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Card index betting explained variance the coral betting account

Card index betting explained variance

With this in mind, systems aim to achieve a balance of efficiency in three categories: [9]. Some strategies count the ace ace-reckoned strategies and some do not ace-neutral strategies. Including aces in the count improves betting correlation since the ace is the most valuable card in the deck for betting purposes. However, since the ace can either be counted as one or eleven, including an ace in the count decreases the accuracy of playing efficiency.

Since PE is more important in single- and double-deck games, and BC is more important in shoe games, counting the ace is more important in shoe games. One way to deal with such tradeoffs is to ignore the ace to yield higher PE while keeping a side count which is used to detect an additional change in EV which the player will use to detect additional betting opportunities that ordinarily would not be indicated by the primary card counting system.

The most common side counted card is the ace since it is the most important card in terms of achieving a balance of BC and PE. Since there is the potential to create an overtaxing demand on the human mind while using a card counting system another important design consideration is the ease of use.

The Running count is the running total of each card's assigned value. When using a Balanced count such as the Hi-Lo system , the Running count is converted into a "True count," which takes into consideration the number of decks used. With Hi-Lo, the True count is essentially the Running count divided by the number of decks that have not yet been dealt; this can be calculated by division or approximated with an average card count per round times the number of rounds dealt.

However, many variations of the True count calculation exist. Back-counting, also known as "Wonging," consists of standing behind a blackjack table that other players are playing on, and counting the cards as they are dealt with. Stanford Wong first proposed the idea of back-counting, and the term "Wong" comes from his pen name. The player will enter or "Wong in" to the game when the count reaches a point at which the player has an advantage.

The player may then raise their bets as their advantage increases, or lower their bets as their advantage goes down. Some back-counters prefer to flat-bet, and only bet the same amount once they have entered the game. Some players will stay at the table until the game is shuffled, or they may "Wong out" or leave when the count reaches a level at which they no longer have an advantage.

Back-counting is generally done on shoe games, of 4, 6, or 8 decks, although it can be done on pitch games of 1 or 2 decks. The reason for this is that the count is more stable in a shoe game, so a player will be less likely to sit down for one or two hands and then have to get up. In addition, many casinos do not allow "mid-shoe entry" in single or double deck games which makes Wonging impossible.

Another reason is that many casinos exhibit more effort to thwart card counters on their pitch games than on their shoe games, as a counter has a smaller advantage on an average shoe game than in a pitch game. Back-counting is different from traditional card-counting, in that the player does not play every hand they see. This offers several advantages.

For one, the player does not play hands at which they do not have a statistical advantage. This increases the total advantage of the player. Another advantage is that the player does not have to change their bet size as much, or at all if they choose. Large variations in bet size are one way that casinos detect card counters, and this is eliminated with back-counting.

There are several disadvantages to back-counting. One is that the player frequently does not stay at the table long enough to earn comps from the casino. Another disadvantage is that some players may become irritated with players who enter in the middle of a game, and superstitiously believe that this interrupts the "flow" of the cards. Their resentment may not merely be superstition, though, as this practice will negatively impact the other players at the table, because with one fewer player at the table when the card composition becomes unfavorable, the other players will play through more hands under those conditions as they will use up fewer cards per hand, and similarly, they will play fewer hands in the rest of the card shoe if the advantage player slips in during the middle of the shoe when the cards become favorable because, with one more player, more of those favorable cards will be used up per hand.

This negatively impacts the other players, whether they are counting cards or not. Lastly, a player who hops in and out of games may attract unwanted attention from casino personnel and may be detected as a card-counter. While a single player can maintain their own advantage with back-counting, card counting is most often used by teams of players to maximize their advantage.

In such a team, some players called "spotters" will sit at a table and play the game at the table minimum, while keeping a count basically doing the back "counting". When the count is significantly high, the spotter will discreetly signal another player, known as a "big player," that the count is high the table is "hot". The big player will then "Wong in" and wager vastly higher sums up to the table maximum while the count is high.

When the count "cools off" or the shoe is shuffled resetting the count , the big player will "Wong out" and look for other counters who are signaling a high count. This was the system used by the MIT Blackjack Team , whose story was in turn the inspiration for the Canadian movie The Last Casino which was later re-made into the Hollywood version The main advantage of group play is that the team can count several tables while a single back-counting player can usually only track one table.

This allows big players to move from table to table, maintaining the high-count advantage without being out of action very long. It also allows redundancy while the big player is seated as both the counter and big player can keep the count as in the movie 21 , the spotter can communicate the count to the big player discreetly as they sit down. The disadvantages include requiring multiple spotters who can keep an accurate count, splitting the "take" among all members of the team, requiring spotters to play a table regardless of the count using only basic strategy, these players will lose money long-term , and requiring signals, which can alert pit bosses.

A simple variation removes the loss of having spotters play; the spotters simply watch the table instead of playing and signal big players to Wong in and out as normal. The disadvantages of this variation are reduced ability of the spotter and big player to communicate, reduced comps as the spotters are not sitting down, and vastly increased suspicion, as blackjack is not generally considered a spectator sport in casinos except among those actually playing unlike craps , roulette and wheels of fortune which have larger displays and so tend to attract more spectators.

A mathematical principle called the Kelly criterion indicates that bet increases should be proportional to the player advantage. In practice, this means that the higher the count, the more a player should bet on each hand in order to take advantage of the player's edge.

Using this principle, a card counter may elect to vary their bet size in proportion to the advantage dictated by a count creating what is called a "Bet ramp" according to the principles of the Kelly criterion. A bet ramp is a betting plan with a specific bet size tied to each true count value in such a way that the player is betting proportionally to the player advantage with aim to maximize overall bankroll growth.

Taken to its ultimate conclusion, the Kelly criterion would demand that a player not bet anything at all when the deck does not offer a positive expectation; the "Wonging" strategy described above implements this. Historically, blackjack played with a perfect basic strategy offered a house edge of less than 0. Advantages of up to 2.

The variance in blackjack is high, so generating a sizable profit can take hundreds of hours of play. Under one set of circumstances, a player with a unit bet spread with only one-deck cut off of a six-deck game will enjoy an advantage of as much as 1. Instead, it comes from the increased probability of blackjacks, increased gain and benefits from doubling, splitting, and surrender, and the insurance side bet, which becomes profitable at high counts.

A range of card counting devices are available but are deemed to be illegal in most U. Card counting with the mind is legal, although casinos in the US reserve the right to remove anyone they suspect of using the technique. Card counting is not illegal under British law, nor is it under federal, state, or local laws in the United States provided that no external card counting device or person assists the player in counting cards.

Still, casinos object to the practice, and try to prevent it, [23] banning players believed to be counters. In their pursuit to identify card counters, casinos sometimes misidentify and ban players suspected of counting cards even if they do not. In , Ken Uston , a Blackjack Hall of Fame inductee, filed a lawsuit against an Atlantic City casino, claiming that casinos did not have the right to ban skilled players.

The New Jersey Supreme Court agreed, [25] ruling that "the state's control of Atlantic City's casinos is so complete that only the New Jersey Casino Control Commission has the power to make rules to exclude skillful players. As they are unable to ban counters even when identified, Atlantic City casinos have increased the use of countermeasures. Macau , the gambling capital of the world and the only legal gambling location in China, [27] does not technically prohibit card counting but casinos reserve the right to expel or ban any customers, as is the case in the US and Britain.

Monitoring player behavior to assist with detecting the card counters falls into the hands of the on-floor casino personnel " pit bosses " and casino-surveillance personnel, who may use video surveillance "the eye in the sky " as well as computer analysis, to try to spot playing behavior indicative of card counting.

Early counter-strategies featured the dealers learning to count the cards themselves to recognize the patterns in the players. Many casino chains keep databases of players that they consider undesirable. For successful card counters, therefore, skill at "cover" behavior, to hide counting and avoid "drawing heat" and possibly being barred, may be just as important as playing skill. Detection of card counters will be confirmed after a player is first suspected of counting cards; when seeking card counters, casino employees, whatever their position, could be alerted by many things that are most common when related to card counting but not common for other players.

These include: [33] [34] [35]. Card counters may make unique playing strategy deviations not normally used by non-counters. Extremely aggressive plays such as splitting tens and doubling soft 19 and 20 are often called out to the pit to notify them because they are telltale signs of not only card counters but hole carding.

Several semi-automated systems have been designed to aid the detection of card counters. The MindPlay system now discontinued scanned card values as the cards we're dealt. The Shuffle Master Intelligent Shoe system also scans card values as cards exit the shoe. Software called Bloodhound and Protec 21 [36] allows voice input of card and bet values, in an attempt to determine the player edge. A more recent innovation is the use of RFID signatures embedded within the casino chips so that the table can automatically track bet amounts.

Automated card-reading technology has known abuse potential in that it can be used to simplify the practice of preferential shuffling —having the dealer reshuffle the cards whenever the odds favor the players. To comply with licensing regulations, some blackjack protection systems have been designed to delay access to real-time data on remaining cards in the shoe. With card values, play decisions, and bet decisions conveniently accessible, the casino can analyze bet variation, play accuracy, and play variation.

Bet variation. The simplest way a card counter makes money is to bet more when they have an edge. While playing back the tapes of a recent session of play, the software can generate a scatter plot of the amount bet versus the count at the time the bet was made and find the trendline that best fits the scattered points. If the player is not counting cards, there will be no trend; their bet variation and the count variation will not consistently correlate.

If the player is counting and varying bets according to the count, there will be a trend whose slope reflects the player's average edge from this technique. Play variation. When card counters vary from basic strategy, they do so in response to the count, to gain an additional edge. The software can verify whether there is a pattern to play variation. Of particular interest is whether the player sometimes when the count is positive takes insurance and stands on 16 versus a dealer 10, but plays differently when the count is negative.

Casinos have spent a great amount of effort and money in trying to thwart card counters. Countermeasures used to prevent card counters from profiting at blackjack include: [41] [42] [30] [43]. Some jurisdictions e. Nevada have few legal restrictions placed on these countermeasures. Other jurisdictions such as New Jersey limit the countermeasures a casino can take against skilled players.

Some countermeasures result in disadvantages for the casino. Frequent or complex shuffling, for example, reduces the amount of playing time and consequently the house winnings. Others, known as continuous shuffle machines CSMs , allow the dealer to simply return used cards to a single shoe to allow playing with no interruption. Because CSMs essentially force minimal penetration, they greatly reduce the advantage of traditional counting techniques.

American mathematician Edward O. These events can be literally defined, but it must be done very carefully when framing a probability problem. From a mathematical point of view, the events are nothing more than subsets and the space of events is a Boolean algebra. Among these events, we find elementary and compound events, exclusive and nonexclusive events, and independent and non-independent events.

These are a few examples of gambling events, whose properties of compoundness, exclusiveness and independency are easily observable. These properties are very important in practical probability calculus. The complete mathematical model is given by the probability field attached to the experiment, which is the triple sample space—field of events—probability function.

For any game of chance, the probability model is of the simplest type—the sample space is finite, the space of events is the set of parts of the sample space, implicitly finite, too, and the probability function is given by the definition of probability on a finite space of events:. Combinatorial calculus is an important part of gambling probability applications. In games of chance, most of the gambling probability calculus in which we use the classical definition of probability reverts to counting combinations.

The gaming events can be identified with sets, which often are sets of combinations. Thus, we can identify an event with a combination. For example, in a five draw poker game, the event at least one player holds a four of a kind formation can be identified with the set of all combinations of xxxxy type, where x and y are distinct values of cards. These can be identified with elementary events that the event to be measured consists of.

Games of chance are not merely pure applications of probability calculus and gaming situations are not just isolated events whose numerical probability is well established through mathematical methods; they are also games whose progress is influenced by human action. In gambling, the human element has a striking character. 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 oldest and most common betting system is the martingale, or doubling-up, system on even-money bets, in which bets are doubled progressively after each loss until a win occurs.

This system probably dates back to the invention of the roulette wheel. 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. Example: 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 varies 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 that 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 to 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.

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Everyone has a responsibility to do this. Please Pass along the Message. This is not a blackjack video. I was not paid by any of the companies or businesses mentioned in this video. Huge blackjack win. Split 'Em and Double Down Baby. The Hand that defined the session. Don't Miss this amazing blackjack session. Biggest Blackjack Win of 12 months Ago i. To discuss Advertising Sponsorships and Blackjack Tournament Hosting please email neversplit gmail.

Biggest Blackjack Loss of 12 months Ago i. Enjoy the newest video of Never Split 10's. Part 3, The conclusion of the latest video series. Thank you for watching and supporting the channel. Part 2 of the latest video series. Please enjoy this roller coaster session.

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Blackjack session with degenerates. Can't find any good tips to discuss on this video. Point out all the mistakes if you want. They play sooo bad. Don't ever play blackjack with poker players. Blackjack Largest Win Ever followed by Learn to play blackjack while learning basic blackjack strategy. Follow along and let us know where we messed up or if you like what we are doing. For example, in a five draw poker game, the event at least one player holds a four of a kind formation can be identified with the set of all combinations of xxxxy type, where x and y are distinct values of cards.

These can be identified with elementary events that the event to be measured consists of. Games of chance are not merely pure applications of probability calculus and gaming situations are not just isolated events whose numerical probability is well established through mathematical methods; they are also games whose progress is influenced by human action. In gambling, the human element has a striking character. 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 oldest and most common betting system is the martingale, or doubling-up, system on even-money bets, in which bets are doubled progressively after each loss until a win occurs. This system probably dates back to the invention of the roulette wheel.

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.

Example: 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 varies 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 that 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 to 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: three above the mean, and three below. 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.