3 or More Cards) | 7.36% | 12.19% |
| 20 | 17.58% | 29.77% |
| 19 | 13.48% | 43.25% |
| 18 | 13.81% | 57.06% |
| 17 | 14.58% | 71.64% |
| 16 | 28.36% | 100.00% |
Player Advantage vs. Dealer Up Card
The first two columns in this odds chart explain the dealer's chance of busting, depending on the up card that he is showing. You should note that the dealer has the highest chance of busting when he is showing a 5. The third column in this chart shows the player advantage of using basic strategy, compared to each up card the dealer is showing. You can see that the player has the highest advantage of 23.9%, when the dealer is showing a 5. When the dealer is showing any card that is 9 value or higher, the player is in the negative advantage range.
| Dealer Up Card | Dealer Bust % | Player Advantage % with Basic Strategy |
|---|---|---|
| 2 | 35.30% | 9.8% |
| 3 | 37.56% | 13.4% |
| 4 | 40.28% | 18.0% |
| 5 | 42.89% | 23.2% |
| 6 | 42.08% | 23.9% |
| 7 | 25.99% | 14.3% |
| 8 | 23.86% | 5.4% |
| 9 | 23.34% | -4.3% |
| J,Q,K | 21.43% | -16.9% |
| A | 11.65% | -16.0% |
Effects of Removing Cards from a Deck
When looking at the odds of removing certain cards from a 52-card deck, some cards have a much greater effect on blackjack odds. To create the strongest card counting system ever invented, you would have to incorporate all of these slight and subtle differences into the numbers to be a completely accurate system.
Removing every 5 from a deck cards would make the largest impact of improving your blackjack odds, as a player. On the other hand, removing every Ace from a deck of cards would make the largest impact on improving the odds for the casino.
| Card | % Effect of Removal |
|---|---|
| 2 | 0.40% |
| 3 | 0.43% |
| 4 | 0.52% |
| 5 | 0.67% |
| 6 | 0.45% |
| 7 | 0.30% |
| 8 | 0.01% |
| 9 | -0.15% |
| 10 | -0.51% |
| A | -0.59% |
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Importance of Blackjack Variances
The importance of blackjack variances and a proper understanding of variance in gambling cannot be underestimated. Blackjack players can come to think they 'know how to beat blackjack' if they go on a lucky streak, or they might come to think that blackjack isn't their game if they have a high negative variance in the early rounds of their blackjack playing. So given how important variances are to your expectations in blackjack, I'll try to explain what blackjack variance is and why it's important to keep in mind when analyzing your blackjack results.
So what are blackjack variances? To answer that question, I'll need to define a few blackjack terms -- so please bear with me.
Payout Percentages and the House Edge
House Odds For Blackjack
The short answer is that blackjack variances are the deviations from expected payback in blackjack. 'Expected payout' is the amount of money (as a percentage) that you might expect to win back when betting on blackjack. It is closely tied to the house edge. The house edge exists so the casino stays in business, because casino games are typically weighted in the favor of the casino and against the player. The house edge in blackjack for a player using 'perfect' or optimal basic strategy is only around 0.5%, which means your expected payout will be around 99.5%.
This makes blackjack actually one of the best games in the casino. So for every $100 you bet at the blackjack table, you can expect to win back $99.50. You'll only lose $0.50 on every hundred dollars you spend (if you play perfect strategy, which all new players won't). For those managing expectations, though, the low house edge makes blackjack variances more subtle and more difficult to analyze, at least when you're going with your 'gut' or gamblers instinct.
Variances in Wins and Losses
That's because your expected payout or expectation is only an average. It's a theoretical expecation, and one not likely to occur too many times in your blackjack sessions. Sometimes you'll lose a whole lot more than $0.50 per $100 bet. You might lose $50.00 on a hundred dollar bet, if the cards aren't hitting right. On the other hand, you'll sometimes walk away from the table with more than you started out. You wouldn't play the game if you never won. So you'll win sometimes, but to account for the winning opportunities, you'll lose more than expected at other times. Losing more than you're expected to lose is a variance from your payback expectations, while winning your bets is also a variance from those expectations. Therefore, the amount your blackjack session deviates from expectation is the variance.
Blackjack Deviations
Your results will vary each time you bet on blackjack. Most of the time when playing blackjack, your results will vary widely, from large losses to large wins. Seldom will a player with a 99.5% expectation actually walk away with 99.5% of the money he or she bet. Expectation involves the odds about what you can expect to win or lose over a long period of time. Actually, it's over an infinite number of blackjack hands, because the possibility always exists that you'll just keep winning more than expected or losing more than expected.
This kind of deviation can fool a player at the blackjack table. If you're not a serious player, but just having fun, you might get the sensation you're having good luck or bad luck. You'll get the feeling you're getting lucky and that's that. Where the problem comes in is when you are a professional or serious amateur blackjack player, and you are trying out some new blackjack tips, recently learned blackjack strategy or card counting techniques. Because even really long sessions of blackjack are just a small sampling of the possibilities. Six months of blackjack sessions aren't a tiny sample, when compared to the idea that the expectation is based on a theoretical infinite number of hands. So you're not getting a full picture (or even a half-full picture) about whether your new blackjack method is working. You may just be riding the highs or lows of the blackjack variances.
So the importance of blackjack variances is they can fool us into false assumptions about our blackjack playing. Maybe you'll come away thinking you have learned how to beat blackjack, or you're a much better player than you really are. Or maybe you're doing all the right things, but the cards aren't falling your way. Players need to understand the nature of blackjack variances, then, and learn to analyze their game based not entirely on results, but on the soundness of the strategy being employed. You can make all the right moves and lose, and you can make all the wrong moves and win. That's the essence of blackjack variances. Sometimes you beat the odds.
Standard Deviation
To get an idea about our real expectations when playing blackjack, consider the standard deviation. This will give you some idea of the kind of blackjack variances you can expect. It's pretty interesting, because it shows how small the gambling margins can be in the short term, even though in the long term, blackjack is a negative expectation game.
Standard Blackjack Strategy Card
You can figure what is called a 'standard deviation'. You might remember this from grade school, where you get an average of a group of numbers, then calculate the standard deviation from that number. In calculating a blackjack standard deviation with a computer software program, though, you won't be testing a select group of five or ten numbers. You'll be testing well over a million deviations.
The standard deviation in blackjack is simply calculating the probabilities you will win or lose and extracting your odds from that. That is, the standard deviation can tell you your odds of winning, losing or pushing when playing blackjack. Without getting too far into the numbers, at least one gambling math expert has figured there are over 723,000,000 (yes, that's 723 million) card combination scenarios where you walk away from the table a winner. But there are over 836,000,000 combinations where you walk away a loser. And there are only a paltry 144,000,000 potential cases where you walk away with the same money you started with or 'push'.
Odds Of Winning Blackjack
Considering all these numbers as percentages of 100%, the standard deviation will tell you that your chances of walking away a net winner in blackjack is around 42.42% of the time, rounded up. Your odds of walking away from the blackjack table a loser are around 49.10%, rounded up. Your odds of walking away with a push is somewhere around 8.47% of the time.
If you want to read more about the numbers behind blackjack variances and standard deviation, visit the blackjack variance page on the Wizard of Odds website. The Wizard of Odds has run statistical breakdowns of the odds on virtually every major game you'll find in a casino.
Negative Expectation, But With Hope
So blackjack is a negative expectation game. There's a house edge that says you will lose in the long run, if you play an infinite number of hands. But in the short term, you'll walk away a winner 42% of the time. In fact, you'll walk away not losing nearly 51% of the time. And over 91% of the time, you'll experience a variance from the expected payouts in blackjack. Blackjack variances will happen 9 out of 10 times you walk up to the blackjack table. You need to keep this in mind when playing blackjack and analyzing your results.