1. Blackjack Probability Tables
2. Odds Of Winning Blackjack Hands
3. Calculating Blackjack Probabilities
4. Odds Of Winning Blackjack At Casino

May 29, 2014  There’s technically nothing wrong with these options, but they are basically giving themselves a lesser chance of winning. By following basic strategy, the house advantage is about 0.5 percent. That means if you are playing for $100 per hand, you can expect to. Dealer Final Hand Probability Odds. This next table shows the odds of what the dealer's final hand will be. Usually in blackjack, the dealer must hit on 16 and stand on 17. These rules are slightly different for other variations of twenty-one. So generally, the odds of the dealer's final score being 16 are 0% because he must hit.

Odds are everywhere you look. Seriously. Odds are in a casino, your workplace, your day-to-day live and habits, your marriage and where in the world you live.

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Don’t believe me? Take a look for yourself:

• Odds of having twins (21st century) – 3 in 100 or 3%
• Odds of getting a divorce – 40 to 50%
• Odds of being stuck by lightning – 1 in 5,000 or 1 in 700,000 in any given year
• Odds of being audited by the IRS – .4% if you make less than $200,000 / year
• Odds of being dealt a blackjack – About 4.83%

Blackjack Probability Tables

Odds are just the likelihood that something will happen. As a blackjack player you deal with this all the time.

Lets look at a couple real examples to show you what I mean.

Here are the odds of you busting your hand, depending on what you were dealt:

• 21 – 100%
• 20 – 92%
• 19 – 85%
• 18 – 77%
• 17 – 69%
• 16 – 62%
• 15 – 58%
• 14 – 56%
• 13 – 39%
• 12 – 31%
• <11 – 0%

Odds of Being Dealt Specific Hands

Here are the probabilities for being dealt a specific hand:

• Blackjack – 4.8%
• Standing Hand (17-20) – 30%
• Decision Hand – (1-16) – 38.7%
• No Bust – 26.5%

Here are the odds for the final hands that the dealer will make:

• Natural 21 – 4.82%
• 21 (3+ cards) – 7.36%
• 20 – 17.58%
• 19 – 13.48%
• 18 – 13.81%
• 17 – 14.58%
• 16 – 28.36%

Dealer vs. Player Odds

Finally, here are the odds of the dealer busting based on their up card:

• 2 – 35.30%
• 3 – 37.56%
• 4 – 40.28%
• 5 – 42.89%
• 6 – 42.08%
• 7 – 25.99%
• 8 – 23.86%
• 9 – 23.34%
• J,Q,K – 21.43%
• A – 11.65%

Of these examples, this is the most useful. Notice what hands the dealer is most likely to bust with. The dealer will most often bust with 4, 5 or 6, followed by 2 and 3.

The odds above are static. There’s nothing you can do to change them. However, you can find ways to improve your odds so that you lose fewer hands and less money. And the less money you lose, the more you can keep to play more blackjack.

Here’s what you can do to improve your odds in blackjack:

• Use basic blackjack strategy. Without basic strategy you’re playing at an 8% disadvantage. With strategy, however, the odds increase significantly. You’ll be playing at only .5 to 1.5% disadvantage.
• Find the best games. The rules make all the difference. For example, if you play a 6:5 blackjack game you’re adding a 1.39% disadvantage. If the dealer hits soft 17 that’s another .18%. However, it’s possible to find games where the player is paid 3:2 for blackjacks and the dealer stands on soft 17. So find those games. Also be careful about which blackjack variation you play. The best games to play are blackjack, Spanish 21, Vegas Strip BJ and Blackjack Switch.
• Avoid side bets. Side bets look exciting, because for a nominal amount you could possibly win a huge jackpot — worth hundreds or even thousands of dollars. The problem is that the odds against winning can be anywhere from 2-40%.
• Avoid wives tales. There are a lot of bad strategies like never busting (never hit a 12+), mimicking the dealer and assume that the dealer has a 10 in the whole (with ace up). The problem with using any of these strategies is that they increase the house edge from 3 to 10 percent.

You can do other things, too, like count cards or read books (usually a mix of basic strategy, card counting and general how-to’s for casino blackjack). However, you’ll improve your odds at winning at blackjack just by following my suggestions above.

Understanding the Long Run – Sample Size and Variance

I wanted to finish up this article with a brief explanation of odds, and how they work over the long run. You see, I think a lot of people will see the numbers above and get confused when they don’t match their own stats. In other words, someone might go to the casino play 500 hands of blackjack, and wonder why they didn’t get 24 natural blackjacks, or the other way around, why they got 42.

The thing is, odds and statistics are all about the long run. Long run usually meaning sample size, or the total number of hands (or games) played.

What that means is that over a significant sample size, hundreds of thousands or even millions of hands, the number of times you’ll receive a blackjack is about 4.82%. The more hands you play the truer this will become.

The reason why odds don’t match up in smaller sessions, say over 500 hands, is because of variance. There’s a technical term and definition for variance, but I’ll just give you my version; variance is the ups and downs you experience on your way to the long term (expected) results.

Mike Caro, a poker player and author, puts it this way:

A measure of the spread of statistical distribution about its mean or centre.

That means in a short time frame, it’s possible to experience more drastic odds. You might win or lose more than you’re supposed to. It also explains why people can go into a casino, not use basic strategy and win 3x as much as what they walked in with. The cards ran in their favor — they experienced a positive streak of variance.

So that’s the gist of it. So the next time you walk into the casino and have a wild swing one way or another, you know that that’s not normal, and that in the long run you’ll be closer to break-even so long as you stick to basic strategy — the plan with the best odds.

Blackjack offers some of the best odds in the casino. Everyone knows that already. But what does it mean to say that one casino games offers better odds than another casino game? This page goes into some detail about how to measure the odds of a casino game. Then it continues with an examination of the specifics related to the game of blackjack.

Odds and Probability Explained

Probability is the branch of math that covers how likely it is to achieve a certain result. Any possible result can be measured as a number between 0 and 1, with a 0 meaning that it will never happen and a 1 meaning that it will always happen. It’s probably easier to think of this number as a percentage, so something with a 0% chance of happening will never happen, while something that will always happen has a probability of 100%.

If you add the probability of something happening with the probability of something not happening, you will always get a total of 100%. So it’s always possible to calculate that number backwards. For example, if you know that there is an 80% chance of something not happening, you also know that there is a 20% chance of it happening, and vice versa.

Probabilities are sometimes explained as odds. This is just a way of expressing a probability as the number of possibilities of it failing versus the number of possibilities of it succeeding. For example, if you want to express the odds of getting an ace with the next card you draw out of a fresh deck of playing cards, then you know that the odds are 12 to 1. (For every ace in the deck, there are 12 cards that are NOT aces.)

Casinos make their money by paying out wagers at odds that are less than their odds of happening. For example, on a single number bet in roulette, the odds of winning are 37 to 1. (There are 38 different numbers, and you only bet on 1 of them in this example.) But that bet only pays out at 35 to 1.

In a mathematically perfect set of spins, you’d win once and lose 37 times. If you’re betting $1 per spin, then you’ve lost $37, but you’ve won $35 the one time you got a winning spin. The casino gets the other $2, and that’s how they stay in business.

All casino games, including blackjack, work on this seemingly-simple principle. In fact, it’s relatively easy to determine a percentage of each bet that you make that the casino can expect to receive over time. This percentage is called the house edge.

In the roulette example above, the house edge is 5.26%. That’s the amount of each bet that will be lost over an infinite number of trials. Of course, in the short term, anything can (and often will) happen, but as you get closer to an infinite number of trials, the closer the results become to the mathematical expectation.

The house edge can be as high as 25% on slot machines in Nevada, or as low as 0.5% on blackjack in the same state. But achieving that 0.5% number requires a certain amount of skill and strategy. Players who just use “common sense” or who “play their hunches” face a house edge of closer to 2-4%.

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Basic Strategy Is the Key to the Best Blackjack Odds

The key to maintaining the lowest possible house edge on blackjack is to use basic strategy every time you play. By doing so, you maximize your expectation and minimize the casino’s expectation. Basic strategy is the mathematically perfect play in every possible blackjack situation.

This might seem like an unearthly number of scenarios to memorize, but it’s actually easier than you think. The dealer’s upcard is limited to 10 possibilities. Your hand is limited to 20 different totals. Since many hands will be played with the same strategy as many others, memorizing basic strategy is far easier than you’d think.

Many websites and almost all blackjack books offer basic strategy charts which can help visual learners memorize the correct strategy. The conditions and house rules can affect a handful of strategy decisions, but even then, it’s a tiny percentage of the potential situations you might face. Learning one basic strategy is better than learning no basic strategy at all. In other words, don’t get hung up on making the occasional error because of local playing conditions.

Playing Conditions and Rules Variations

The other key to getting the best odds in blackjack is to make intelligent choices about which blackjack games you’ll play. The biggest variation that you need to watch out for is the payout on a natural 21. At most casinos, a natural 21 pays out at 3 to 2 odds, but you’ll often find games that pay out at 6 to 5 odds instead.

The difference in that single rules variation is tremendous. In fact, it gives the casino an additional edge of 1.39%. In most blackjack games, this doubles or even triples the house’s edge. The easiest way to avoid that additional “tax” on your game is to just say no to any blackjack game that doesn’t pay out at least 3 to 2 for a natural.

Other variations in the rules can actually improve the player’s odds. For example, a single deck blackjack game versus a game with two decks or more gives 0.48% back to the player. That’s not nearly as significant as the 1.39%, so don’t fall for the trap of playing a single deck game with a 6 to 5 payout on a natural blackjack.

Most other rules variations have smaller effects on the house edge, but they can add up quickly when combined. For example, if the dealer hits on soft 17 (instead of standing), the house gains 0.22%. But if the player is also limited to only being able to double down on 10 or 11, the house gains another 0.18%, for a total gain to the house of 0.4%.

The Effects of Card Counting on the Odds

Entire books have been written about counting cards and how it affects the player’s odds in the game of blackjack, but for the purposes of this page, I just want to explain how card counters get an edge over the casino. Suppose you found a way to get another 1-2% edge on the casino by raising your bets when you have better odds and lowering your bets when you have worse odds?

Odds Of Winning Blackjack Hands

For example, if you had a deck with nothing but aces and tens in it, your chances of getting a natural (and the corresponding 3 to 2 payout) would be much greater, wouldn’t it? So it would make sense to bet more in that situation.

On the other hand, if all the aces in the deck have already been dealt, it’s impossible to get a natural, which means you should lower your bet.

It turns out that each card that’s dealt out of a blackjack show affects the odds by a certain amount. By tracking the ratio of high cards versus low cards that have already been dealt, a card counter can raise or lower her bets in order to take advantage of favorable situations.

Calculating Blackjack Probabilities

By doing so, the counter can actually gain an edge over the casino. This is mostly the result of putting more money into action when the odds are good, but some card counters also make strategy adjustments based on their count, too.

Odds Of Winning Blackjack At Casino

Summary

This page provides an introduction to blackjack odds. Many other pages on this site go into more details about the rules variations that increase or decrease the odds in the players and the casinos’ favor. The most important things to remember are that you should always play using basic strategy, in order to minimize the house’s edge, and also to avoid playing 6:5 blackjack games.