Card counting
Card counting is a blackjack strategy used to determine whether the player or the dealer has an advantage on the next hand. Card counters try to overcome the casino house edge by keeping a running count of high and low valued cards dealt. They generally bet more when they have an advantage and less when the dealer has an advantage. They also change playing decisions based on the composition of the deck and sometimes play in teams.
Basics
Card counting is based on statistical evidence that high cards benefit the player, while low cards, benefit the dealer. High cards benefit the player in the following ways:- They increase the player's probability of hitting a Blackjack, which often pays out at 3 to 2 odds.
- Doubling down increases expected value. The elevated ratio of tens and aces improves the probability that doubling down will succeed. The most common hand values that the player doubles down on are 11, 10, and 9; and drawing a high card to these will make a strong hand.
- They provide additional splitting opportunities for the player.
- They can make the insurance bet profitable by increasing the probability of dealer blackjack.
- They also increase the probability the dealer will bust, in the event that the dealer shows a low up-card. This also increases the odds of the player busting, but the player can choose to stand on lower totals based on the count.
Card counters do not need unusual mental abilities; they do not track or memorize specific cards. Instead, card counters assign a point score to each card that estimates the value of that card. They track the sum of these values with a running count. The myth that counters track 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 comments that it is impossible to do so.
Systems
Basic card counting systems assign a positive, negative, or zero value to each card. When a card is dealt, the count is adjusted by that card's counting value. Low cards increase the count; they increase the percentage of high cards in the deck. High cards decrease the count for the opposite reason. For example, the Hi-Lo system subtracts one for each 10, jack, queen, king, or ace and adds one for any card between 2 and 6. 7s, 8s, and 9s count as zero and do not affect the count.A card counting system aims to assign point values roughly correlating to a card's effect of removal. The EOR is the estimated effect of removing a given card from play. Counters gauge the effect of removal for all cards dealt and how that affects the current house edge. Larger ratios between point values create better correlations to actual EOR, increasing the efficiency of a system. Such systems are classified as level 1, level 2, level 3, and so on. The level corresponds to the ratio between values.
The Hi-Lo system is a level-1 count; the running count never increases or decreases by more than one. A multilevel count, such as Zen Count, Wong Halves, or Hi-Opt II, further distinguishes card values to increase accuracy. An advanced count includes values such as +2 and −2, or +0.5 and -0.5. Advanced players might also keep a side count of specific cards like aces. This is done where betting accuracy differs from playing accuracy.
Many side count techniques exist, including special-purpose counts used for games with nonstandard profitable-play options such as an over/under side bet.
Keeping track of more data with higher level counts can hurt speed and accuracy. Some counters earn more money playing a simple count quickly than by playing a complex count slowly.
This table illustrates some example counting systems.
| Card Strategy | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10, J, Q, K | A | Level of count |
| Hi-Lo | +1 | +1 | +1 | +1 | +1 | 0 | 0 | 0 | −1 | −1 | 1 |
| Hi-Opt I | 0 | +1 | +1 | +1 | +1 | 0 | 0 | 0 | −1 | 0 | 1 |
| Hi-Opt II | +1 | +1 | +2 | +2 | +1 | +1 | 0 | 0 | −2 | 0 | 2 |
| KO | +1 | +1 | +1 | +1 | +1 | +1 | 0 | 0 | −1 | −1 | 1 |
| Omega II | +1 | +1 | +2 | +2 | +2 | +1 | 0 | −1 | −2 | 0 | 2 |
| Red 7 | +1 | +1 | +1 | +1 | +1 | 0 or +1 | 0 | 0 | −1 | −1 | 1 |
| Halves | +0.5 | +1 | +1 | +1.5 | +1 | +0.5 | 0 | -0.5 | −1 | −1 | 3 |
| Zen Count | +1 | +1 | +2 | +2 | +2 | +1 | 0 | 0 | −2 | −1 | 2 |
| 10 Count | +1 | +1 | +1 | +1 | +1 | +1 | +1 | +1 | −2 | +1 | 2 |
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, 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
; Playing efficiency
; Insurance correlation
Some strategies count the ace and some do not. 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. 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%.
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.
Running counts versus true counts in balanced counting systems
The running count is the running total of each card's assigned value. When using a balanced count, 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 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
Back-counting, or "Wonging", consists of standing behind a blackjack table and counting the cards as they are dealt. Stanford Wong first proposed the idea of back-counting, hence the 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.