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Stephen McDouglas
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September 3, 2021
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Our Associate Stephen is a former poker player from Las Vegas, Nevada, and online media editor. His in-depth view of the US online poker industry and his skills in playing the game are allowing him to write high-class and well-researched articles about regulation, legalization and poker events. He has an M.B.A in math and worked for several Universities.
Our Associate Stephen is a former poker player from Las Vegas, Nevada, and online media editor. His in-depth view of the US online poker industry and his skills in playing the game are allowing him to write high-class and well-researched articles about regulation, legalization and poker events. He has an M.B.A in math and worked for several Universities.

Blackjack Probability

Blackjack is one of the most popular classic casino games, and players can count on excellent odds. It features a low house edge, and it is one of the most attractive aspects for blackjack players. You can increase your chances of winning thanks to your skills, not only by relying on luck. Therefore, a proper strategy and skills can make a real difference between losing and winning. That is another reason why blackjack is so famous in casinos. The ability to predict the likelihood of receiving a certain card can bring you an advantage over a dealer. In this article, we will deal with the blackjack probability and ways you can increase your chances of winning in an online casino.

Everything you need to know about Blackjack Probability
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  • It can help you develop proper strategies

  • Calculate the probability of losing streaks

  • Estimate how a removed card can affect your odds

Blackjack probability: The mathematics behind the game

If you can calculate the chances of getting a "small" or "big" card, it can help you make better decisions. For being successful in the long run, knowing the house edge and the odds is not enough. You should have a reliable plan and establish a proper strategy to get better results. Some players rely on card counting techniques such as speed count, but you can use probability as your weapon.

Probability deals with the likelihood of a particular event, and it is a very popular branch of mathematics. It applies to many industries, and it became inevitable in the casino world for performing casino games analyses. The probability formula is the foundation for determining the outcome of an event, and it is a ratio between the number of paths and possible events.

Thanks to this formula, you can easily determine the probability of getting the ace of spades. Knowing that there is only one card of that kind in the deck and that the standard card deck contains 52 cards, the probability of getting it is 1/52, or 1.92%. The likelihood of any event is between 0% and 100%, and if you know its exact percentage, you can drive your decisions upon it.

Speaking about blackjack, the following two terms will help you understand the game better. The odds you may get under particular circumstances during the game are known as the positive and negative expected win rates. Professional blackjack players also speak of another term – true odds. It is the case when the probability percentage matches the payout of a particular bet.

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If you know your chances of winning, you can easily determine the probability of losing the game as well. This can provide you a good insight into a position you are currently in. For example, your chances of losing when having a total of 12, 13, or 14 in hand are 31%, 39%, and 56%, respectively. Of course, when you have 11 or fewer, your chances of losing are equal to zero.

Remember, your ultimate goal in a blackjack game is to beat the dealer by getting a higher total. However, you should pay attention not to go over 21, as you will lose. As you have two options during gameplay, hitting and standing, the probability can help you make a better decision for the next move.

This drives to a conclusion that the chances of busting increase when having a higher total in your hands. Consequently, when you have 19 or 20 in your hands, you will likely lose if hitting another card. Therefore, standing would be a much better option in this case. If you wonder what the probability of getting a blackjack is, we have an answer. The figure stands at 4.77% for the two-decks game, while the chances are slightly higher for a single-deck blackjack game – 4.83%.

Probabilities of different-length losing streaks in blackjack

As blackjack is the game with one of the lowest house edges, your chances of winning each hand are just below 50%. However, that doesn't mean that winning or losing streaks are impossible. Of course, entering a winning streak is every blackjack player's goal, but what about having a bad run?

The math says that the majority of streaks last up to three hands. Therefore, losing four times in a row or more is, statistically speaking, less possible. However, it doesn't mean they cannot happen despite the low probability. Let's check the blackjack probability table of losing streaks based on the streak length.

Streak LengthProbability of a Losing Streak
227.7%
314.6%
47.6%
54%
62.1%
71.1%
80.6%
90.3%

As we can see, the probability of losing five straight hands is as low as 4%, but it will inevitably happen at some point in your gaming experience. Therefore, it is crucial to handle the losing streaks properly. The first thing you should do is start reducing your stakes, so you can extend your budget. Eventually, it can give you more chances of getting back on the winning track. On the other hand, chasing losses is what you should avoid at all times. This way, you will not damage your bankroll even more and run out of your playing funds quickly.

Taking a break after five lost hands might be a sound choice as well. It can help you collect your thoughts and get back on the winning track. Remember, the ultimate goal is generating profits, so it's not a shame to walk away from the game.

The house edge for blackjack under review

The concept of a house edge shouldn't be underestimated when calculating your odds of winning a blackjack game. The house edge represents the built-in advantage that casinos have over players, ensuring they win in the long term. In other words, it is the percentage of each bet that a casino keeps as a profit, indicated in a long period.

The house edge is not the same for different variants of a blackjack game. For example, if the house edge is 1.20%, it means that on every $1000 wagered on that particular game, a casino would theoretically win $12. In other words, a player would lose $1.2 on every $100 wagered.

Other casino games have a considerably higher house edge, like roulette. A double-zero roulette has a 5.26% house edge, meaning that you would lose $5.26 on every $100 wagered. Suppose you spin the wheel 60 times per hour, it means you would lose more than $300 per hour. Of course, this is just a statistical percentage measured in the long run, and it doesn't imply that every player would lose this amount of money.

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How card removal influences blackjack odds and probabilities

Card removals can affect your odds of winning a hand in both directions. Particular card removals can increase the house edge but also boost your chances of winning. Generally speaking, the odds increase in your favor if smaller cards are removed from the deck. On the other hand, your chances of winning decrease when a larger card is dealt. Some people use card counting to estimate better their chances of winning. If you want to try it out, here is a table of the odds movements for each removed card.

Removed CardOdds movement
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%
Jack-0.51%
Queen-0.51%
King-0.51%
Ace-0.59%

Expected hourly loss and/or win

Another convenient metric that can help you estimate how much money you can win or lose over a more extended period is the Expected hourly loss/win. Of course, it can only give you insights into the estimated figures, which doesn't necessarily mean it will happen. Also, the results may hugely vary for a small number of sessions. Let's see how this works on a practical example.

  • You are a perfect basic strategy player in a game with a 0.5% house edge.
  • Your stake is $100 per hand, and you're averaging 40 hands per hour.
  • You stake $4,000 per hour
  • 0.5% of $4,000 is $20.
  • Your expected losses are $20 per hour.

If you are a skilled card counter, the estimation might be different.

  • You can get a 1% edge over the casino by counting cards.
  • You're playing the same 40 hands per hour at $100 per hand.
  • You stake $4,000 per hour
  • 1% of $4,000 is $40.
  • In this case, your estimated winnings are $40 per hour.

The blackjack basic strategy: Does it work online?

The Basic Blackjack Strategy is essential if you want to be successful in this game. Back in the '50s, a group of mathematicians developed the basic strategy to help players optimize their decisions. Again, it relies on the probability and calculates which player's decision is optimal at a certain point to generate profits. Therefore, it prevents you from making irrational decisions at a blackjack table, which is exactly what an online casino hopes you would do. Thanks to the blackjack probability charts that basic strategy provides, you can easily see what would be your optimal move in a given situation.

Since blackjack is a game of skill and not just a pure game of chance, this strategy works online as well. Of course, this strategy can help you become more successful in your blackjack gaming experience, but it doesn't guarantee you profits. You should also make sure to use the correct basic strategy developed for specific blackjack rules. Although it cannot guarantee you profits, a basic blackjack strategy can help you lower the house edge.

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Try It Out in Practice

As we already stated, understanding how the maths work in the blackjack game can increase your chances of winning. At this point, you should apply everything you learned from this article in practice. Sign up for one of our recommended online casinos, apply your strategy, and start winning at a blackjack table!

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Conclusion

Learn to Become a More Successful Blackjack Player
Since blackjack is a game of skill, you shouldn't underestimate maths and probabilities when playing at a blackjack table. Understanding the concepts and basic blackjack strategy can help you boost your chances of winning. Don't rely just on your luck, as you can develop blackjack skills and become successful in the long term!
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