1. Odds Of Winning With A 20 In Blackjack

Blackjack Probability Odds. Blackjack is actually one of the most popular games in the casino and also has some of the lowest odds of all the casino games, except casino craps of course. Generally their edge ranges from 1% to 15% depending on what variation of blackjack you are playing. Winning Blackjack takes luck and a relatively small amount of skill. The dealer relies as much on luck as the players do, so the odds of winning are pretty even. In most casinos, the advantage to the dealer is about one percent.

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.

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.

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%

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.

Odds Of Winning With A 20 In Blackjack

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 is unlike many other casino games because the player is actively involved in the outcome of his hands (rather than betting on a random event over which he has no influcene). As a result, a player’s chances of winning depend on not only the random outcome of the draw but also upon the decisions he makes during the game—to hit or to stand, to exercise options such as doubling or splitting.

Chances of Winning Blackjack

Throughout several rounds, the chances of winning each hand will also be skewed by the cards that have been removed from the deck. The player’s net loss or gain (the amount in money, rather than a tally of hands won or lost) over a session will be affected by how much he wagers, and at which times he elects to increase or decrease the wagered amount. Finally, house rules can be imposed to change the parameters of the game and restrict the player’s options.

With all of these factors in effect, it’s not possible to affix a specific number to all situations or all styles of play—but three figures are often cited:

• Most casinos expect each blackjack table to have a hold of about 20%—that is, they expect to be able to keep about 20% of the wagers made. Correspondingly, the average player can expect to lose about 20% of his stake over the course of every session.
• The “core odds” reduce the house’s advantage to 10.99%. Based on the assumption the player will elect to hit or stand by the same criteria as the house, the house will win roughly 10.99% more hands than the player.
• The net odds—which consider the amount of money won or lost rather than the core number of hands, generally work out to an 8.89% advantage to the house (given a two-deck game played by the most common set of rules).

An interesting, if somewhat premature, note on these figures is that the house expects to earn more than double (20% as compared to 8.89%) what the odds would seem to indicate it will and that these expectations generally hold. This demonstrates how the player’s decisions can affect the outcome of the game—and that the average player will lose more than double the mathematically probably amount because of uninformed decisions.

The basic blackjack, intermediate, and advanced blackjack strategies described in the blackjack strategy section of this site can further impact the odds. By using blackjack basic strategy consistently, the player can decrease the house’s advantage to less than 1%. By adding the intermediate and advanced strategies, a player can make the game completely even (hence fair) and, in rare situations, also turn the odds in his favour by a fraction of a percentage.

What are Odds?

In its purest sense, odds are the chances a given outcome will occur given the possible alternatives. The most comfortable metaphor is a coin toss: if a coin is tossed in a genuinely random fashion (nothing influences the outcome), it is just as likely to come up heads as tails. If it is tossed ten times, you can expect it to come up heads five times, and tails five times.

Granted, it is possible, even with true randomness, that the toss will result in heads ten times in a row—which is why odds consider likely rather than specific outcomes. In the long run, the mathematical probability will bear itself out in practice—if a coin is tossed 1,000 times, it is likely to come up heads 500 times (though, in practice, it will be plus or minus a few). Thus, it’s not necessary to spend several years flipping a coin million of times to determine the likely outcomes or rig a supercomputer to simulate the same—though some stubbornly have.

Casino games are carefully designed to exploit the odds, always taking advantage for the house: a player will never be paid a wager that is strictly equal to the true odds. A good example of this practice is roulette, in which a wager on a single number pays 35 to 1 even though the odds of winning are 1 in 37.

What are the odds of winning blackjack

Blackjack, however, foils the computation of odds based on random events because there are a number of influences that prevent it from being completely random—most significantly the player’s choices during the course of the game. In such cases, the odds are set to turn a reasonable profit from the average player. (Actually, they’re set to turn a reasonable profit from the reasonable intelligent player, an exorbitant one from the average player, and flat-out milk a “sucker.”) This is why an attentive player who makes the right decisions can come out ahead.

The odds of the hand’s outcome are determined not only by the initial hand dealt and by the number of hits that are added. This can vary greatly, because a player can take as many or as few as he desires—a player may opt to hit every hand he is dealt until it exceeds 21 and lose 100% of the time.

We can, however, be reasonably certain of the dealer’s behavior, as he is forced to play by certain rules, regardless of his instincts, superstitions, or desires. Most often, the rules require the dealer to stop taking hits when his hand reaches a total of seventeen or greater, and no sooner. Before the cards are dealt, it’s possible to predict the chances that the dealer’s hand will have the following outcomes.

Blackjack win percentage

All the totals for hands remain equal—so a player’s 20 will beat a dealer’s 19 equally as often as a dealer’s 20 beats a player’s 19, and the dealer will bust as often as the player while the other stands on a viable hand. The only remaining difference is that the dealer will bust of the instances in which the player busts—which is 33.15% likely to happen in 33.15% of the time, for a core odds value of 10.99% of all hands played.

These odds are computed according to mathematical probabilities. More detailed information is available on the blackjack hand calculator post.

The outcome of the player’s hand, meanwhile, will depend on the way his hands are played. If he chooses exactly the same course as the dealer, the outcome of his hands will be exactly the same as is shown above. If he plays according to a different set of rules, the results will be different, and by comparing the two tables, that player’s individual likelihood of winning can be computed. If however, the player is erratic, and he chooses to play his hands differently each time with no predictable rationale, no mathematical model can be used to compute his chances of winning.

Determining the core odds

The “core odds” of the game assume that the player will follow the house rules for hitting his hands. In this example, to stop taking hits when his hand reaches a total of seventeen or greater, and no sooner. In this case, all things seem to be equal, and the player should have a 50% chance of winning or losing each hand. This would be true only if the player’s wager was returned the dealer busts his hand but one rule of the game that is never varied is that a player who busts loses his wager, even if the dealer busts afterward.

Again, the core odds shown here apply only to a player who strictly adheres to the same rules as the dealer in playing his hands, which is clearly not the best approach. The strategy section of this site will demonstrate a system that can virtually eliminate the house’s advantage over the player—and the intermediate and advanced sections will turn the tables further in the player’s advantage.