## Randomization

There are exactly 52 factorial (expressed in shorthand as 52!) possible orderings of the cards in a 52 card deck. In other words there are 52 × 51 × 50 × 49 × ··· × 4 × 3 × 2 × 1 possible combinations of card sequence. This is approximately 8×1067 possible orderings or specifically 80,658,175,170,943,878,571,660,636,856,403,766,975,289,505,440,883,277,824,000,000,000,000. The magnitude of this number means that it is exceedingly improbable that two randomly selected, truly randomized decks will be the same. However, while the exact sequence of all cards in a randomized deck is unpredictable, it may be possible to make some probabilistic predictions about a deck that is not sufficiently randomized.

### Sufficient number of shuffles

The number of shuffles which are sufficient for a “good” level of randomness is a fundamental question, and the answer depends on the type of shuffle and the measure of “good enough randomness”, which in turn depends on the game in question. Broadly, for most games, four to seven good riffle shuffles (GRS) are both necessary and sufficient: for unsuited games such as blackjack, four GRSs are sufficient, while for suited games with strict conditions on randomness, seven GRSs are necessary. There are some games, however, for which even seven GRSs are insufficient.

In practice the number of shuffles required depends both on the quality of the shuffle and how significant non-randomness is, particularly how good the people playing are at noticing and using non-randomness. Two to four shuffles is good enough for casual play. But in club play, good bridge players take advantage of non-randomness after four shuffles, and top blackjack players supposedly track aces through the deck; this is known as “ace tracking”, or more generally, as “shuffle tracking”.

### Research

Following early research at Bell Labs, which was abandoned in 1955, the question of how many shuffles was required remained open until 1990, when it was convincingly solved as seven shuffles, as elaborated below. Some results preceded this, and refinements have continued since.

A leading figure in the mathematics of shuffling is mathematician and magician Persi Diaconis, who began studying the question around 1970, and has authored many papers in the 1980s, 1990s, and 2000s on the subject with numerous co-authors. Most famous is (Bayer & Diaconis 1992), co-authored with mathematician Dave Bayer, which analyzed the Gilbert-Shannon-Reeds model of random riffle shuffling and concluded that the deck did not start to become random until five good riffle shuffles, and was truly random after seven, in the precise sense of variation distance described in Markov chain mixing timae; of course, you would need more shuffles if your shuffling technique is poor.Recently, the work of Trefethen et al. has questioned some of Diaconis’ results, concluding that six shuffles are enough. The difference hinges on how each measured the randomness of the deck. Diaconis used a very sensitive test of randomness, and therefore needed to shuffle more. Even more sensitive measures exist, and the question of what measure is best for specific card games is still open. Diaconis released a response indicating that you only need four shuffles for un-suited games such as blackjack.

On the other hand variation distance may be too forgiving a measure and seven riffle shuffles may be many too few. For example, seven shuffles of a new deck leaves an 81% probability of winning New Age Solitaire where the probability is 50% with a uniform random deck. One sensitive test for randomness uses a standard deck without the jokers divided into suits with two suits in ascending order from ace to king, and the other two suits in reverse. (Many decks already come ordered this way when new.) After shuffling, the measure of randomness is the number of rising sequences that are left in each suit.

## How many times have you won and how many times have you lost while playing precisely the Basic Strategy?

Basic Strategy plights that if you precily apply it during your game,you will lose in long-term only 1% of your money.But how much is long-term?Most likely when t extends to infinity (t>oo)…

And how many years live an average person?
Eventually we could assume that the Basic Strategy was established to be using by Aliens who live eternal…
It is said that probably the condition long-term of Basic Strategy means a definite time as it is proved by computers.But computers can shuffle the decks infinite times while casinos can’t do that.
A few years ago, Harvard University studied the shuffling of cards
* (primary assortmentand is:

Α,2,3,4,5,6,7,8,9,10,J,Q,K,Α,2,3,4,5,6,7,8,9,10,J,Q,K,Α,2,3,4,5,6,7,8,9,10,J,Q,K,Α,2,3,4,5,6,7,8,9,10,J,Q,K,Α,2,3,4,5,6,7,8,9,10,J,Q,K,Α,2,3,4,5,6,7,8,9,10,J,Q,K )
and concluded that one pack of 52 sorted cards needed 7 shuffles (constant). So, if a casino uses a shuffling machine with 6 packs of cards to achieve a good assortment, the packs must be shuffled 77777*7=117.649 times.

It’s practically unobtainable in good time, because it takes days for this slowing down games at casinos and limits their gain.

So casinos can’t avoid the appearance of the ”pack phainomenon”!

The Basic Strategy necessitates infinite shuffles of the decks (shuffle machines can’t do it practically) to achieve chance setting of the cards,and infinite time to apply the Law Of Large Numbers.Casinos rely in the above condition playing 24 hours a day with a inexhaustible capital!!That’s why Casinos win constantly,because Basic Strategy is the certain way for a player to lose all his money rapidly!!
The question is how we could turn to advantage the “packs phainomenon”…How can we manipulate these capricious distributions of the decks?If we only could (in a way) “make” these distributions and thereafter seek for the appropriate strategy that will turn to account the prospects of our cards and dealer’s card. That is exactly what our program do!!It “makes” any distribution of the decks and demonstrates the odds of our success in a definite time:
• You don’t have to remember numbers.
• You don’t have to practice constantly, it’s
ֺ easy in it’s use!
• You don’t need to strain effort ֺ just clever way!
• It shows precily the array of the cards that
ֺ appear!
• It simulates any Casino without regard to ֺthe number of decks that it uses.
• It’s versatile in any financial ֺ strategy of the player!
• It rejects Basic Strategy!
• It’s based in a stunning random algorithm
ֺ that generates numbers!
• The first Program worldwide that ֺ simulates the Black Box (shuffles ֺthe cards with replacement)ֺand the “Shoe” (withought ֺreplacement)!
• It has accuracy of many digital numbersֺ in it’s results with percentage %!
• It draws up to 1,000,000 times and
ֺ uses 1-30 decks in a few seconds!!
• It has simple apearance and use!
• It has small size (2 MB), but fast in it’s results!

The BlackjackASSUS occupies exclusively with the discovery of new theories and concepts in the Theory Of Numbers,which is the capstone of Maths (as it’s called by the scientific community) and by extension Blackjack,which the only technical and not lucky game in the Casinos.

# Shuffling cards

The present invention provides an apparatus and method for moving playing cards from a first group of cards into a second group of cards, wherein the second group of cards is randomly arranged or shuffled. The apparatus comprises a card receiver for receiving the first group of cards, a single stack of card-receiving compartments generally adjacent to the card receiver, the stack generally vertically movable, an elevator for moving the stack, a card-moving mechanism between the card receiver and the stack for moving cards one at a time into a selected one of the compartments, another card moving mechanism for moving cards from one of the compartments to a second card receiver and a microprocessor that controls the card-moving mechanisms and the elevator.

## What is claimed is:

1. An apparatus for continuously shuffling playing cards, said apparatus comprising:

a card receiver for receiving a first group of cards Continue reading “Device and method for continuously shuffling cards”

# When a person is banned from playing at a casino, the casino..

must protect the player. Most casinos across the country have a list and if you are included for some reason by the casino or if you place yourself on the list, the casino must make sure that you do not gamble. The Revel Casino in New Jersey recently had to pay a large fine due to letting two men who were blocked from game play to play the game of blackjack.

The New Jersey Division of Gaming Enforcement filed a complaint which stated that the casino allowed two men to play blackjack from July to August of last year even though the two men were on the banned gamblers list. The casino must now pay \$27,500 due to the incident.

In total, the casino must now pay \$37,500 in fines for four different charges for this month. The violations include the blackjack charges and failing to follow the rules for the table game drop boxes collection. The casino has yet to comment on the incurring fines.

The largest fine in the bunch is from the two men who were able to take part in the gaming without being flagged as on the banned list. The gamblers are named AD and PY in the case documents. PY was listed as being banned since 2005 and he was able to gamble due to a misspelling of his name on the banned list.

AD was put on the list by his person in 2006 and was given a cash advance last year for \$5,000 and was able to play blackjack for three hours before he was found at the casino. It was not until a third cash advance attempt that the player was determined to be on the list and was excluded from game play but by then it was too late.

## Rule change at two casinos in Las Vegas for Blackjack

An apparently tiny rule change at two casinos in Las Vegas will have pretty serious negative consequences for gamblers

USPoker.com An apparently tiny rule change at two casinos in Las Vegas will have pretty serious negative consequences for gamblersreported that the Las Vegas Sands company just changed its payout rules for blackjack at the Venetian and Palazzo casinos in a way that greatly hurts players’ chances of coming out ahead.

In blackjack, players receive two cards and then decide if they want to “hit” and get more cards, or “stand” and use the cards they already have. The goal is to get a higher score than the dealer, based on the values of the cards, without going over 21. Should you do this, you get a payout of 1-to-1; you win as much money as you bet.

A special situation happens when the first two cards dealt are a 10 and an ace (valued at 11), adding up to 21 right away, a situation called a natural blackjack. In this case, the standard payout, and the old rule at the Venetian and Palazzo, is 3-to-2. This means that if someone bets \$10, they will win \$15 when getting a blackjack.

Now, at blackjack tables at the Venetian and Palazzo, the payout for a blackjack has been reduced to 6-to-5, that \$10 now just wins \$12 instead of \$15.

This seems like a small change, but it has a pretty serious effect on the game. Natural blackjacks are not completely uncommon; about 1 in 20 hands will come up with a natural 21. The rule change means that the casinos will be paying out quite a bit less money.

In terms of the industry, the rule change greatly increases the “house edge.” This is how casinos make their money. Games are set up to be slightly unfair to players in the long run, paying out a little bit less in total than what is taken in.

The house edge is usually expressed as a percentage. A house edge of 2% for a game means that, on average, for every \$100 in bets made by players on that game, the house will pay out \$98 to winners and keep \$2.

## Glossary of blackjack terms

Blackjack: Name of game, also known as 21.

Anchorman Third Baseman: The player who sits on the last   chair and plays card last.One initial card with two cards (one Ace and one of 10 points -10 or picture-), which gives 3:2 of the bet placed by player.

Chips: Roundlike coins given by the   casino in exchange for money, to be used in the game.

Dealer: An employee of the casino who is responsible for BLACKJACK game at table. He deals cards, accepts and pays out on bets.

Doubling down: Double of player’s initial bet, who is to receive only one more card.

Ten points card: Ten points or picture card, value of ten points.

Twenty one: Another name of the game BLACKJACK.

Dangerous card: Any card which may bust (or burn). Like a  hard 12-16 (taking over 21).

Hole card: The face down card of the dealer.

Insurance: A bet made by the player when the dealer shows his first card   as Ace. This bet wins if the dealer makes BLACKJACK (and rest of the players bets lose).

Bust (or burn): When card is taken and more than 21 is calculated on hand.   Player or dealer lose.

Burning of card: The removal of the first card from the dealer in first round, before dealing begins.

Soft total/card: Cards that contain an Ace that is counted as eleven.

Card count: Observation of cards that have been already played. This is very difficult when a game is played with 6 sets of cards, but does happen in casinos.

Natural: Term meaning BLACKJACK. Many sets:
The use of more than one set of cards for BLACKJACK in casino.

Push: Tie between dealer and player, so money does not change hands.

Round: A full round in game so that all players and dealer plays their cards.

Shoe: A box containing 4-6 sets of cards which dealer uses for BLACKJACK etc.

Hard card: Total of players cards which don?t include an Ace, or include other countable as unit (not as 11).

Splitting pairs: Separation of two cards even value (e.g two eights) so they can be played as separate cards.

Standing, Standing Pat: Not taking other cards.

Upcard: The face up card of dealer which players see before playing their own cards.

Card/Hand: The total of cards which one player holds and will play with.

First Baseman: The player who is dealt first and plays first.Usually seated in the first seat at the table

Hit and draw: The taking of more cards for the initial card.