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Blackjack Math – A Complete Guide

Blackjack Math – A Complete Guide

Do you want to know the math behind blackjack? This article gives you all the information about blackjack math.

Blackjack is a game in which everyone plays against the house. With our cards, we must reach 21 or a value higher than the dealer without going over without winning. We will instantly lose our stake if we add more than 21 or less than the dealer. Following the placing of the bets, each player receives two visible cards, while the dealer receives just one. 

Talking about Blackjack math, there are lots of things and we are here to explain everything in detail so that you can use it as an advantage while playing blackjack. Therefore, continue reading below without wasting any more time. 

What is Variance

Variance is a concept that we all frequently hear but may not completely comprehend. By definition, it is only the discrepancy between the benefit anticipated and the outcomes obtained. You should have lots of card counting practice to master blackjack mathematics. Let’s imagine, for illustration purposes, that you are engaging in a respectable counting game and your hourly EV is $25.

You anticipate making $2,500 from your 100 hours of playing. Your logs reveal that you are barely $2000 ahead. This demonstrates that you are $500 below your expected value, or EV, which is the VARIANCE of what you would anticipate winning. On the other hand, you may always be $500 ahead of the EV.

What is Standard Deviation (SD)

A standard deviation is defined as the amount or frequency by which an outcome deviates from the average. Standard deviation and variance are related concepts (SD is actually the square root of variance).  You can evaluate if you are playing a profitable game or how much money you need to bring to a session by calculating the variance you have in a game and the SD for any specific game at all stakes.

What is N-Zero (N0)

N0 is something that isn’t commonly considered, especially by rookie players. Theoretically, it takes N hands to go ahead by one standard deviation (4*N0 gives you the hours needed to get ahead by 2 SD). The same set of rules and betting/playing methods must be followed in order to provide the most accurate evaluation of N0. Reverting to the $25 EV per hour example from before, we may get our N0 using the following formula: N0=Variance/EV2. You will need blackjack math practice to understand this more.

What is Certainty Equivalence (CE)

This is the end result of taking the projected win rate and changing it to reflect the risk level relative to the available funds and level of risk tolerance. This will demonstrate if the game is “worth playing” given the size of your bankroll. 

Due to your limited bankroll, even though you have $100 in EV, your CE may only show that the game is worth $50. You might even reach the point where your CE is in the negative range, which means you are significantly overspending your bankroll. The fundamental formula for calculating CE is: CE = EV-((bet size*Standard Deviation)/(2*Kelly factor*BR))

Blackjack Math on Splitting Eights

Imagine that you start with a pair of eights. In exchange for avoiding having to start with a hard 16, you must lay another bet, which is worthwhile. On each of your eights, you are dealt another card. The cards on this list are extremely helpful for an eight. An ace, two, three, nine, ten, jack, queen, or three of a kind all place you in a favorable situation. 

Eight of the 13 cards are in this hand. A hard 16 is preferable to anything from a four to seven. Thus, splitting cannot potentially put you in a worse position than playing it as a hard hand. Another split is possible if you receive eight more. This is why blackjack math is very important to understand.

Blackjack Math on Splitting Aces

There is the math behind blackjack splitting aces. Starting with two aces gives you either two or twelve cards. Both of these are undesirable beginning totals. However, you have a chance to significantly improve when you divide aces. You may add up your total to 21 with any card from 10 to King. A soft 17 or greater is achieved with a six through a nine. 

Only cards two through five don’t really assist you, and even with each of these you still have a soft hand. You’ve still got a chance to triumph. Once again, getting eight of the 13 possible outcomes greatly improves your hand.

Blackjack Math on Bets

Calculating how much you should bet when playing blackjack is another task for which blackjack math is useful. And figuring this out is really rather easy. When playing blackjack when the house has an advantage, you should place the smallest bet feasible. This implies that you must always place a minimal bet at the table when playing blackjack without counting cards. The casino still has the advantage even when you’re playing a strategy card. Though it isn’t a significant edge, it nonetheless exists. This translates to greater bets equaling higher losses.

When you have an advantage, you should bet as much as necessary, depending on the amount of your bankroll. In real life, it might be challenging to constantly place the smallest or largest bets based on the circumstances. However, you will discover how to accomplish this as you get more card counting knowledge.

Blackjack Math on Counting Cards

You must contend with a house edge even if you utilize a strategy card. As a result, even if there is a slight house advantage, you still lose money when playing blackjack.

However, you may make this work in your favor and get a slight advantage over the casino by using math. Card counting is a method to do this. Card counting is merely a technique to utilize math to play with an advantage, even if it may initially appear difficult. When you have an advantage, you increase your bets based on the high and low cards that have been played.

You should gain greater card counting knowledge if you play blackjack. You may gain from it every time you play because it’s not as difficult as you probably believe. To utilize good card counting techniques, understand how to do it. You can also do the card counting practice online. The card counting practice is important if you want to win in a blackjack game. Once you learn the card counting math, then you will become very good at blackjack. The math behind blackjack is simple once you learn about it.

Probability of exceeding 21

To determine the likelihood of exceeding 21 we must determine the likelihood of exceeding for any hand, which requires hand-by-hand analysis. Let’s say the worth of our hands adds up to, 12:

  • 12 + AS = 13
  • 12 + 2 = 14
  • 12 + 3 = 15
  • 12 + 4 = 16
  • 12 + 5 = 17
  • 12 + 6 = 18
  • 12 + 7 = 19
  • 12 + 8 = 20
  • 12 + 9 = 21
  • 12 + 10 = 22
  • 12 + J = 22
  • 12 + Q = 22
  • 12 + K = 22

As we can see, there are four scenarios in which we start off with more than 21. With a 12 value, there is a roughly 30% probability that we will go beyond 21.

Doubling Down Blackjack

Tips to win with Blackjack Math

Using Cards

You can make judgments since blackjack employs a standard deck of cards. With the exception of a few side bets in select countries, blackjack games do not employ the suit of the cards. Therefore, the card ranks are the only thing that should concern you.

This holds true regardless of the number of decks in the blackjack game you are playing—1 or 8. Each deck has 4 cards from each of the 13 tiers. In other words, each deck has four sixes and four eights. Being aware of the cards you’ve seen and the ones still in the deck or shoe makes this knowledge handy. You can play blackjack more skillfully if you have this knowledge.

This suggests that 31 of the remaining 50 cards will help you make a hand with a total of 17 to 21. Additionally, you cannot burst with any card in the deck. Due to this, double on an 11 may be quite rewarding. Each time you play a hand at the blackjack table, you may apply basic math like this.

House Edge Math

The casino’s revenue from each blackjack game and your chances of winning are both determined mathematically. According to the regulations and how you play your hands, each blackjack game has a basic house edge and a base return to player %.

The percentages for the house edge and return to the player indicate how much money you may anticipate losing and how much money the casino expects to earn. Between the house edge and 100 percent, there is a percentage called the return to player. In addition, the return to player percentage’s margin of error is expressed as a percentage between 0 and 100.

Knowing that there is a 3% house advantage lets you know that there is a 97 percent return to the player. Alternatively, if you know that the return to the player is 98 percent, you will also know that the house edge is 2 percent. These figures are significant because the best probability of winning in blackjack is achieved by playing the games with the highest return and lowest house edge.

Insurance Math

When playing blackjack, you should decline the insurance offer. Good blackjack books and articles frequently offer this information. The math demonstrates that it’s a lousy bet, thus it’s sound counsel. Insurance in blackjack isn’t actually a part of the standard game. This is a covert side bet that appears to be associated with the standard blackjack game. Whether the dealer has a card in the hole worth 10 points or not is the subject of the bet. When the dealer has a 10-point card, the bet pays 2 to 1, but it loses on all other cards.

The chances of the card having a value of 10 points are 4 to 9. The deck has 9 ranks of cards that are not worth 10 points and 4 ranks of cards that are. Moreover, 9 to 4 against is another way to put it. Take a look at the odds (9 to 4) and how much the bet pays (2 to 1). 

The bet does not pay an amount equal to or more than the likelihood that the down card will score 10 points. For the bet to be considered fair, the pay must be 2.25 to 1 or the odds must be 8 to 4. With more blackjack math practice, you can become stronger.


Blackjack math begins with a fundamental knowledge of the cards used in the game and how they are employed. The following stage is to comprehend return to player and house edge and how they affect how much you win or lose. When you comprehend the math underlying these concepts, you will utilize it to choose the blackjack games with the best rules, which will ultimately increase your chances of winning. This all leads to using math to determine the ideal blackjack strategy moves.

The 13 ranks of cards in the deck are where the power of blackjack math begins. Your outcomes will immediately improve once you realize how to use this knowledge. Start by using the blackjack mathematics chart, then learn how to count cards. You may develop an edge every time you play if you practice consistently.

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