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Introduction to Blackjack Card Counting

Card counting is, as the name indicates, a technique of counting the cards that have already been dealt to have an estimation, by their absence, of those that remain to be dealt from the deck. Various systems have been developed for counting cards, none of which require a photographic memory or a genius IQ. All a player needs do is to keep track of a running total that reflects whether the remainder of the shoe is favorable, by a relatively simple system that's accessible to a person of average intelligence. That running total, or "count," leads the player to increase his bets when the deck is in his favor and decrease them (or leave the game) when it is in favor of the house.

Isn't This Cheating?

The practice of counting cards it is discouraged by casinos, which have succeeded in casting the practice in a negative light to the point that many players erroneously believe that it is illegal. Where it is permissible for casinos to do so, they will gladly eject a player who counts cards (or ban card counters altogether). However, this is all a marketing campaign on the part of the casinos to discourage players from making the smart bet. Simply stated, card counting is not illegal, nor can it fairly be considered a form of cheating.

Cheating is, by definition, an intrusion that offsets the odds. A cheater may collude with the dealer, alter equipment, use sleight of hand to increase his wager or switch his cards after the deal, or in other ways actively alter the situation or circumvent the rules to force the odds in his own favor. The card counter, meanwhile, merely observes phenomena that are visible to anyone at the table under normal circumstances. When the natural course of events happens to turn in his favor, he makes the best of it. This does not violate the rules of the game or alter the situation at all, any more than a sports bettor who considers the past performance of a team before placing a wager for or against them.

Neither does card counting absolutely guarantee a victory. Even in situations where the deck seems to favor the player by a wide margin, the order and value of the cards remain random. Regardless of the "weight" of the deck, the cards will fall as they may. There is a higher likelihood of winning in some situations, and the card counter will increase his wager accordingly—but the possibility of losing always remains.

For these reasons, casinos have been unsuccessful in their attempts to lobby for legislation or win court cases against card counters. The practice remains completely legal. In locations where a casino is permitted to refuse service to anyone, card counters are actively pursued, expelled, and banned from the premises. Simply put, the house does not want to serve the gambler who stands a good, or even fair, chance of winning.

How Card Counting Works

A popular aphorism is: "past performance is no guarantee of future results." This saying is often used to discourage players from paying attention to the previous outcomes because history offers no advantage. In most cases, this is correct.

For example, a coin may land on heads five tosses in a row, defying probability—but that does not mean that the next toss is more likely to be tails, because each toss is an independent random event. There is still a 50/50 chance of heads or tails on the sixth toss. The same holds true for most casino games: roulette, craps, slots, baccarat, and so on, because each involve a sequence of events that are (largely) both independent and random.

However, blackjack is an exception to this general rule because the outcome, while still random, is not entirely independent. Once card has been dealt, it will not be dealt again—and its absence from the remaining deck affects the likelihood of the outcomes of future hands (until the cards are shuffled).

If all four aces have come out of a single deck in the first hand dealt, this absolutely guarantees that no others will appear in the next hand, or the next, until the deck is shuffled. If two aces came out in the first deal, it doesn't guarantee the aces will not come out as players hit their hands—but it makes it 50% less likely. This is the basis for card counting.

Various mathematical models and computer simulations have been run to determine the precise effect that removing an individual card has on the deck. Most arrive at the figures shown to the right. In general, the removal of low cards favors the player, removal of the high cards favors the dealer. It's also important to remember that this is the effect per deck. In a six-deck game, six fives must be dealt before the remaining deck is shifted by 0.64% in the player's favor.

At first blush, the concentration of high cards in the deck wouldn't seem to matter, as the high cards are just as likely to be dealt to the dealer as to the player—but consider these factors:

1. A player is paid a 50% bonus (3 to 2) when a blackjack is dealt, and loses only the original wager if the dealer receives blackjack. (And at a point, insurance and even money options become smart bets to prevent this loss.)
2. A player can double down on a low or soft hand, and generally does best when dealt a high card.
3. A player can surrender any hand that he does not feel will win, rescuing half his original wager.
4. They player can stand at any time, whereas the dealer must hit to 17 or bust. A bust is more likely when there are more high-value cards in the deck.

A Situational Example

As an example of how the absence of cards alters the odds in the remaining deck, take this example of a single-deck game in which seven players are present. In the first hand:

• The dealer's upcard is a queen.
• The first player draws six-five, doubles down and draws an eight.
• The second player draws nine-five, hits and draws an ace, hits again and draws a seven, busting the hand.
• The third player is dealt a pair of aces. He splits them and draws a four and a six.
• The fourth player draws a five and an eight, hits and draws a three, hits again and draws an eight, busting.
• The fifth draws a pair of fours, hits and draws a six, hits again and draws a four, standing on 20.
• The sixth player draws a nine and an eight, stands on hard 17.
• The last player draws two jacks and stands on 20.
• The dealer turns over his hole card, a two, and hits twice, drawing threes, to stand on an 18.

After this hand is played, these cards are moved to the discard rack and the next hand is dealt with a partial deck. In the deck that remains, there are three twos; one of each three, five, and six; three sevens; two nines, fifteen ten-value cards (ten, jack, queen, king), and a single ace. In other terms, there are only six low cards (two through six) and eighteen high cards (nine, ten, ace) left, along with three sevens (which are neutral by most systems). The "count," according to a common card counting system (High-Low) is +8, meaning that the deck is skewed heavily in favor of the players.

ORIGINAL VAL # % 4 1 0.59% 5 2 1.18% 6 3 1.78% 7 4 2.37% 8 5 2.96% 9 6 3.55% 10 7 4.14% 11 8 4.73% 12 15 8.88% 13 14 8.28% 14 13 7.69% 15 12 7.10% 16 11 6.51% 17 10 5.92% 18 9 5.33% 19 8 4.73% 20 16 9.47% S12 1 0.59% S13 2 1.18% S14 2 1.18% S15 2 1.18% S16 2 1.18% S17 2 1.18% S18 2 1.18% S19 2 1.18% S20 2 1.18% 21 8 4.73%

AFTERWARD VAL # % 4 6 1.00% 5 6 1.00% 6 0 0.00% 7 6 1.00% 8 8 1.33% 9 20 3.33% 10 18 3.00% 11 2 0.33% 12 88 14.67% 13 32 5.33% 14 10 1.67% 15 30 5.00% 16 38 6.33% 17 78 13.00% 18 2 0.33% 19 52 8.67% 20 156 26.00% S12 0 0.00% S13 6 1.00% S14 2 0.33% S15 0 0.00% S16 2 0.33% S17 2 0.33% S18 6 1.00% S19 0 0.00% S20 4 0.67% 21 26 4.33%

The effect this will have on the next hand dealt is dramatic. The table to the right demonstrates the way that the odds of the second hand compare to the one that was just dealt from a freshly shuffled deck: At the start of the hand, there is a 54.00% likelihood (compared to 33.76%) of receiving a pat hand, and only a 19.33% chance (compared to 32.54%) of receiving a hand that's likely to bust. Granted, this is true on both sides of the table—but even before the hand is dealt, players are at a distinct advantage because of the four factors listed in the previous section.

Once the cards are dealt, there is a very high likelihood that the majority, if not all, of the cards left to be used as hits will be ten-value cards. If all of the low cards show, this is an absolute certainty, and players can deviate from basic strategy accordingly. A player should surrender rather than hit his thirteen against the dealer's seven (because the dealer certainly has 17 and the player is certain to bust) or double down on a two-three if the dealer shows a six (because the dealer is certain to bust).

Again, victory is not guaranteed. If the dealer draws a 20 and all the low cards come out in the player's hands, it's certain doom—any hit will bust a stiff hand and nothing will save it. Just as with any other player, the cards must turn in the counter's favor—but because he has a reliable estimate of the outcome, he can make the best possible choice whatever the situation.

The Rewards of Counting

As with any other player, a card counter will not walk away with a heap of winnings every time he plays. Because the order of the cards is always random, and because there are equal chances of a good hand being dealt to either side of the table when the count is high, it is by no means a guaranteed winning system—but it does instruct players to wager heavily when their chances of winning are better than usual.

Basic strategy alone reduces the house's edge to about half a percent, and after a shuffle, the card counter has no advantage. From there, the balance shifts to the player by about half a percent times the count (the "true count," which will be explained later). On average, the player who combines basic strategy with card counting can enjoy a 1% advantage over the house over the course of each shoe—which means he will lose slightly less and win slightly more than a player who uses basic strategy alone.

At the end of a 120-hand playing session, the counter is likely to reap a profit of five to six times his base wager. A red-chip player will earn about $25-30, a green-chip about $125-150, and a black-chip about $500-600 (less tips in all cases). Of course, this would be an average session: the player may just as easily lose his entire stake in one session and win an extraordinary amount in another. In the end, the mathematical likelihood will even things out.




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