Card Counting

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.

Basics

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, (especially 4s, 5s, and 6s) 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.

Contrary to the popular myth, card counters do not need unusual mental abilities to count cards, because they are not tracking and memorizing specific cards. Instead, card counters assign a point score to each card they see that estimates the value of that card, and then they track the sum of these values – a process called keeping a “running count.” The myth that counters keep track of every card was portrayed in the 1988 film Rain Man, in which the savant character Raymond Babbitt counts through six decks with ease and a casino employee erroneously comments that it is impossible to count six decks.

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 shoe, while high cards decrease it for the opposite reason. For instance, the Hi-Lo system subtracts one for each dealt ten, 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 larger and larger numbers and are broken into classes such as level 1, level 2, level 3, and so on, with regards to the ratio between the highest and lowest assigned point values.

The High-Low system is considered a single-level or level-one count, because the count never increases or decreases by more than a single, predetermined value. A multilevel count, such as Zen Count or Wong Halves, 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. 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.

Card Strategy	2	3	4	5	6	7	9	10, J, Q, K	A
Hi-Lo	+1	+1	+1	+1	+1	0	0	−1	−1
Hi-Opt I	0	+1	+1	+1	+1	0	0	−1	0
Hi-Opt II	+1	+1	+2	+2	+1	+1	0	−2	0
KO	+1	+1	+1	+1	+1	+1	0	−1	−1
Omega II	+1	+1	+2	+2	+2	+1	−1	−2	0
Red 7	+1	+1	+1	+1	+1	+0.5	0	−1	−1
Zen Count	+1	+1	+2	+2	+2	+1	0	−2	−1

The KO Strategy was first introduced in 1992 as the “All Sevens” count in The Book of British Blackjack.

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 optimum 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.

The observation of the ace plays a key role in such a way that when the ace has a distinct point value, you will see an increase in betting correlation since the ace is the most valuable card in the deck. However alerting the player to the presence of additional aces in a deck decreases the efficiency of altering play decisions based on the count lowering a system’s PE since the ace offers very little value when playing out a hand. If a system does not assign a point value to an ace, it will see a decrease in BC with an increase in PE; in a situation in which the change in PE will offer a greater gain than a slight loss of BC, such a system is preferable.

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.

It is most common to keep a side count of aces 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/deck that have already entered play typically at the expense of lowering PE.

Running counts versus True counts in Balanced counting systems

The Running count is the running total of each card’s assigned value. When using 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 haven’t yet been dealt; this can be calculated exactly or approximated with an average card count per round times the number of rounds dealt. However, many variations of True count calculation exist.^[10]

Back-counting

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. Stanford Wong first proposed the idea of back-counting, and the term “Wong” comes from his 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 his/her 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.

Advantages

Back-counting is different from traditional card-counting, in that the player does not play every hand he sees. This offers several advantages. For one, the player does not play hands at which he does not have a statistical advantage. This in turn reduces variance and fluctuations, and 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.

Disadvantages

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. 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.

Group counting

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 21.

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 he/she sits 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 as normal. The disadvantages of this variation are reduced ability of the spotter and big player to communicate, reduced comps as the spotters aren’t 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).

Ranging bet sizes and the Kelly criterion

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 edge. Using this principle, a card counter may elect to vary his 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 aims to maintain a constant risk of ruin for every bet made. Taken to its ultimate conclusion, the Kelly criterion would demand that a player not bet anything at all when the deck doesn’t offer a positive expectation; the “Wonging” strategy described above implements this.

Expected profit

Blackjack played with a perfect basic strategy typically offers a house edge of less than 0.5%, but a typical card counter who ranges bets appropriately in a game with six decks will have an advantage of approximately 1% over the casino. Advantages of up to 2.5% are possible at normal penetrations from counting 6-deck Spanish 21, for the S17 or H17 with redoubling games. This amount varies based on the counter’s skill level, penetration (1 – fraction of pack cut off), and the number of betting units that the counter is able to spread from. The variance in blackjack is high, so generating a sizable profit can take hundreds of hours of play. The deck will only have a positive enough count for the player to raise bets 10%-35% of the time depending on rules, penetration and strategy.

At a table where a player makes a $100 average bet, a 1% advantage means a player will win an average $1 per hand. This translates into an average hourly winning of $50 if the player is dealt 50 hands per hour.

With typical bet ranging and typical Las Vegas six-deck rules, a player whose strategy yields an average profit of $50 per hour will likely face a standard deviation in the neighborhood of $1,400 per hour. Therefore, it is highly advisable for counters to set aside a large dedicated bankroll; one popular rule of thumb dictates a bankroll of 100 times the maximum bet per hand.

Another aspect of the probability of card counting is that, at higher counts, the player’s probability of winning a hand is only slightly changed and still below 50%. The player’s edge over the house on such hands does not come from the player’s probability of winning the hands. Instead it comes from the increased probability of blackjacks, increased gain and benefit from doubling, splitting and surrender, and the insurance side bet, which becomes profitable at high counts.

Many factors will affect a player’s expected profit while attacking a game, such as:

The overall efficiency of a card counting system at detecting player advantage, this affects how often the player will actually play a hand at an advantage per period of time
The overall efficiency at creating player advantage as a whole, a system may indicate a small advantage when in fact the advantage is much larger, this reduces the overall ROI of the system while in play.
The rules of the game.
Penetration will almost directly affect the magnitude of player advantage that is exploitable, and the rate that hands are dealt to a player at an advantage.
The number of players seated at a table will slow game pace, and reduce the number of hands a player will be able to play in a given time frame.
Game speed, table with side bets will be dealt at a slower pace than tables without them which will reduce the number of hands dealt over time.
The use of an automatic shuffle machine or in rare cases, a dealer dedicated solely to shuffling a new shoe while another is in play, will eliminate the need for the dealer to shuffle the shoe prior to dealing a new one increasing game speed.