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
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
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).
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.
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.
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.
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.
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.
1: Mastering the numbers allocated to each card on the table.
Point of Values:
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).
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.
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
2: The Running Card
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)
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.
3: Running Count in Multiple Decks: “True Count”
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
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.
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
True Count Deviation:
4: The necessity to alter your bets depending on the actual count value.
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.
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.
Burton, Bill. Blackjack
Card Counting. 8 March 2017. Article. 15 January 2018.
David. What is the mathematics behind card counting in Blackjack? 18 October
14 January 2018.
Snyder, Arnold. Big Book
of Blackjack. Cardoza Publishing, 2013. Book.
Wattenberg, Norm. Modern
Blackjack Second Edition. Lulu.com, 2010. Book.
What is Card Counting? 10 September 2000. Article. 14
How to Count Cards. 2 February 2017. Article. 14 January 2018.