# Card Counting

Unlike other casino table games like Craps and Roulette, where outcomes are independent events unaffected by past results, Blackjack has a built-in bias. The removal of cards from the deck during play has a direct affect on the probability of certain combinations being dealt. It stands to reason that an observant player, one who knows exactly what cards remain to be dealt, can modify betting and play accordingly, reducing the house advantage and perhaps even turning the odds to his/her advantage.

In his 1962 book “Beat the Dealer,” Dr. Edward O. Thorp described the so-called “Basic Strategy for Blackjack,” which is the mathematically optimum way to play. Thorp used statistics and computations to show that when a deck of 52 cards is low in 5’s, a greater advantage accrues to the player than when it is low on other cards. By keeping track of how many 5’s have been dealt, a player can know how many are remaining and how to bet and play.

The so-called “Five Count” system was the first basic Blackjack card-counting strategy ever devised. The player is advised to wager the maximum whenever all of the 5’s are gone from the deck. A table showing the appropriate amount to bet for other situations was developed based upon the number of 5’s removed and how many cards remain.

Once this simple strategy has been mastered, the player can incorporate the counting of 10’s and face cards—what is known as the “Ten Count” system. In this case, the removal of such high-value cards favors the house. Wagers should be increased when the deck is “rich” in cards valued at ten and decreased when it is “lean.”

The only problem, of course, it that players with average IQs and lacking the benefit of photographic memories find it almost impossible to count individual cards. Especially when playing Blackjack against a dealer who uses more than one deck and surrounded by distractions, it is extremely easy to lose track of the count.

A variation on Thorp’s Basic Strategy was proposed a few years later by Stanford Wong and Julian Braun. Their “Hi Lo” system was based upon calculations showing that the removal of low cards (2~6) from a deck helps the player, while the removal of high-value cards (10~A) favors the house.

In 1969, author Lawrence Revere popularized this simpler way of counting in his classic bestseller, “Playing Blackjack as a Business.” Instead of remembering what has been played, all the card counter has to do is add or subtract small numbers from a running total and wager according to whether the count is positive or negative.

Revere’s “Plus Minus” system is still the most commonly used strategy among card counters to this day. In a nutshell, revealed low cards (2, 3, 4, 5, and 6) are each given a value of +1. Each high card that is dealt (10, Jack, Queen, King and Ace) counts as -1. All the other cards in the deck (7, 8, and 9) have no value and can be ignored.

When playing with a single deck, players are advised to bet the minimum, one unit, when the count is +1 or less or bet two units when it is +2 or more. If multiple decks are used, the procedure is adjusted accordingly. With four decks, the tipping point becomes +4 or lower for a one-unit bet and +5 or higher for a two-unit wager. For six decks, it is +6/+7 and for eight decks it is +8/+9.

Wagering is not the only aspect of the game affected by card counting. Basic play changes, too. For example, when the count is a high positive number, Revere would often stand on a hand totaling 12~16 or double down on an 8 or 9. He developed elaborate tables indicating exactly how to play in any situation, with all possible card totals and facing any count value.

Not surprisingly, card counting is still difficult to master. Revere himself once said that the system must be played perfectly to deliver reliable profits, and “if you make two mistakes an hour, you are not going to win anything.”

Using computers or other computational devices to help count cards is strictly illegal in most casinos of the world, but there are no laws against keeping count in your head. For that reason casinos use other tactics, such as changing table stakes, shuffling more often, and varying the speed of play, to throw counters off their systems. Pit bosses know that very few players can count cards well enough to win consistently, but those who do have a real advantage at the tables.