Contents

Rationale: 1

Introduction: 2

Step 1: Mastering the figures

assigned for each card in a deck. 4

Step 2: A Running Card. 5

Step 3: Multiple Decks

Running Count: “True Count”. 8

Step 4: The necessity to

alter your bets depending on a actual tally value. 10

Conclusion. 10

Works Cited. 11

Figure 1Different cards with

their weighted values. 5

Figure 2 Calculating a

running card from Weighted values. 7

Figure 3 Round 2 has a

running card sum of 1. 7

Figure 4 Round 3 has a

value of 1. 8

Calculating Blackjack Cards

Name

Institution

Date

Rationale:

As

part of this semester’s curriculum, students must choose a topic that meets the

Internal Assessment provisions in line with Mathematics. This paper aims at

demonstrating how analytical principles of probability and statistics correlate

with the controversial card counting tricks used in Blackjack gambling. The article is broken down into steps that

illustrate how players employ probability and statistics to calculate odds when

dealing cards. However, the underlying concepts of card counting are not as

simple as many might perceive, it demands a lot of practice, skill and hard

work to master the fundamental principles. This topic is selected for study

because it is intriguing to learn how gamblers earn a lot of bucks from

blackjack by merely applying simple mathematical skills. No wonder most casinos

nowadays prohibit card counting in their Blackjack games (Snyder).

This

article will illustrate that the mathematical skills used in blackjack marry

well with the basics of Statistics and Probability taught in the Math SL course.

Moreover, the paper will not only outline the critical steps involved when

counting cards and predicting moves but also use pictures and real-life

examples to give a visual impression of the entire process. At the end of the

paper, the reader should acknowledge and marvel at the Blackjack skills that

players use to calculate probabilities in their heads at high speeds while

paying attention to the game.

Introduction:

Blackjack

is a universal game witnessed in casinos, and people make a living out of it.

The game, commonly referred to as ‘twenty- one’ has risen to fame and caught

the attention of many gamblers across the globe. Hitherto it is preferred as

the most lucrative banking game across Europe and America, and its contagious

charm is spreading fast to Asia and Africa. People are trying their luck with

this bet because it is easy to learn and it assimilates many participants.

However, the gambler usually competes against the broker but not against the

other competitors. To succeed, one needs to make sure that his or her cards achieve

a better value against the broker amid a specific set of rules. With an

aggregate of 52 pieces on a level, the participant must beat the broker at attaining

21 marks using the opening two cards. Nonetheless, the value should not surpass

21 mark. Smart players who have learned the art of forecasting this game end up

collecting vast stacks of cash, and they are not willing to share the secret

and math behind it. Thanks to Math IS, you are going to be enlightened.

Using

Statistics and Probability mingled with a high level of intuition, a player can

formulate a mental algorithm that will help them calculate their next moves and

judgment on whether to stake more or less. Gamblers achieve this by totaling

the undealt cards on the deck applying a probability system to foresee if the incoming

card can be sufficient enough to challenge the opponent (Wattenberg). Some

companies have barred gamblers from tallying cards in their casinos. Even

though such practices are legally acceptable, corporations are justified in

denying such services to anyone in a bid to balance tradeoffs. In other terms,

counting is not by any means a form of cheating but casinos value equal grounds

that are free of prejudice against the dealers.

How

does this card tallying circus work? Well, a gambler knows that if the value of

Aces and Tens dealt are less than those remaining on the table (commonly

referred to as Shoe), he or she will be handled more blackjacks (which return a

profit of 150% depending on one’s stake). Consequently, the dealer is expected

to bust or in other words overshoot the 21 points target infrequently (Burton).

Contrariwise, if the sum of minority cards on the table is higher, the competitor

gets lesser number of blackjacks, and the broker is less prone to busts. A

competitor can use these scientific realities to stake more top gambles when high

cards left in the shoe are more or spread their risks by staking low when low

cards left are more. Nonetheless, applying these principles in real life is an

uphill task, it takes a lot of effort and determination to master these

concepts and effect than in real life.

For a practical card

counting ordeal, this paper highlights the four significant steps involved:

1. The first step is to master the score values assigned to

each card of the deck.

2. Then, one needs to be aware of the “Running-Card”

which is substantial when evaluating the next card to be dealt

3. Third, use the data acquired in step 2 to determine the

“true-count” of cards for individual deck.

4. Use the actual count number

as feedback in each step to predict your future bets.

The

article has summarized the primary and most essential steps undertaken to tally

cards efficiently during a Blackjack betting game. Now, the subsequent section

will elaborate a detailed explanation of what each level means and what it

entails in a clear and logical manner.

Step

1: Mastering the numbers allocated to each card on the table.

Point of Values:

1.

Low cards: these cards represent a score

of +1. They include cards 6, 5, 4, 3, and 2. These tickets are favorable in the

hands of brokers, and a score of 17 and below prompts them to take a hit.

Furthermore, the broker is unlikely to get a bust (value of more than 21) if

they have more low cards at their disposal (www.wikihow.com).

2.

High cards: these cards represent a value

of -1. They comprise of maps Ace, King, Queen, Jack, and 10. These cards mostly

favor the contestant throughout the game. When the card table has more 10s and

aces, it will undoubtedly increase the chance of a competitor obtaining a

“Pat hand” (17 points or over) or the natural 21.

3.

Neutral cards: in the Hi/Lo carding strategy,

these cards represent a null value; they include cards 7, 8, and 9.

The Hi/Lo system is the

most accepted method of counting cards. It allocates values to every individual

card such that the aggregate of the 52 cards in the box is zero. In other terms,

the deck contains a balanced spread of high or low cards in the pack.

Figure 1various cards and their weighted values

Step

2: The Running Card

After

learning the values allocated to various high, low and impartial cards and

getting acquainted with all card types, it is essential to know how these cards

are added or subtracted in every shoe as the game goes along. To make the

counting of the cards faster and simpler to memorize, the paper proposes an

“easy speed tip”: the “plus one” for low cards assumes a

value of “one” whereas the “minus one” high cards of are denoted as

“M-one.” The neutral cards maintain their state and represent a zero number.

For instance. Queen = M-one, 8 = nothing, and 2 = one. Cards are spread from a lone

card deck and added and subtracted as the following:

– 1st card: Ace (+1), total: M-One

– 2nd card: King (+1), total: M-two

– 3rd card: 8 (0), total: M-two

– 4th card: Queen (+1), total: M-three

– 5th card: 4 (-1), total: M-two

– 6th card: 2 (-1), total: M-one

– 7th card: 3 (-1), total: even (say anything)

– 8th card: 7 (-1), total: One

– 9th card: 9 (0), total: still One

A more complex and

illustrated example can be represented below

Figure 2 Using Weighted values to calculate a running card.

For this round, we can

see that the running card has a sum of 0 (-2+1+1+0 = 0)

Figure 3 Round 2 has a running card sum of 1

For our second round, the

running card is +1 (0+0+0+1 = +1)

Figure 4 Round 3 has a running card of 1

In our last round, the

running card is also +1 (0+0+0+1 = +1)

From

these three examples above, it is clear to see that, when it comes to counting

cards, the player should count the running card for every single round, and

repeat the process until the game is over or shuffled. However, recent

blackjack games use two decks of cards, and it becomes a risky affair to start

betting using the skills discussed above. Two decks can make it difficult for

you to evaluate your assumptions and probabilities when staking your money

(Shi). In the past, when people played blackjack on a single deck, card

counting was a tranquil task for experts. They could bet with certainty because

their probabilities were relatively accurate and safe. Based on one deck, when

the calculated running card has a positive sum all through the rounds, a gambler

is more advantaged, but when the figure turns the other way round, it is the

dealer that benefits more. Therefore a smart gambler should always memorize and

keep track of such values when staking to avoid losses and gain profit.

Step

3: Running Count in Multiple Decks: “True Count”

Most

gambling clubs have installed compound decks in a Blackjack game as a stratagem

to complicate the prospects of card-counting. But some professionals have found

a way to maneuver through numerous tiers by employing an additive plan known as

the True Count tactic. This new algorithm is a supplement and works in tandem

with the previous concepts to enable players to count cards in multiple decks

(www.blackjackapprenticeship.com). The professionals borrow the information

collected in the initial steps discussed above and translate them into the

True-Count analogy.

Having

a counting-card sum of +5 in a game with six decks undealt is an entirely

different case to when you have an amount of +5 with single layer to be dealt.

For the players, the value strength of high cards measured up against that of

low tickets matters a lot, but this factor is dependent on other factors that

one has to consider. For instance, with the counting-card value reads +5, there

will be not more than one high card in each of the undealt five decks, meaning

that a card counter still will not have the ability to favor them. In the case

of a single pack with a counting-sum of +5, the undealt deck will have five

other 10s or Aces within the 52 pack in the box. This information regarding

True-Count is precious to any player.

The following formula is

used to evaluate the True-Count:

When looking at a situation

whereby the counting-card reads +8 with only two decks yet to play, for instance,

one could convert this data into equation form:

Looking at another

example: +10 when five decks yet to be dealt:

Bonus Tip: How a player

can evaluate his/her edge in a game.

In

any manifold deck game, the value of true-count is handy since it informs the

gambler prevailing chances of gain at any instance of the game. One can obtain

the true-count number in manifold decks merely by dividing the existing running-count

number against the remaining levels that are undealt hitherto. For instance, a

universal six level game can shift the house-edge by a half percent in favor of

a gambler for individual true-count values. A true-count value of one can

basically square out the game by erasing the house-edge. A true-count value of

two will shift the house-edge by a margin of a half percent towards the gambler

hence the luck plays to his or her gain. A true-count value of three will imply

that the player benefits from an upper edge of one percent. However, the rules

employed and the number of cards dealt before a reshuffle can alter true count

benefits.

True Count Deviation:

Step

4: The necessity to alter your bets depending on the actual count value.

Throughout

the game, it’s imperative to when the house-edge flips into the gambler’s favor

by establishing a running-count and a corresponding actual count. Players who

do not align their game concerning the shifting edge values are prone to

unnecessary exhaustion with little or no benefits. Capitalizing on the exact

count information means raising the stake when edge values flip to your favor

and folding hands when the situation is not favorable. In other terms, increase

your bets when the actual count values rise and stake low when the costs fall

to a neutral or negative. However, these strategies can somehow get complicated

if one lacks sufficient knowledge and underlying principles in betting.

Blackjack gambling can indeed cause severe damage to your bankroll if you don’t

correctly understand laws of probability and statistics.

Conclusion

Blackjack

is a productive game that has won its place in the hearts of many gamblers.

Veteran professionals who have mastered the gambling art hitherto have

collected vast sums of money from this game by merely using accrued skills and

intuitions. The most intriguing thing about this game is how it applies

mathematical concepts: statistics and probability to predict moves and regulate

stakes. The paper has outlined the fundamental steps required to achieve this

process while highlighting how mathematical concepts blend in. Be warned that

irresponsible betting can damage one’s bankroll regardless of the one’s prowess

in betting strategies. This paper recommends a further look at how statistics and

probability influence reasoning and decision making in other games.

Works

Cited

Burton, Bill. Blackjack

Card Counting. 8 March 2017. Article. 15 January 2018.

Shi,

David. What is the mathematics behind card counting in Blackjack? 18 October

2014.

Article.

14 January 2018.

Snyder, Arnold. Big Book

of Blackjack. Cardoza Publishing, 2013. Book.

Wattenberg, Norm. Modern

Blackjack Second Edition. Lulu.com, 2010. Book.

www.blackjackapprenticeship.com.

What is Card Counting? 10 September 2000. Article. 14

January

2018.

www.wikihow.com.

How to Count Cards. 2 February 2017. Article. 14 January 2018.