Theoretic Methodology

Theoretic probability is based on math induced into logic thinking. for instance, if there were three
doors. You have a 3:1 chance of picking the door with a prize. When one door is eliminated your chances
change to 2:1. In theory, it is obvious that the door you least expected to win is the winner because the
probability of winning is greater than before. There is a 50% chance of winning, but the chances of the
same number reoccurring more than once are the chance you are willing to risk when the odds are in
your favor. Card counting is a method used to determine probability theoretic win. When used with true
count of the deck and counting cards will give you a better game strategy against the house. Casino
games is a game of chance. The house has at least a 2% advantage on all the casino games.

In the casino game, Blackjack, there is a procedural process of systematic method of how to bet from
the time you sit at the table until you want to leave. To play, the player must place a bet on the table.
The dealer then deals the cards. The player first initial thought is to see if he has a blackjack (21). Next,
the player must look to see if the dealer has an ace showing. If the dealer does not have an ace showing,
the dealer pays the player 2 to 1. If the dealer has an ace showing, the player should ask for even money
and the bet is paid 1 to 1. If the dealer and player both have blackjack, the bet pushes and nothing
happens. If the player does not have a blackjack, ask yourself if the dealer does? If dealer has an ace
showing, take insurance. Bet ½ your original bet-to-bet insurance. If the dealer does not have blackjack
and you have a busting hand (12 or more), surrender ½ your bet. If the dealer does not have blackjack,
the player hits. If your hand bust, the dealer will take your bet. If you have a good hand and decide to
stand on your hand, the dealer will draw to 17 or more. If the dealer draws over 21, the dealer will pay
you even money. If your hand is higher than the hand, the dealer will take your hand and your bet loses.
Blackjack can be a fun game to play. Your chances of winning lots of money are determined by how
much you want to spend. In most cases, it is best to leave the table while you are ahead. Good luck!

BLACKJACK

The game of Blackjack is played with 1, 2, 6 or 8 decks of cards. An ace is counted as 1 or 11, 10, J, Q and
K is counted as 10 and everything else is counted at face value. The player is dealt two cards. The dealer
gets one face card up and one face card down. If the dealer as an Ace showing and the player does not
have blackjack, insurance is available. If the dealer has blackjack, the player will automatically lose/push
the bet or win insurance. If the player has blackjack, he will win 3:2. The players have a chance to wager
their bets before the dealer acts. The dealer will then compare hands. If the player goes over 21, he
loses. If the player stops with a hand of up to 21, the dealer will take the cards until they reach 17 or
more. The person who comes closest to 21 wins. If the dealer has over 21, you win.

Game strategy is a known mathematical problem, given completely random cards using basic strategy.
Basic strategy is the most proven game by running simulations on a few million hands and analyzing
results. The average house advantage of basic strategy uses surrender, doubling down and splitting
based on the number of decks used in the game.

Number of Decks House Advantage

Single Deck 0.17%

Double Deck 0.46%

Four Decks 0.60%

Six Decks 0.64%

Eight Decks 0.66%

A counting system can generate an advantage. The casino’s greatest advantage is that the player goes
first (if both bust, the casino wins). The player’s greatest advantage is that the dealer must hit 12 – 16
(making the hand bust). When there are enough high cards left in the deck, (10 – 35% of the time), the
player’s advantage outweighs the casinos advantage. There is a certain strategy decision that will
increase the advantage that depends on the number of cards remaining in the deck.

Value of Cards in Single Deck Blackjack Basic Strategy

Removed Card Change in Player Expectation

2 +0.40%

3 +0.43%

4 +0.52%

5 +0.67%

6 +0.45%

7 +0.30%

8 +0.01%

9 -0.15%

Ten -0.51%

Ace -0.59%

The betting correlation is the advantage gained from increasing the bet at the right time. A playing
correlation is the advantage gained from playing the correct strategy at the right time. There are levels
involved in counting systems. The level is how many different values are in the counting system. A side
count determined by counting cards on the side. Some counts are modified to consider opportunities to
place side bets such as dealer’s bust.

COUNTING SYSTEMS

Strategy 2 3 4 5 6 7 8 9 Ten Ace

Hi Lo +1 +1 +1 +1 +1 0 0 0 -1 -1

Hi opt I 0 +1 +1 +1 +1 0 0 0 -1 0

Hi opt II +1 +1 +2 +2 +1 +1 0 0 -2 0

KO +1 +1 +1 +1 +1 +1 0 0 -1 -1

Omega II +1 +1 +2 +2 +2 +1 0 0 -2 -1
Zen +1 +1 +2 +2 +2 +1 0 0 -2 -1

The Hi Lo Basic counting system is the most basic balanced system out there. It requires running count
to true count conversion. It uses a generic strategy that continues throughout the shoe. This system has
a .3% player advantage over the house depending on the number of decks, cut penetration and level of
skill.

The KO counting system is the simplest un-balanced counting system. The initial running count for the
number of decks is 2 = -4, 6 = -20 and 8 = -24. The pivot points for the number of decks are 2 = 0, 6 = 4
and 8 = -6.

Casinos implements several techniques to identify counters. Some of the techniques used are for
dealers to call out sudden large bet increases or for dealers to call out extremely aggressive plays such
as doubling on hard 12 or splitting 10s. Cheating in Blackjack has a consequence of being banned from a
casino.

Basic Strategy Expectation

Benchmark -0.02%

One-half deck +0.71%

Two decks -0.32%

Four decks -0.48%

Six decks -0.53%

Eight decks -0.55%

Dealer wins ties. -9.34%

Natural pays 1 to 1 -2.32%

Natural pays 2 to 1 +2.32%

Dealer hits soft 17 -0.20%

No re-splitting of any pairs -0.03%

Respecting of aces +0.06%

No soft doubling -0.11%

Double down only on 10 or 11 -0.21%

Double down only on 11 -0.69%

Double down on any number of cards +0.24%

Double down after pair splitting +0.13%

Late surrender +0.06%

A good rule for counting is to expect a standard deviation of +500 minimum bets unless you spread
more than 1 – 10. Most spreads are between 1 and 12. The average bet is $2 to $4 depending on the
advantage play. Play a $5 minimum with a bankroll of $2500. Do not spend more than what is intended.
Double you bets when the running count is good. Bet according to basic strategy. Use card counting to
determine the amount you bet at a given time. Take advantage of side bets to know when to double
down, split or take insurance. Bet even money on side bets. Double down on blackjack if the player has
an ace showing. Do not spend more than what is allowed.

Blackjack Risk of Ruin Formula:

The risk of ruin formula predicts the player's expectancy of the amount they win or lose within a given
rate. If the ratio is better when the ratio is above 1%. If the ratio is below 0, you are losing your money.

K(K+1) * PE + K(K-1) * BE/BR

K = Amount of Bet,

BE (bet efficiency - standard deviation ratio) = 9%,

PE (Player Efficiency) (player efficiency or mean ratio) = 6%,

BR (bank roll) = Amount Planning to Spend,

(K + 1) = amount earned,

(K - 1) = amount lost

The word “Probability” is to use the letter “P” when referring to the probability of an event. What is not
evident by the equation for probability is how to count the size of various collections. The following
examples will help clarify the concept of probability. In Poker, there are 52 possible first cards you can
be dealt and 51 possible second cards you can be dealt. Because the order of the cards does not matter,
we divide by 2 to take account of symmetry.

(52 × 51) / 2 = 1326.

To have a straight, we must get one of the hands A23, 234, 345, 456, 567, 678, 789, 89T, 9TJ, TJQ, JQK,
QKA in one of the four suits. There are 12 straights and each straight can happen in one of the four suits,
so there are 12 × 4 = 48 ways to get a straight flush. The probability of getting a straight flush is .002
percent.

P (Straight Flush) = 48 / 22,100 = 0.002172

To count three of a kind, we must count these directly. For deuces, we can get trips with any of the
hands [2C,2D,2H], [2C,2D,2S], [2C,2H,2S] and [2D,2H,2S]. There are four trips for any rank and there are
thirteen ranks, so there are 13 × 4 = 52 ways to get three of a kind. The probability of getting a three of a
kind is 0.002 percent.

P (Three of a Kind) = 52 / 22,100 = 0.002353.

In order get a straight we begin by counting all straights, including the straight flushes. As above, a
straight consists of one of the hand types A23, 234, 345, 456, 567, 678, 789, 89T, 9TJ, TJQ, JQK, QKA.
Look at A23. We can have any suits for the A, 2 and 3; there are four choices for the suit of each (clubs,
diamonds, hearts, and spades). Therefore, the A23 straight consists of picking a card from each of {AC,
AD, AH, AS}, {2C, 2D, 2H, 2S} and {3C, 3D, 3H, 3S}. There are 4 × 4 × 4 = 64 ways of choosing these three
cards. Therefore, there are 64 straights of type A23. There are 12 types of straights and each straight can
happen in 64 ways. Therefore, the total number of straights is 12 × 64 = 768. However, this number
includes the 44 straight flush hands that we already counted, so we must subtract those. This leaves 768
– 48 = 720 straights that are not a straight flush. The probability of getting a straight is 0.03 percent.

P(Straight) = 720 / 22,100 = 0.032579.

To get a flush, we need to count all the hands XYZ where X, Y and Z have the same suit and the hand is
not a straight flush. We will pick on the suit Clubs. There are 13 cards. We can choose any of these 13 for
the first card, any of the remaining 12 for the second card, and any of the remaining 11 for the third
card. Because three cards can be rearranged in six ways and the order the cards were dealt does not
matter, it follows that the number of ways of getting a flush in clubs is (13 × 12 × 11) / 6 = 286. Of these
flushes, 12 of them are a straight flush. This leaves 286 – 12 = 274 flushes in clubs that are not straight
flushes. Because there are four suits, it follows that the total number of flushes is 274 × 4 = 1,096. The
probability of getting a flush is 0.049 percent.

P(Flush) = 1,096 / 22,100 = 0.049593

We determine there are 6 ways of getting a pair of any rank. For example, to get a pair of deuces the
player must hold one of the pairs [2C,2D], [2C,2H], [2C,2S], [2D,2H], [2D,2S] or [2H,2S]. Once the pair is
dealt, the third card must be a card of a different rank (otherwise, the hand would be trips). There are
48 cards that are not the same rank as the pair. Putting this together, there are 13 ranks for the pair, 6
pairs of that rank, and 48 possible third cards of a different rank. Multiplying these together, we get a
total of 13 × 6 × 48 = 3,744 pairs. The probability of getting a pair is 0.16 percent.

P(Pair) = 3,744 / 22,100 = 0.169412.

To get null hand, it simply means that the hand is not any of the above. We simply subtract all the
results above from the total number of hands. This gives 22,100 – 48 – 52 – 720 – 1,096 – 3,744 = 16,440
hands that are losing hands for the Pair Plus wager. The probability of getting a dead hand is 0.74
percent.

P(Nothing) = 16,440 / 22,100 = 0.743891.

If we add all the probabilities together, the probability that something is going to happen is 1, a
certainty.

The probability of the ball rolling on red or black is determined by the spin of the ball, the number of
rotations in one spin, the location of the ball to the distance of where the ball will land, and the friction
of the ball makes against the wheel and hitting its pockets. The probability of the player profiting after
100 spins could be determined by the expected value to win or how much the player wagers on each
spin. The probability could be determined by the amount of expected return from winning each spin.
The probability could be determined by the number of times the ball lands on red or black. Even if the
player has a good betting strategy, the cost of playing will not measure the player level of success
against the house.
The American Roulette table has 38 slots on a roulette wheel. There are 18 red spots and 18 black spots
on a Roulette wheel. If a player made a bet on red or black, he has a 50:50 chance of getting that
number. The player has a bankroll of $15 and he expects to win at least $16 in 100 spins. If the player
were to bet $1 each spin what would determine the outcome?

On an American Roulette wheel, there are 18 black numbers and 18 red numbers with 2 numbers that
are neither. The odds are 18:36 of getting a red or black number and -18:36 odds of that number not
landing on red or black within 100 spins. The permeable probability of that number landing on the red
or black within 100 spins is deducted between 18:37 to 1:36 times of the ball rotating 100 times.

The linear expectation for that bet to occur within 100 spins is determined on return probability of it
happening. There is an expected probability of 18:38 that the ball is going to land on red or black. There
is an expected probability of -20:38 that the ball will not land on red or black. The expected probability is
5.26 percent.

What if the player could predict how many spins he will lose? If the player were to lose his bet four
times in a row, the expected value would be 14.77 per cent. For the player to profit we need to
determine the probability of the ball landing on a red or black number. To derive at that conclusion, we
must first determine what the expected win is. The player will take a positive unit 1, subtract the
probability from 1, and multiply the number each by the exponent 4. The expected probability is
14.77%.

The probability of getting red or black is 18:38 or 9:19. The random variable number of getting a red or
black in 100 consecutive spins is .47 percent. Nine multiplied by 100 is equal to 900 divided by 19 is
equal to 47.37 percent. You will have a 92% chance of walking away with $16 after 100 spins. If the
expected win were $2 for every $1 bet, 2 times 27.37 is equal to $94.74. The player is expected to win
$97.74 if the player bet $2 after 100 spins.

The probability of the ball not landing on either red or black determines the probability of losing four
times in a row. To figure this out the player will take 20:38 which fraction is broken down to 10:19 and
the percentage is 0.526%.

The probability of not getting black is .0767 percent. To determine this factor multiply 10:19 four times
and you have a losing strategy of 7.7%. Your expected strategy is equal to the probability of the red or
black selected multiplied by the total payout minus the cost of playing or $0.2277.

The house is always going to make a profit after every bet made. The house always wins. The probability
of getting a red or black number in 100 spins every time and your expected value to profit off every spin
is in the house favor. The player is expected to lose more than he wins. If the player wanted to play to
win $1 profit, the chances of having a good betting strategy will not win against the house.