# Counting Edge Basic blackjack Strategy

These methods are generally legal although their status in particular jurisdictions may vary. A "hard" hand is one that either has no aces, or has aces that are forced to count as point, lest the hand bust. Video and online blackjack games deal each coup from a fresh shoe, rendering card counting much less effective. Casino game Game of chance Game of skill List of bets. In all other cases, a stand, hit or surrender is called for. This short story was written between and , implying that ventiuna was played in Castile since the beginning of the 17th century or earlier. Thank you Last edited by:

## Probability Theory

The player is not only interested in the mathematical probability of the various gaming events, but he or she has expectations from the games while a major interaction exists. To obtain favorable results from this interaction, gamblers take into account all possible information, including statistics , to build gaming strategies. The predicted average gain or loss is called expectation or expected value and is the sum of the probability of each possible outcome of the experiment multiplied by its payoff value.

Thus, it represents the average amount one expects to win per bet if bets with identical odds are repeated many times. A game or situation in which the expected value for the player is zero no net gain nor loss is called a fair game. The attribute fair refers not to the technical process of the game, but to the chance balance house bank —player.

Even though the randomness inherent in games of chance would seem to ensure their fairness at least with respect to the players around a table—shuffling a deck or spinning a wheel do not favor any player except if they are fraudulent , gamblers always search and wait for irregularities in this randomness that will allow them to win.

It has been mathematically proved that, in ideal conditions of randomness, and with negative expectation, no long-run regular winning is possible for players of games of chance. Most gamblers accept this premise, but still work on strategies to make them win either in the short term or over the long run. Casino games provide a predictable long-term advantage to the casino, or "house", while offering the player the possibility of a large short-term payout. Some casino games have a skill element, where the player makes decisions; such games are called "random with a tactical element.

For more examples see Advantage gambling. The player's disadvantage is a result of the casino not paying winning wagers according to the game's "true odds", which are the payouts that would be expected considering the odds of a wager either winning or losing.

However, the casino may only pay 4 times the amount wagered for a winning wager. The house edge HE or vigorish is defined as the casino profit expressed as a percentage of the player's original bet. In games such as Blackjack or Spanish 21 , the final bet may be several times the original bet, if the player doubles or splits. In American Roulette , there are two zeroes and 36 non-zero numbers 18 red and 18 black.

Therefore, the house edge is 5. The house edge of casino games vary greatly with the game. The calculation of the Roulette house edge was a trivial exercise; for other games, this is not usually the case. In games which have a skill element, such as Blackjack or Spanish 21 , the house edge is defined as the house advantage from optimal play without the use of advanced techniques such as card counting or shuffle tracking , on the first hand of the shoe the container that holds the cards.

The set of the optimal plays for all possible hands is known as "basic strategy" and is highly dependent on the specific rules, and even the number of decks used. Good Blackjack and Spanish 21 games have house edges below 0. Online slot games often have a published Return to Player RTP percentage that determines the theoretical house edge.

Some software developers choose to publish the RTP of their slot games while others do not. The luck factor in a casino game is quantified using standard deviation SD. The standard deviation of a simple game like Roulette can be simply calculated because of the binomial distribution of successes assuming a result of 1 unit for a win, and 0 units for a loss.

Furthermore, if we flat bet at 10 units per round instead of 1 unit, the range of possible outcomes increases 10 fold. After enough large number of rounds the theoretical distribution of the total win converges to the normal distribution , giving a good possibility to forecast the possible win or loss. The 3 sigma range is six times the standard deviation: There is still a ca. The standard deviation for the even-money Roulette bet is one of the lowest out of all casinos games.

Most games, particularly slots, have extremely high standard deviations. As the size of the potential payouts increase, so does the standard deviation. Unfortunately, the above considerations for small numbers of rounds are incorrect, because the distribution is far from normal.

Moreover, the results of more volatile games usually converge to the normal distribution much more slowly, therefore much more huge number of rounds are required for that. As the number of rounds increases, eventually, the expected loss will exceed the standard deviation, many times over.

From the formula, we can see the standard deviation is proportional to the square root of the number of rounds played, while the expected loss is proportional to the number of rounds played. As the number of rounds increases, the expected loss increases at a much faster rate. This is why it is practically impossible for a gambler to win in the long term if they don't have an edge.

It is the high ratio of short-term standard deviation to expected loss that fools gamblers into thinking that they can win. The volatility index VI is defined as the standard deviation for one round, betting one unit. Therefore, the variance of the even-money American Roulette bet is ca. The variance for Blackjack is ca.

Additionally, the term of the volatility index based on some confidence intervals are used. The first scientific and mathematically sound attempt to devise an optimal blackjack playing strategy was revealed in September This paper would become the foundation of all future sound efforts to beat the game of blackjack. At a casino blackjack table, the dealer faces five to seven playing positions from behind a semicircular table.

Between one and eight standard 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. 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. 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. If a player receives 21 on the 1st and 2nd card it is considered a "natural" or "blackjack" and the player is paid out immediately unless dealer also has a natural, in which case the hand ties. 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 Wins are paid out at 1: Many casinos today pay blackjacks at less than 3: 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.

After receiving an initial two cards, the player has up to four standard options: Each option has a corresponding hand signal. Some games give the player a fifth option, "surrender". 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 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: 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. 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 , they might choose 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. 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 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. The loss rate of players who deviate from basic strategy through ignorance is generally expected to be greater.

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 to 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.

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. 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.

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: 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: A, surrender 15 or 17 vs.

A, double on A,7 vs. 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. Casino promotions such as complimentary matchplay vouchers or 2: 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: 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,, which falls to 3 in , for a six-deck game.

Blackjack has been a high-profile target for advantage players since the s. Advantage play is the attempt to win more using skills such as memory, computation, and observation. These techniques, while generally legal, can be powerful enough to give the player a long-term edge in the game, making them an undesirable customer for the casino and potentially leading to ejection or blacklisting if they are detected.

The main techniques of advantage play in blackjack are as follows:. During the course of a blackjack shoe, the dealer exposes the dealt cards. Careful accounting of the exposed cards allows a player to make inferences about the cards which remain to be dealt. These inferences can be used in the following ways:. A card counting system assigns a point score to each rank of card e. When a card is exposed, a counter adds the score of that card to a running total, the 'count'.

A card counter uses this count to make betting and playing decisions according to a table which they have learned. The count starts at 0 for a freshly shuffled deck for "balanced" counting systems. Unbalanced counts are often started at a value which depends on the number of decks used in the game. Blackjack's house edge is usually between 0.

Card counting is most rewarding near the end of a complete shoe when as few as possible cards remain. Single-deck games are therefore particularly susceptible to card counting. As a result, casinos are more likely to insist that players do not reveal their cards to one another in single-deck games. In games with more decks of cards, casinos limit penetration by ending the shoe and reshuffling when one or more decks remain undealt.