Advantage Play

Card counting is a casino card game strategy used primarily in the blackjack family of casino games to determine whether the next hand is likely to give a probable advantage to the player or to the dealer. Card counters are a class of advantage players, who attempt to decrease the inherent casino house edge by keeping a running tally of all high and low valued cards seen by the player. Card counting allows players to bet more with less risk when the count gives an advantage as well as minimize losses during an unfavorable count. Card counting also provides the ability to alter playing decisions based on the composition of remaining cards.

Card counting, also referred to as card reading, often refers to obtaining a sufficient count on the number, distribution and high-card location of cards in trick-taking games such as contract bridge or spades to optimize the winning of tricks.

CARD COUNTING

The most common variations of card counting in blackjack are based on statistical evidence that high cards (especially aces and 10s) benefit the player more than the dealer, while the low cards, (3s, 4s, 6s, and especially 5s) help the dealer while hurting the player. A high concentration of aces and 10s in the deck increases the player's chances of hitting a natural Blackjack, which pays out 3:2 (unless the dealer also has blackjack). Also, when the shoe has a high concentration of 10s, players have a better chance of winning when doubling. Low cards benefit the dealer, since according to blackjack rules the dealer must hit stiff hands (12-16 total) while the player has the option to hit or stand. Thus a dealer holding (12-16) will bust every time if the next card drawn is a 10, making this card essential to track when card counting.

SYSTEMS

Basic card counting assigns a positive, negative, or zero value to each card value available. When a card of that value is dealt, the count is adjusted by that card's counting value. Low cards increase the count as they increase the percentage of high cards in the remaining set of cards, while high cards decrease it for the opposite reason. For instance, the Hi-Lo system subtracts one for each dealt 10, Jack, Queen, King or Ace, and adds one for any value 2-6. Values 7-9 are assigned a value of zero and therefore do not affect the count.

The goal of a card counting system is to assign point values that roughly correlate to a card's Effect of Removal (EOR). The EOR is the actual effect of removing a given card from play, and the resulting impact on the house advantage. The player may gauge the effect of removal for all cards dealt, and assess the current house advantage of a game based on the remaining cards. As larger ratios between point values are used to create better correlation to actual EOR with the goal of increasing the efficiency of a system, such systems use more different numbers and are broken into classes depending on such as level 1, level 2, level 3, and so on, with regard to the ratio between the highest and lowest assigned point values.

The High-Low system is considered a level-one count, because the running count never increases or decreases by more than a single, predetermined value. A multilevel count, such as Zen Count, Wong Halves or Hi-Opt II, makes finer distinctions between card values to gain greater play accuracy. Rather than all cards having a value of +1, 0, or −1, an advanced count might also include card ranks that are counted as +2 and −2, or +0.5 and -0.5. Advanced players might additionally maintain a side count (separate count) of specific cards, such as a side count Aces, to deal with situations where the best count for betting accuracy differs from the best count for playing accuracy.

Many side count techniques exist including special-purpose counts used when attacking games with nonstandard profitable-play options such as an over/under side bet.

The disadvantage of higher-level counts is that keeping track of more information can detract from the ability to play quickly and accurately. A card-counter might earn more money by playing a simple count quickly—more hands per hour played—than by playing a complex count slowly.

The following table illustrates a few ranking systems for card counting. Many others exist.

DESIGN AND SELECTION OF SYSTEMS

The primary goal of a card counting system is to assign point values to each card that roughly correlate to the card's "effect of removal" or EOR (that is, the effect a single card has on the house advantage once removed from play), thus enabling the player to gauge the house advantage based on the composition of cards still to be dealt. Larger ratios between point values can better correlate to actual EOR, but add complexity to the system. Counting systems may be referred to as "level 1", "level 2", etc., corresponding to the number of different point values the system calls for.

The ideal system is a system that is usable by the player and offers the highest average dollar return per period of time when dealt at a fixed rate. With this in mind, systems aim to achieve a balance of efficiency in three categories:

Betting correlation (BC)

When the sum of all the permutations of the undealt cards offer a positive expectation to a player using optimal playing strategy, there is a positive expectation to a player placing a bet. A system's BC gauges how effective a system is at informing the user of this situation.

Playing efficiency (PE)

A portion of the expected profit comes from modifying playing strategy based on the known altered composition of cards. For this reason, a system's PE gauges how effectively it informs the player to modify strategy according to the actual composition of undealt cards. A system's PE is important when the effect of PE has a large impact on total gain, as in single- and double-deck games.

Insurance correlation (IC)

A portion of expected gain from counting cards comes from taking the insurance bet, which becomes profitable at high counts. An increase in IC will offer additional value to a card counting system.

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 addition change in EV which the player will use to detect additional betting opportunities which ordinarily would not be indicated by the primary card counting system.

The most commonly side counted card is the ace since it is the most important card in terms of achieving a balance of BC and PE. In theory a player could keep a side count of every card and achieve a near 100% PE, however methods involving additional side counts for PE become more complex at an exponential rate as you add more side counts and the ability of the human mind is quickly overtasked and unable to make the necessary computations.

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. Higher level systems, and systems with side counts will obviously become more difficult and in an attempt to make them easier, unbalanced systems eliminate the need for a player to keep tabs on the number of cards/decks that have already entered play typically at the expense of lowering PE.

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