Most casino players think of card counting as an esoteric skill requiring feats of superhuman memory and computer-like mathematical prowess. The reality is that thousands of players know how to count cards in blackjack, and most of them have average intelligence. Counting cards is one of the only ways to get a consistent mathematical edge over a casino, but it does require significant amounts of dedicated practice and study before you can reliably count on that edge.
Entire books and websites have been written about this particular method of advantage gambling. The purpose of this page isn’t to provide a comprehensive guide to card counting, but it does aim to provide a detailed discussion of the basics.
Edward Thorp published Beat the Dealer in 1962, and this date is considered the genesis of advantage play at blackjack. According to multiple sources, including Thorp, but also according to Stanford Wong’s Big Book of Blackjack and Andrew Brisman’s Mensa Guide to Casino Gambling, early blackjack players intuitively gained an edge over the casino game by using primitive counting techniques. The idea wasn’t popularized or a concern of the casinos until the publication of Thorp’s book, though.
The casinos’ reaction to the publication of Beat the Dealer was a comical overreaction. They were afraid that mobs of blackjack players would start taking them for all they were worth, and so they made dramatic changes to their house rules in order to make it impossible to get an edge. Before Beat the Dealer, it was common for a casino to deal blackjack from a single deck and to deal all the way to the bottom of that deck. This practice was eliminated, and several other rules designed to eliminate a counter’s edge were put into place. This backfired, though—the rules had become so restrictive that even the people who weren’t counting stopped playing blackjack.
The reality is that the casinos probably didn’t have much to worry about in the 1960s. Thorp’s methods were a little on the unwieldy side, and even though blackjack was the fresh new “beatable” casino game for intelligent players, most players didn’t study or practice enough to actually get an edge. What had happened instead was that a lot of clueless players started playing, which probably made more money for the casinos’ blackjack tables than they would have before. In fact, one of the reasons that blackjack makes up 50% of a casino’s table game revenue is that it’s considered a game that an intelligent player can beat.
Card counting systems in blackjack are a means of advantage play in which you gauge how favorable or unfavorable the deck is, and then betting more or less based on that estimate. This estimate is arrived at, not by memorization, but by a heuristic system which assigns a point value to various cards in the deck. Once a card has been removed from the deck, it either makes the deck more favorable for the player or less favorable for the player. This effect is tracked by adding and subtracting numbers from a mental tally called “the running count”.
Imagine that you’re playing roulette, and you place a bet on red, and you want to know what your chances of winning are. The calculations are simple enough; you simply divide the number of red slots on the wheel by the total number of slots on the wheel. On an American roulette wheel, you’d have 18 red slots, 18 black slots, and 2 green slots, for a total of 38 slots on the wheel. 18 divided by 38 is 47.37%, which is your chance of winning. No matter whether you win or lose on that bet on red, if you bet red again on the next spin of the wheel, your odds of winning are the same: 47.37%. They don’t change based on what’s happened before.
Now suppose you’re playing a card game similar to roulette, where the dealer turns over a card, and you bet on whether or not the next card is going to be red or black. The deck of cards has 18 red cards in it, 18 black cards in it, and 2 jokers. If you bet on red, you have a 47.37% chance of getting a red card. Now suppose that card is discarded, and you’re dealt another card. Have the odds of getting another red card changed? The answer should be obvious, because now there are only 37 cards total in the deck, and only 17 of them are red, so the odds of winning become 17/37, which equates to 45.95%. The odds of getting a black result have increased to 18/37, or 48.65%.
Now suppose you get red five times in a row. If you’re playing roulette, then your odds of winning your next bet on red is still 47.37%–they don’t remove red slots on the wheel when you’ve won. But in this imagined card game we’ve come up with, the difference is significant after five red wins in a row. The chances of being dealt a red card on the next play have gone down to 13 divided by 33, or 39.4%. Meanwhile, the chances of being dealt a black card on the next play have gone up to 18/33, or 54.54%.
Now suppose you only bet a single dollar on the first five bets, so you’ve lost $5. But now that your odds of winning (by betting on black) are more likely than not, you raise the size of your bet to $20. Your expected value is 54.54% of that $20, or $10.90. And if you kept playing long enough, you’d continue to find opportunities to make bets with a positive expectation.
That’s a remarkably accurate description of how card counting systems work, but instead of tracking the colors of the cards, you’re tracking whether the cards are high or low. In some systems, what constitutes “high” or “low” varies based on goals having to do with accuracy and ease of play. Either way, you’ll know when the deck is in your favor, because when the deck has lots of high cards in it, you’re more likely to get a 3/2 payout on a natural 21, and you can bet more to take advantage of the situation. You’ll bet less when the deck has lots of low cards in it, because the dealer is less likely to bust, which isn’t a favorable situation for the player.
Some of the most commonly used counting systems include the following:
Each card has a value to a blackjack counter, and that value is called “the effect of removal”, or “EOR”. The EOR for the aces and fives have the largest effect on a player’s chances. If you remove all the aces from the deck, then a natural 21 is impossible, which subtracts considerably from the player’s chances of getting ahead. On the other hand, if you remove all of the fives from a deck, the EOR is so great that it would make almost any blackjack game a positive expectation game for the player.
The simplest card counting system is called an “Ace-Five Count”, and you simply add 1 to the count every time a five is dealt and subtract 1 from the count every time an ace is dealt. The higher the count is, the more you bet. If you have a wide enough betting range, say anywhere from 1 unit to 10 units, this is a remarkably easy and effective system. Most people are looking for more of an edge than this simple count offers, though, and they use slightly more complicated systems. (Something to notice about this system is that there are just as many +1 cards in the deck as there are -1 cards in the deck—this is called a “balanced” counting system, as a result. Not all systems are balanced.)
All card counting systems estimate multiple factors related to their effectiveness. The first of these is called “betting correlation”, and it’s probably the most important one. This number determines how well the count estimates the player’s edge—this is important for making decisions about betting amounts. The second of these is called “playing efficiency”, and this estimates how well the count takes into account changes to basic strategy. This factor isn’t as important as it may seem, but players who want to squeeze every percentage point of value out of their blackjack card counting system pay attention to it. The third and possibly least important factor is the “insurance correlation”, which is an estimate of how well the system predicts whether or not insurance is a good bet.
We already discussed balanced systems versus unbalanced systems, but just to reiterate, a balanced system is one in which the count evens out to 0 when you count through the entire deck. For example, the Hi-Lo system, which is quite popular, is a balanced system that counts aces and tens as -1 and counts any card ranked 2 through 6 as +1. There are 20 cards in each category, positive or negative, and when you finish counting through a deck, you’ll have a total running count of 0. In an unbalanced system, this isn’t true.
The Hi-Lo system is also an example of a single level system, because the cards are all valued at either +1 or -1. A higher level system might give different values to different cards. For example, if a system counts aces as -2 and fives as +2, and then counts tens as -1 and 2s, 4s, and 6s as +1, then the system would be a multi level technique.
Some card counting systems go even further and require you to keep a side count of the aces that have been dealt. The more complicated the rules for the system are, then the more accurate it is, but you need to remember that your system should also be practical. You’ll be counting cards in a crowded and noisy casino, so you need to be able to concentrate without looking like your concentrating. Practice is necessary, but so is a simple enough strategy.
In almost all casino games, each wager is made on an independent event, so there’s no way to overcome the game’s insurmountable mathematical edge. Blackjack is an exception, though—the odds change with every card that’s dealt in a blackjack game. For example, if you spin the wheel on a roulette game, and you wager on black, then 18 of the possible outcomes are winners. On your second spin, that same wager on black has the same number of potential winning outcome: 18. In blackjack, though, the cards that have been dealt change the number of potential outcomes. For example, if all four aces have been dealt, the probability of being dealt a natural 21 have been reduced to 0%. (You can’t get a natural blackjack without an ace in the deck.)
As a general rule, a deck with a lot of high cards (tens and aces) left in it is better for the player, while a deck with a lot of low cards (twos, threes, fours, fives, and sixes) is better for the dealer. When the deck is rich in high cards, the player has a better chance of being dealt a natural, which pays out at 3 to 2. Perceptive readers might notice that the dealer also has a better chance of getting a blackjack, too, but the dealer doesn’t get a 3 to 2 payout—only the player does.
Some of the advantage from counting cards is had from making some simple basic strategy changes. For example, in a deck that’s rich in tens and aces, it makes sense to avoid hitting stiff hands. The dealer doesn’t get to make this decision; the dealer has to hit a certain total and stand on a certain total, regardless of whether or not it’s the right play given the composition of the deck.
Another strategy change with a deck that’s composed more than 2/3 of high cards is to take insurance. Normally that’s a sucker bet with a huge negative expectation, but not when you’re counting cards and know the score.
When the deck is rich in lower ranked cards, the dealer is less likely to bust, making it harder for the player to win that way. It’s also less likely that a player will be dealt a natural when there are still a lot of low cards in the deck.
The bulk of the player’s advantage comes from betting more when the deck is rich in high cards and betting less when the deck is rich in low cards. The 3 to 2 payout for a blackjack is where the counter gets most of his edge. Most counters range their bets from 1 to 5 units based on how favorable the count is, but some even range their bets from 1 to 10 units. The casinos watch players who ranger their bets, though, so don’t be surprised if you don’t get some “heat” from the casino. Professional blackjack players use various means of “camouflage” to disguise the fact that they’re counting, and they even sometimes work in teams. You can see examples of camouflage in action in the movie 21, which shows one way in which a team takes advantage of a hot deck.
You don’t have to memorize all the cards that have been played in order to count cards. Card counting uses a heuristic method of tracking the ratio of high cards to low cards. The Hi-Lo system is one of the most common ways of doing this. It assigns the following values to the following cards:
You start your count at 0, and then as each card is dealt, you adjust the account by either adding 1 or subtracting 1. That running total is called the “running count”, but the running count alone isn’t enough to make you profitable. Most casinos use multiple decks, so you have to convert the running count into what’s called the “true count” in order to make the correct decisions.
In order to calculate the true count, you first estimate how many decks are still left in the shoe (the device which holds the cards for the blackjack dealer). Then you divide the running count by the number of decks left. For example, if your running count is +4, and you estimate that 4 decks remain in the shoe, then the true count is +1.
The higher the count, the more you bet. Competent counters can reduce the house edge, in which the player has a disadvantage of 1% or 2% to the casino, to an edge of 0.5% to 1.5% over the casino. If you’re playing for $20 per hand on average, and you play 100 hands per hour, then you’re putting $2000 per hour into action. With a 1% advantage, that means you can expect, in the long run, to earn $20 per hour for your efforts.
Keep in mind that this number isn’t guaranteed, either. In the short run, anything can happen, and even card counters with large bankrolls can go broke quickly if luck turns against them. Besides short term fluctuations in the mathematics of the game, casinos will often refuse to let you play blackjack. In Atlantic City, it’s illegal for a casino to bar a player from blackjack, but they’ve made the rules there so tight that it’s practically impossible to get an edge over the casino.
Other card counting strategies offer varying degrees of complexity in exchange for varying degrees of accuracy. Most players look for a balance of practicality and play-ability when choosing a system. Other pages on our site look at the specifics of these other counting techniques.