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Card counting
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=== 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:<ref name="tob-19794"/> ; Betting correlation (BC) : When the sum of all the permutations of the undealt cards offers 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 the 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 (cards)|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. 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. Without any side counts, PE can approach 70%.<ref name="tob-19794" /> 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.<ref name="qfitcc2"/>
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