Blackjack Probability

Posted : admin On 3/29/2022

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Mathematical Studies Project Probability of Blackjack Content Page Page Statement of task 2 Introduction 3 - 4 Data collection 5 - 6 The four Blackjack strategies 7 - 15 Conclusion 16 Bibliography 17 Statement of Task This project aims to investigate how mathematics works in one of the most popular card games in the world - Blackjack. Probability is calculated on the basis of known data but cannot be used to predict exact outcomes, like the outcome of a hand in the game of blackjack, for example. It simply shows you the likelihood of an event happening, based on the knowledge of the number of desired outcomes and the number of all possible outcomes.

Odds Of Getting A Blackjack
Blackjack Probability Worksheet

The bust probability is calculated by dividing the number of Dealer's busted hands to the total possible blackjack actions. Blackjack actions is a parameter that counts everything: Busted hands, pat hands (17 to 21), blackjack hands, and draws or hits to the first 2-card hands ( incomplete hands ).
In this course, you'll analyze three specific casino games: blackjack, craps, and poker. And, while you're learning how to master these games, you'll also strengthen your skills working with many foundational probability topics including probability trees and conditional probability.
Tom from Communication Group 34 takes you through the maths of blackjack!Hub Video: Video: https://www.youtub.

Probability is measuring the possibility of occurring a particular event. Probabilities are usually expressed as a percentage. However, fractions and odds can also denote it.

Blackjack is a purely mathematical game and is all about probability and odds. Blackjack Hall of Famer Edward Thorp was among the earlier players who realised this phenomenon in the 50s’ and created a statistical simulation to increase his chances of winning.

In the short run, it is almost impossible to predict a result, but in the long term, outcomes can match with prediction. So, today, let us explore the ways of predicting Blackjack probability. Stay with us to know more on this subject.

Understanding Blackjack Probability

Probability is the division of mathematics that deals with the occurrence of a specific event. It is always a digit between 0 and 1, where 0 denotes, the event will never happen, and 1 indicates, the event is bound to happen. Probability can be expressed in odds. For example, an event with a 50% probability has 1 to 1 odd or even odd.

Calculating probability in odds is useful in Blackjack, especially when you want to know whether you have the edge over the house or not. For example, you, having a 1 to 1 odds in a $1 bet, means you have an expected value of zero so, you won’t gain or lose any money over a long time.

Every casino game has a negative expected value. That is how casinos stay in profit. You cannot beat the house in the long run. However, you can study the previous rounds and make a positive expected value for yourself in one particular bet. That’s how card counters operate and make a fortune in Blackjack.

Independent and Dependent Trial

Before moving into all the calculations, let us give a brief introduction about two types of contrasting events, that can be seen happening in a typical casino game. An independent event is one that does not affect the upcoming events. Like the dice toss in Craps, the probability of throwing a 2 in a six-sided dice will always be ⅙. It doesn’t change with any previous outcome.

On the other hand, in the case of dependent trials, probability changes with each round of bets. Blackjack is the prime example of a dependent trial. With each card dealt, the probability of getting any of the remaining card increases.

The Probability of Getting a Blackjack

Naturals are the most potent combination you can get. With a natural in your disposal, not only it ensures your win in most of the cases, but you’ll get 1.5 times your original bet. This is why understanding the probability of getting a blackjack is essential.

If you know the number of card decks in play, you can effortlessly determine the possibility of receiving a natural. For this purpose, you have to multiply the probability of getting an ace with the probability of pulling a ten-valued card, i.e., 10, J, Q, K. You also have to double up the result to get the actual probability. There are two probable combinations of the card in a Blackjack hand, for example, A-K and K-A.

4/52 is the probability of getting an ace while the possibility of pulling a ten-valued card from the rest of the deck in 16/51. Therefore, the probability of getting a natural in the first hand itself is

2*P(ace)*P(10-valued cards)
2*4/52*16/51 = 0.0482 or 4.82%

Difference Between the Probability of Blackjack and Other Casino Games

The main difference between Blackjack and other games is players can get a strategic edge in Blackjack. With each card being dealt with, the composition of the remaining deck changes. If someone with an identical memory can memorise the cards which have already been dealt with, then he/she can have an idea about the cards that are on the way.

For example, if in the first couple of hands, all four aces are out, then your probability of getting a natural is 0. In the same way, if you are getting lower value cards at the start of the game, then you can assume higher value cards are coming and can plan your moves accordingly.

However, when you play Roulette or Craps, the odds won’t change with every outcome. That’s because Roulette wheels will not eliminate a number that has already come previously. You will always have an equal probability for all 38 numbers are coming up.

Odds Of Getting A Blackjack

Final Thoughts

Blackjack probability is an amusing yet vast subject with no end of topics to discuss. In this article, we could barely scratch the upper surface. This is just an aerial view of the subject. If your ultimate goal is to get success as a card counter, you can read many exciting journals on this topic.

However, for most people, card counting can be a daunting task. It may sound easy in theory, but in reality, only a fraction of our popularity can remember cards in a fast-paced casino game. Casino’s strict monitoring policy to prevent card counters has made the task even more challenging nowadays.