Blackjack

1 (17)

Blackjack, also known as twenty-one, is the most widely played casino banking game in the world. Blackjack is a comparing card game between a player and dealer, meaning that players compete against the dealer but not against any other players. It is played with one or more decks of 52 cards. The object of the game is to beat the dealer, which can be done in a number of ways:

  • Get 21 points on the player’s first two cards (called a blackjack), without a dealer blackjack;
  • Reach a final score higher than the dealer without exceeding 21; or
  • Let the dealer draw additional cards until his or her hand exceeds 21.

The player or players are dealt an initial two-card hand and add together the value of their cards. Face cards (kings, queens, and jacks) are counted as ten points. A player and the dealer can count his or her own ace as 1 point or 11 points. All other cards are counted as the numeric value shown on the card. After receiving their initial two cards, players have the option of getting a “hit”, or taking an additional card. In a given round, the player or the dealer wins by having a score of 21 or by having the highest score that is less than 21. Scoring higher than 21 (called “busting” or “going bust”) results in a loss. A player may win by having any final score equal to or less than 21 if the dealer busts. If a player holds an ace valued as 11, the hand is called “soft”, meaning that the player cannot go bust by taking an additional card; 11 plus the value of any other card will always be less than or equal to 21. Otherwise, the hand is “hard”.

The dealer has to take hits until his or her cards total 17 or more points. (In some casinos the dealer also hits on a “soft” 17, e.g. an initial ace and six.) Players win if they do not bust and have a total that is higher than the dealer’s. The dealer loses if he or she busts or has a lesser hand than the player who has not busted. If the player and dealer have the same total, this is called a “push” and the player typically does not win or lose money on that hand.

Many rule variations of blackjack exist. Since the 1960s, blackjack has been a high-profile target of advantage players, particularly card counters, who track the profile of cards that have been dealt and adapt their wagers and playing strategies accordingly.

Other casino games inspired by blackjack include Spanish 21 and pontoon. The recreational British card game of black jack is a shedding-type game and unrelated to the subject of this article.

History

Blackjack’s precursor was twenty-one, a game of unknown origin. The first written reference is found in a book by the Spanish author Miguel de Cervantes, most famous for writing Don Quixote. Cervantes was a gambler, and the main characters of his tale Rinconete y Cortadillo, from Novelas Ejemplares, are a couple of cheats working in Seville. They are proficient at cheating at ventiuna (Spanish for twenty-one), and state that the object of the game is to reach 21 points without going over and that the ace values 1 or 11. The game is played with the Spanish baraja deck, which lacks eights, nines and tens. This short story was written between 1601 and 1602, implying that ventiuna was played in Castilla since the beginning of the 17th century or earlier. Later references to this game are found in France and Spain.

When twenty-one was introduced in the United States, gambling houses offered bonus payouts to stimulate players’ interest. One such bonus was a ten-to-one payout if the player’s hand consisted of the ace of spades and a black jack (either the jack of clubs or the jack of spades). This hand was called a “blackjack” and the name stuck to the game, even though the ten-to-one bonus was soon withdrawn. In the modern game, a blackjack refers to any hand of an ace plus a ten or face card, regardless of suits or colours.

Rules of play at casinos

Blackjack example game
Initial deal
Player action
Dealer’s hand revealed
Bets settled

At a casino blackjack table, the dealer faces five to seven playing positions from behind a semicircular table. Between one and eight standard 52-card decks are shuffled together. At the beginning of each round, up to three players can place their bets in the “betting box” at each position in play. That is, there could be up to three players at each position at a table in jurisdictions that allow back betting. The player whose bet is at the front of the betting box is deemed to have control over the position, and the dealer will consult the controlling player for playing decisions regarding the hand; the other players of that box are said to “play behind”. Any player is usually allowed to control or bet in as many boxes as desired at a single table, but it is prohibited for an individual to play on more than one table at a time or to place multiple bets within a single box. In many U.S. casinos, however, players are limited to playing two or three positions at a table and often only one person is allowed to bet on each position.

The dealer deals cards from his/her left (the position on the dealer’s far left is often referred to as “first base”) to his/her far right (“third base”). Each box is dealt an initial hand of two cards visible to the people playing on it, and often to any other players. The dealer’s hand receives its first card face up, and in “hole card” games immediately receives its second card face down (the hole card), which the dealer peeks at but does not reveal unless it makes the dealer’s hand a blackjack. Hole card games are sometimes played on tables with a small mirror or electronic sensor that is used to peek securely at the hole card. In European casinos, “no hole card” games are prevalent; the dealer’s second card is neither drawn nor consulted until the players have all played their hands.

Cards are dealt either from one or two handheld decks, from a dealer’s shoe, or from a shuffling machine. Single cards are dealt to each wagered-on position clockwise from the dealer’s left, followed by a single card to the dealer, followed by an additional card to each of the positions in play. The players’ initial cards may be dealt face up or face down (more common in single-deck games).

The players’ object is to win money by creating card totals that turn out to be higher than the dealer’s hand but do not exceed 21 (“busting”/”breaking”), or alternatively by allowing the dealer to take additional cards until he/she busts. On their turn, players must choose whether to “hit” (take a card), “stand” (end their turn), “double” (double wager, take a single card and finish), “split” (if the two cards have the same value, separate them to make two hands) or “surrender” (give up a half-bet and retire from the game). Number cards count as their natural value; the jack, queen, and king (also known as “face cards” or “pictures”) count as 10; aces are valued as either 1 or 11 according to the player’s choice. If the hand value exceeds 21 points, it busts, and all bets on it are immediately forfeit. After all boxes have finished playing, the dealer’s hand is resolved by drawing cards until the hand busts or achieves a value of 17 or higher (a dealer total of 17 including an ace, or “soft 17”, must be drawn to in some games and must stand in others). The dealer never doubles, splits, or surrenders. If the dealer busts, all remaining player hands win. If the dealer does not bust, each remaining bet wins if its hand is higher than the dealer’s, and loses if it is lower. In the case of a tied score, known as “push” or “standoff”, bets are normally returned without adjustment; however, a blackjack beats any hand that is not a blackjack, even one with a value of 21. An outcome of blackjack vs. blackjack results in a push. Wins are paid out at 1:1, or equal to the wager, except for winning blackjacks, which are traditionally paid at 3:2 (meaning the player receives three dollars for every two bet), or one-and-a-half times the wager. Many casinos today pay blackjacks at less than 3:2 at some tables.

Blackjack games almost always provide a side bet called insurance, which may be played when dealer’s upcard is an ace. Additional side bets, such as “Dealer Match” which pays when the player’s cards match the dealer’s up card, are sometimes available.

Player decisions

After receiving an initial two cards, the player has up to four standard options: “hit”, “stand”, “double down”, or “split”. Each option has a corresponding hand signal. Some games give the player a fifth option, “surrender”.

  • Hit: Take another card from the dealer.
Signal: Scrape cards against table (in handheld games); tap the table with finger or wave hand toward body (in games dealt face up).
  • Stand: Take no more cards, also known as “stand pat”, “stick”, or “stay”.
Signal: Slide cards under chips (in handheld games); wave hand horizontally (in games dealt face up).
  • Double down: The player is allowed to increase the initial bet by up to 100% in exchange for committing to stand after receiving exactly one more card. The additional bet is placed in the betting box next to the original bet. Some games do not permit the player to increase the bet by amounts other than 100%. Non-controlling players may double their wager or decline to do so, but they are bound by the controlling player’s decision to take only one card.
Signal: Place additional chips beside the original bet outside the betting box, and point with one finger.
  • Split: If the first two cards of a hand have the same value, the player can split them into two hands, by moving a second bet equal to the first into an area outside the betting box. The dealer separates the two cards and draws an additional card on each, placing one bet with each hand. The player then plays out the two separate hands in turn; except for a few restrictions, the hands are treated as independent new hands, with the player winning or losing their wager separately for each hand. Occasionally, in the case of ten-valued cards, some casinos allow splitting only when the cards have the identical ranks; for instance, a hand of 10-10 may be split, but not one of 10-king. However, usually all 10-value cards are treated the same. Doubling and further splitting of post-split hands may be restricted, and blackjacks after a split are counted as non-blackjack 21 when comparing against the dealer’s hand. Hitting split aces is usually not allowed. Non-controlling players may follow the controlling player by putting down an additional bet or decline to do so, instead associating their existing wager with one of the two post-split hands. In that case they must choose which hand to play behind before the second cards are drawn. Some casinos do not give non-controlling players this option, and require that the wager of a player not electing to split remains with the first of the two post-split hands.
Signal: Place additional chips next to the original bet outside the betting box; point with two fingers spread into a V formation.
  • Surrender (only available as first decision of a hand): Some games offer the option to “surrender”, usually in hole-card games and directly after the dealer has checked for blackjack (but see below for variations). When the player surrenders, the house takes half the player’s bet and returns the other half to the player; this terminates the player’s interest in the hand. The request to surrender is made verbally, there being no standard hand signal.

Hand signals are used to assist the “eye in the sky“, a person or video camera located above the table and sometimes concealed behind one-way glass. The eye in the sky usually makes a video recording of the table, which helps in resolving disputes and identifying dealer mistakes, and is also used to protect the casino against dealers who steal chips or players who cheat. The recording can further be used to identify advantage players whose activities, while legal, make them undesirable customers. In the event of a disagreement between a player’s hand signals and their words, the hand signal takes precedence.

Each hand may normally “hit” as many times as desired so long as the total is not above hard 20. On reaching 21 (including soft 21), the hand is normally required to stand; busting is an irrevocable loss and the players’ wagers are immediately forfeited to the house. After a bust or a stand, play proceeds to the next hand clockwise around the table. When the last hand has finished being played, the dealer reveals the hole card, and stands or draws further cards according to the rules of the game for dealer drawing. When the outcome of the dealer’s hand is established, any hands with bets remaining on the table are resolved (usually in counterclockwise order): bets on losing hands are forfeited, the bet on a push is left on the table, and winners are paid out.

Insurance

If the dealer’s upcard is an ace, the player is offered the option of taking “insurance” before the dealer checks the hole card.

Insurance is a side bet that the dealer has blackjack and is treated independently of the main wager. It pays 2:1 (meaning that the player receives two dollars for every dollar bet) and is available when the dealer’s exposed card is an ace. The idea is that the dealer’s second card has a fairly high probability (nearly one-third) to be ten-valued, giving the dealer blackjack and disappointment for the player. It is attractive (although not necessarily wise) for the player to insure against the possibility of a dealer blackjack by making a maximum “insurance” bet, in which case the “insurance proceeds” will make up for the concomitant loss on the original bet. The player may add up to half the value of their original bet to the insurance and these extra chips are placed on a portion of the table usually marked “Insurance pays 2 to 1”.

Players with a blackjack may also take insurance, and in taking maximum insurance they commit themselves to winning an amount exactly equal to their main wager, regardless of the dealer’s outcome. Fully insuring a blackjack against blackjack is thus referred to as “taking even money”, and paid out immediately, before the dealer’s hand is resolved; the players do not need to place more chips for the insurance wager.

Insurance bets are expected to lose money in the long run, because the dealer is likely to have blackjack less than one-third of the time. However the insurance outcome is strongly anti-correlated with that of the main wager, and if the player’s priority is to reduce variation, it is reasonable to pay for this.

Furthermore, the insurance bet is susceptible to advantage play. It is advantageous to make an insurance bet whenever the hole card has more than a chance of one in three of being a ten. Advantage play techniques can sometimes identify such situations. In a multi-hand, face-up, single deck game, it is possible to establish whether insurance is a good bet simply by observing the other cards on the table after the deal; even if there are just 2 player hands exposed, and neither of their two initial cards is a ten, then 16 in 47 of the remaining cards are tens, which is larger than 1 in 3, so insurance is a good bet. This is an elementary example of the family of advantage play techniques known as card counting.

Bets to insure against blackjack are slightly less likely to be advantageous than insurance bets in general, since the ten in the player’s blackjack makes it less likely that the dealer has blackjack too.

Rule variations and their consequences for the house edge

Doubling down. The third card is placed at right angles to signify that the player cannot receive any more cards.

The rules of casino blackjack are generally determined by law or regulation, which establishes certain rule variations allowed at the discretion of the casino. The rules of any particular game are generally posted on or near the table, failing which there is an expectation that casino staff will provide them on request. Over 100 variations of blackjack have been documented.

As with all casino games, blackjack incorporates a “house edge”, a statistical advantage for the casino that is built into the game. The advantage of the dealer’s position in blackjack relative to the player comes from the fact that if the player busts, the player loses, regardless of whether the dealer subsequently busts. Nonetheless, blackjack players using basic strategy will lose less than 1% of their total wagered amount with strictly average luck; this is very favorable to the player compared to other casino games. The loss rate of players who deviate from basic strategy through ignorance is generally expected to be greater.

  • Dealer hits soft 17

A “soft 17” in blackjack. An ace and any combination of 6.

Each game has a rule about whether the dealer must hit or stand on soft 17, which is generally printed on the table surface. The variation where the dealer must hit soft 17 is abbreviated “H17” in blackjack literature, with “S17” used for the stand-on-soft-17 variation. Substituting an “H17” rule with an “S17” rule in a game benefits the player, decreasing the house edge by about 0.2%.
  • Number of decks
All things being equal, using fewer decks decreases the house edge. This mainly reflects an increased likelihood of player blackjack, since if the players draws a ten on their first card, the subsequent probability of drawing an ace is higher with fewer decks. It also reflects a decreased likelihood of blackjack-blackjack push in a game with fewer decks.
Casinos generally compensate by tightening other rules in games with fewer decks, in order to preserve the house edge or discourage play altogether. When offering single deck blackjack games, casinos are more likely to disallow doubling on soft hands or after splitting, to restrict resplitting, require higher minimum bets, and to pay the player less than 3:2 for a winning blackjack.
The following table illustrates the mathematical effect on the house edge of the number of decks, by considering games with various deck counts under the following ruleset: double after split allowed, resplit to four hands allowed, no hitting split aces, no surrender, double on any two cards, original bets only lost on dealer blackjack, dealer hits soft 17, and cut-card used. The increase in house edge per unit increase in the number of decks is most dramatic when comparing the single deck game to the two-deck game, and becomes progressively smaller as more decks are added.
Number of Decks House Advantage
Single deck 0.17%
Double deck 0.46%
Four decks 0.60%
Six decks 0.64%
Eight decks 0.65%
Late/early surrender

Surrender, for those games that allow it, is usually not permitted against a dealer blackjack; if the dealer’s first card is an ace or ten, the hole card is checked to make sure there is no blackjack before surrender is offered. This rule protocol is consequently known as “late” surrender. The alternative, “early” surrender, gives player the option to surrender before the dealer checks for blackjack, or in a no-hole-card game. Early surrender is much more favorable to the player than late surrender. Most medium-strength hands should be surrendered against a dealer Ace if the hole card has not been checked.

For late surrender, however, while it is tempting opt for surrender on any hand which will probably lose, the correct strategy is to only surrender on the very worst hands, because having even a one in four chance of winning the full bet is better than losing half the bet and pushing the other half, as entailed by surrendering.

Resplitting
If the cards of a post-split hand have the same value, most games allow the player to split again, or “resplit”. The player places a further wager and the dealer separates the new pair dealing a further card to each as before. Some games allow unlimited resplitting, while others may limit it to a certain number of hands, such as four hands (for example, “resplit to 4”).
Hit/resplit split aces
After splitting aces, the common rule is that only one card will be dealt to each ace; the player cannot split, double, or take another hit on either hand. Rule variants include allowing resplitting aces or allowing the player to hit split aces. Games allowing aces to be resplit are not uncommon, but those allowing the player to hit split aces are extremely rare. Allowing the player to hit hands resulting from split aces reduces the house edge by about 0.13%; allowing resplitting of aces reduces house edge by about 0.03%. Note that a ten-value card dealt on a split ace (or vice versa) is a “soft 21” and not a “natural”.
No double after split
After a split, most games allow doubling down on the new two-card hands. Disallowing doubling after a split increases the house edge by about 0.12%.
Double on 9/10/11 or 10/11 only
Under the “Reno rule”, double down is only permitted on hard totals of 9, 10, or 11 (under a similar European rule, only 10 or 11). Basic strategy would otherwise call for some doubling down with hard 9 and soft 13–18, and advanced players can identify situations where doubling on soft 19–20 and hard 8,7 and even 6 is advantageous. The Reno rule prevents the player from taking advantage of double down in these situations and thereby increases the player’s expected loss. The Reno rule increases the house edge by around one in 1000, and its European version by around two in 1000.
No hole card and OBO

In most non-U.S. casinos, a ‘no hole card’ game is played, meaning that the dealer does not draw nor consult his or her second card until after all players have finished making decisions. With no hole card, it is almost never correct basic strategy to double or split against a dealer ten or ace, since a dealer blackjack will result in the loss of the split and double bets; the only exception is with a pair of A’s against a dealer 10, where it is still correct to split. In all other cases, a stand, hit or surrender is called for. For instance, holding 11 against a dealer 10, the correct strategy is to double in a hole card game (where the player knows the dealer’s second card is not an ace), but to hit in a no hole card game. The no hole card rule adds approximately 0.11% to the house edge.

The “original bets only” rule variation appearing in certain no hole card games states that if the player’s hand loses to a dealer blackjack, only the mandatory initial bet (“original”) is forfeited, and all optional bets, meaning doubles and splits, are pushed. “Original bets only” is also known by the acronym OBO; it has the same effect on basic strategy and house edge as reverting to a hole card game.

Altered payout for a winning blackjack
In many casinos, a blackjack pays only 6:5 or even 1:1 instead of the usual 3:2. This is usually at tables with the lowest table minimums and single-deck games. Among common rule variations in the U.S., these altered payouts for blackjack are the most damaging to the player, causing the greatest increase in house edge. Since blackjack occurs in approximately 4.8% of hands, the 1:1 game increases the house edge by 2.3%, while the 6:5 game adds 1.4% to the house edge. Video blackjack machines generally pay 1:1 payout for a blackjack. The 6:5 rule is most commonly employed on table blackjack at single deck games, where they help the house to compensate for low house edge intrinsic in using one deck only.
Dealer wins ties
The rule that bets on tied hands are lost rather than pushed is catastrophic to the player. Though rarely used in standard blackjack, it is sometimes seen in “blackjack-like” games such as in some charity casinos.

Blackjack Basic Strategy

strategy

Each blackjack game has a basic strategy, which is playing a hand of any total value against any dealer’s up-card, which loses the least money to the house in the long term.

An example of basic strategy is shown in the table below, and includes the following parameters:

  • Four to eight decks
  • The dealer stands on a soft 17
  • A double is allowed after a split
  • Only original bets are lost on dealer blackjack
Player hand Dealer’s face-up card
2 3 4 5 6 7 8 9 10 A
Hard totals (excluding pairs)
17–20 S S S S S S S S S S
16 S S S S S H H SU SU SU
15 S S S S S H H H SU H
13–14 S S S S S H H H H H
12 H H S S S H H H H H
11 Dh Dh Dh Dh Dh Dh Dh Dh Dh H
10 Dh Dh Dh Dh Dh Dh Dh Dh H H
9 H Dh Dh Dh Dh H H H H H
5–8 H H H H H H H H H H
Soft totals
2 3 4 5 6 7 8 9 10 A
A,8–A,9 S S S S S S S S S S
A,7 S Ds Ds Ds Ds S S H H H
A,6 H Dh Dh Dh Dh H H H H H
A,4–A,5 H H Dh Dh Dh H H H H H
A,2–A,3 H H H Dh Dh H H H H H
Pairs
2 3 4 5 6 7 8 9 10 A
A,A SP SP SP SP SP SP SP SP SP SP
10,10 S S S S S S S S S S
9,9 SP SP SP SP SP S SP SP S S
8,8 SP SP SP SP SP SP SP SP SP SP
7,7 SP SP SP SP SP SP H H H H
6,6 SP SP SP SP SP H H H H H
5,5 Dh Dh Dh Dh Dh Dh Dh Dh H H
4,4 H H H SP SP H H H H H
2,2–3,3 SP SP SP SP SP SP H H H H

Key:

S = Stand
H = Hit
Dh = Double (if not allowed, then hit)
Ds = Double (if not allowed, then stand)
SP = Split
SU = Surrender (if not allowed, then hit)

The bulk of basic strategy is common to all blackjack games, with most rule variations calling for changes in only a few situations. For example, if the above game used the hit on soft 17 rule, common in Las Vegas Strip casinos, only 6 cells of the table would need to be changed: double on 11 vs. A, surrender 15 or 17 vs. A, double on A,7 vs. 2, double on A,8 vs. 6, surrender(if not allowed, then hit) on 8,8 vs. A. Also when playing basic strategy never take insurance or “even money.”

Estimates of the house edge for blackjack games quoted by casinos and gaming regulators are generally based on the assumption that the players follow basic strategy and do not systematically change their bet size. Most blackjack games have a house edge of between 0.5% and 1%, placing blackjack among the cheapest casino table games. Casino promotions such as complimentary matchplay vouchers or 2:1 blackjack payouts allow the player to acquire an advantage without deviating from basic strategy.

Composition-dependent strategy

Basic strategy is based upon a player’s point total and the dealer’s visible card. Players may be able to improve on this decision by considering the precise composition of their hand, not just the point total. For example, players should ordinarily stand when holding 12 against a dealer 4. However, in a single deck game, players should hit if their 12 consists of a 10 and a 2. The presence of a 10 in the player’s hand has two consequences:

  • It makes the player’s 12 a worse hand to stand on (since the only way to avoid losing is for the dealer to go bust, which is less likely if there are fewer 10s left in the shoe).
  • It makes hitting safer, since the only way of going bust is to draw a 10, and this is less likely with a 10 already in the hand.

However, even when basic and composition-dependent strategy lead to different actions, the difference in expected reward is small, and it becomes even smaller with more decks. Using a composition-dependent strategy rather than basic strategy in a single deck game reduces the house edge by 4 in 10,000, which falls to 3 in 100,000 for a six-deck game.

Card Counting

Blackjack Player Who Won $15 Million From 3 Casinos Reveals How

123

It’s the stuff that gamblers’ dreams are made of. Blackjack player Don Johnson revealed in a magazine interview how he won $15 million from three Atlantic City’s casinos in about five months.

Previously tightlipped about how he did it, Johnson said he played “fair and square” but he did have some favorable conditions when he played single blackjack hands of up to $100,000.

He won $6 million from the Tropicana; from the Borgata, $5 million, and he took $4 million from Caesar’s, all between December 2010 and April 2011. In an interview with, Johnson described how the casinos gave him a 20 percent discount on his losses and slightly more favorable house rules that let him break the bank.

“I guess for the first time in 30 years, a group of casinos actually had a huge setback on account of one player,” Johnson told the magazine. “Somebody connected all the dots and said it must be one guy.”

Perks for high rollers, like free hotel stays and trips on jets, are not new to gambling houses. But two years ago with revenues tanking in an unstable market, casinos became desperate to attract big spenders, to the point that they began calling to invite Johnson, a known player, to play in late 2010 with special deals.

Johnson negotiated for discounts as high as 20 percent after his losses hit $500,000 at the Tropicana and then decided to play. So if he were to lose the whole $500,000 he’d only have to pay $400,000.

Johnson admitted, taking some losses along the way.

But Tropicana “pulled the deal” after he won a total of $5.8 million, the Borgata cut him off at $5 million, and the dealer at Caesars refused to fill the chip tray once his earnings topped $4 million, according to The Atlantic.

The 49-year-old resident of Bensalem, Pa., said in the interview with The Press that he began playing blackjack 15 years ago, starting with $25 bets. His profession is gambling-related as chief executive officer of Heritage Development LLC, which develops computer-assisted wagering systems for horseracing. His prowess in blackjack, he says, has gotten him banned from some casinos.

Johnson said he did not count cards, which is considered cheating and will get you banned from some casinos, but not illegal. Blackjack players with a trained memory and enough acuity can keep track of which cards have been played and which are still in the deck, thereby maximizing their chances for beating the house.

Explains Richard, a former card counter who today works on Wall Street (and who asks that his last name not be used), “As the composition of the cards in the deck fluctuates, the player’s advantage fluctuates. When he knows he has the advantage, he bets higher. When he knows the advantage has shifted to the house, he bets lower. Not only do you change the amount of your bets, you change your playing strategy: When you know it’s to your advantage, you hit a hand you’d otherwise have decided to stand on.”

Alan, a professional gambler who asks that his last name not be used, adds, “Even under normal circumstances, the house’s edge is small against a knowledgeable player. The size of the edge depends on the variation of the game that’s being played, but it can get down to less than 1 percent. Card counting can turn the edge against the casino, which is why management bans card counters when they’re caught.”

Macau trumps Vegas with $270 minimum bet

Las Vegas has first class shopping, dining and nightlife. But for serious gamblers, Macau holds all the aces.

The city’s $45 billion casino industry is now roughly seven times bigger than Vegas, and eye-popping growth has attracted the biggest players, including Las Vegas Sands and Wynn Resorts.

Gambling in the former Portuguese outpost has been fueled by a relaxation of regulations and a Chinese populace eager to try their luck.

Here are three things to know about Macau:

1) Mountains of cash

Gamblers in Macau are not messing around. Stakes at top casinos have been rising for years and it’s nearly impossible to find a table with a minimum bet of less than $65.

The average minimum bet at a non-VIP table is now at least $270, according to Aaron Fischer, the regional head of consumer and gaming research at CLSA. At Galaxy Macau, it’s even higher: $320.

The mind-boggling stakes leave Macau’s international competitors in the dust.

hk macau incredible min

But the runaway bets could become a problem, Fischer says. Some gamblers are burning through their stacks of cash too quickly.

“It might be fun to lose $1,000 in two to three hours, but it is definitely not enjoyable to lose your entire gaming budget in one hand of Baccarat,” he said.

hk macau betting min 2

2) Gambling with Chinese characteristics

Macau is the only place in China where gambling is legal, making it a dream destination for millions of Chinese tourists.

The city of 600,000 is almost entirely dependent on gambling. When the industry thrives, tax revenue jumps and residents — most of whom are employed in the business — receive payouts from the government.

The boom started in earnest in 2002, when restrictions on foreign operators were lifted. But foreign casinos owners must cater to Chinese preferences. And that means baccarat instead of poker or blackjack.

hk macau revenue

3) Macau has problems, too

Casino stocks have taken a beating in recent months following a rare slide in casino revenue.

Analysts say the poor performance is due to Beijing’s campaign against corruption and lavish spending, a reduction in tourist visas and a crackdown on junket operators who recruit gamblers.

There is still huge potential in the territory, however. Hotels are planning to increase capacity by 70% over the next few years.

With the VIP market saturated, much of the growth is likely to come from more modest players.

“Macau is merely scratching the surface now, with ample pent-up demand to be captured by new casinos opening from 2015 onwards,” Fischer”.

Blackjack Tournament Strategy

123

So you’ve got a good grasp of basic blackjack strategy-you’ve studies up on your odds and strategy charts, you understand the rules of blackjack like the back of your hand and you understand how blackjack tournaments work. Where do you go from here? If you want to increase your odds of winning in the next tournament you play in then you will have to learn some more advanced blackjack tournament strategies.

One of the most important parts of advanced strategy is to understand that you are not playing against the dealer-you are playing against the other players. Therefore, focus on beating the other players. Your knowledge of basic strategy is enough to help you decide whether to hit, stand, split or double down. Focus your attention on maximizing your stack of chips.

A lot of blackjack players make the mistake of playing too conservatively early on. Sure, you don’t want to lose all your chips in one fell swoop. However, if you don’t build your bankroll enough you won’t make it to the next round and that’s almost as bad as risking your entire stack and losing. Make sure to pay attention to the other players at your table. See how big their stacks are and what kind of bets they are placing. Then, place your bets accordingly. If possible, try to avoid going all in and betting everything at once. However, if that’s the only thing that will get you to the next round then take the risk. Better to try and fail than not to try at all and be eliminated at the end of the round with a small stack of chips.

You can adjust your betting patterns based on what’s going on with the other players at the table. That’s called risk management. For instance, if you are well ahead of everyone else you can take it easy. You have no need to take big risks that could result in a big hit to your bankroll until other players are approaching you. However, if you are falling behind in the chip count you should swing ahead with a big bet in the hopes of making up the difference between your bankroll and the bankrolls of your competitors.

By learning to manage your money and your risk, in addition to your basic blackjack tournament strategies, you can greatly increase your odds of winning in tournament play.

MIT Blackjack Team

21blackjack

“The first year I played, we returned 154 percent to our investors. That’s after paying off expenses. You try and do that on Wall Street.” – Jeff Ma, member of the MIT Blackjack Team.

How did a bunch of college kids from the Massachusetts Institute of Technology (MIT) and Harvard University become the most feared blackjack team on earth in the 1980’s and ’90’s. Individual players on that blackjack card counting squad routinely made $100,000 to $180,000 per session in profits, and Las Vegas treated them like royalty. That is, until they found out these fresh faced blackjack bandits were using an intricate card counting system and confederates to uncover the most favorable circumstances for a big bet. While blackjack card counting itself by using your brain is not illegal, the MIT team which has been the subject of films like the documentary “Breaking Vegas” and the more recent Hollywood production “21” sometimes went above and beyond simply using great math skills, and paid the price. But not until after winning tens of millions of dollars at blackjack and bringing Vegas to its knees.

And if you think the claims above made by Jeff Ma of 154% returns are a little outlandish, they actually started off much better than that. Bill Kaplan is a 1980 Harvard MBA graduate who had run a very successful blackjack team out of Las Vegas in the late 1970’s, and in 1977 used a blackjack card counting strategy to generate a 35X rate of return over a nine-month period (that’s turning $1,000 into $36,000 in 9 months). In 1980, Kaplan headed up a team of MIT and Harvard students that hit Las Vegas using formal management procedures and approaching a blackjack card counting and betting system as a business. On August 1, 1980 that original MIT team began with a stake of $89,000, with player names like Massar, Jonathan, Goose, and Big Dave doubling the original stakes in less than 10 weeks. An investor prospectus had estimated profits of $170 per hour, and actual play delivered realized profits of $162.50 per hour. Mostly undergraduates, the MIT team, as it came to be known, earned across-the-board an average of over $80 an hour while investors enjoyed annualized profits of 250%.

All this while Las Vegas showered the young players with free rooms, lavish suites and other Sin City comps. Andy Bloch, now a professional poker player that holds two electrical engineering degrees from MIT and a Juris Doctorate from Harvard Law School, was one of the MIT blackjack members. He has claimed “tens of millions” of dollars won by his fellow teammates and subsequent team members, and it is hard to argue with that estimate. And all those millions started to draw attention. Henry Houh, at the time a grad student at MIT, noticed his office-mate lugging around thousands of dollars of casino chips at work. Saddled with massive debt, he eagerly joined the card counting team, stating, “It was great fun.” With plenty of “crazy stories” of partying and staying in $1,000 a night suites complements of Las Vegas casinos, Houh also said that the MIT blackjack team was the reason it took him 13 years to finish school.

But these brilliant blackjack brains did not simply decide to get together and then hit Las Vegas. The mysterious Mister M and Kaplan put potential blackjack team candidates through grueling training sessions. A fully trained card counter then had to undergo a “trial by fire” final exam by playing through 8 six-deck shoes without mistakes, all while being lambasted with loud noises, music and other distractions typical to the average casino. Players learned to stagger their betting patterns as to disguise the fact that they were counting cards and waiting for the perfect scenario. They would then make a massive bet when they had an extreme advantage, and while losses naturally occurred, the profits were far greater. Advanced techniques like ace tracking and shuffle tracking were also employed, but John Chang, an MIT undergraduate that joined the team in late 1980, stated that the most consistent profits came from straight blackjack card counting.

Playing throughout the ’80s, and growing to as many as 35 players in 1984, a full 22 different partnerships composed MIT blackjack teams from 1979 through 1989. A total of 70 people played at one time or another in some capacity, either as card counters, “Big Players”, or in other supporting roles. Many times a player would count cards at a blackjack table while placing small bets without wavering his play. When the table was right for the picking, that player would signal someone sitting at a nearby bar or appearing to simply be watching, and that Big Player would swoop into the table for a single large bet, collect and leave. Incredibly enough, every single MIT blackjack team was successful during that tenure, paying in some cases over 300% per year to investors. In 1992 and ’93, MIT blackjack team members Bill Kaplan, J.P. Massar and John Chang formed Strategic Investments as a limited partnership to run the blackjack card counting enterprise. Through the early and mid-90s, the MIT team grew to nearly 80 players, with 30 players playing simultaneously at different casinos around the world. While blackjack teams consistently come and go, the MIT blackjack card counting team of the 1980s and ’90s will always live on in memory as one of the most brash and successful blackjack teams of all-time.

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.

World BlackJack Originalities by BLACKJACKASSUS

mit-blackjack-professor

How many times have you played Basic Strategy and lost all your capital rapidly?

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.

Really, Blackjack conceals so much science in it’s depth that verges art…

Device and method for continuously shuffling cards

part1

images

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”