Mysterium: Card Counting 101
Posted by Jonathan Bayme on 23 January 2013
Editor's Note: This article is the second in a new, weekly series by Jason England: MYSTERIUM. Each article in this series will be posted on Wednesday at 11:00am EST - every post on a different subject. This week's article is all about the count...
Mysterium: Card Counting History & Methods - By Jason England
Within the realm of gambling games using playing cards, the concept of keeping track of cards that have been played has been around for centuries. In some games, mechanical devices have been used to assist the player by displaying the number of cards of a given value that have appeared.
The game of faro comes to mind. The faro ‘casekeeper’ is a wooden frame that resembles an abacus. Beads of wood or ivory were used to keep track of the number of cards that had been removed from the deck as the game progressed.
After the deck was exhausted, the beads were moved back to their starting positions and the next game started anew.
In other games, it’s just as crucial to keep track of the cards that have been played, but it’s up to the individual players to do so on their own. The game of Gin Rummy comes to mind. To be successful at this game, you must have an excellent memory for what cards have been played and what cards have been picked up by your opponent.
In the late 1940's, there were a number of “systems” players that apparently managed to play winning games of blackjack by devising a crude, but effective strategy through sheer brute-force observation and some rudimentary mathematics. Depending on how you define the game of blackjack, it’s possible that similar players had been attacking the game, in its variant forms, for decades.
In the 1950's a group of mathematicians at an Army base in Maryland developed the first mathematically derived basic strategy for the game of blackjack.
This basic strategy has been refined over the years, but the essence of it came from this team of Roger Baldwin, Wilbert Cantey, Herbert Maisel, and James McDermott. Basic Strategy is a compilation of all the correct ways of playing the various hand totals against the possible dealer upcards. For instance, when the player has a total of 13 against a dealer upcard of a 9, the player should hit until he or she has a total of 17 or higher, or until he or she busts.
If the player has a total of 11 against a dealer upcard of a 6, then the player should double-down. Basic Strategy has been confirmed as accurate by the computer simulations of millions upon millions of hands of blackjack. It is absolutely the right decision to make in any situation, unless you have other information that you wouldn’t normally have. And that concept brings us to card counting…
Building on the work done by the group of mathematicians led by Roger Baldwin et al, a professor from UCLA named Ed Thorp devised what most experts consider the first truly accurate card counting system#. He called it the “Ten Count” and published it in Beat the Dealer (1962).
Beat the Dealer took the nation by storm and scared many casinos into changing the rules. However, when they did this, the players stayed away in droves. Eventually the casinos decided to change the rules back to the old ways, and the players began to return to the tables. Blackjack remains the most popular table game on the casino floor to this day, surpassing craps in the late 60s or early 70s.
Thorp’s original Tens Count was very difficult to play in a real casino environment. More than likely there were just as many people losing money with the system by using it improperly as there were people making money with it. But, a breakthrough was just around the corner.
In Thorp’s second edition of Beat the Dealer, he introduced a new card counting system called the “Hi-Lo.” The Hi-Lo was actually invented by Harvey Dubner, and refined over the years by Thorp, Julian Braun of IBM, and Stanford Wong.
The Hi-Lo is easily the most popular count ever developed. It works like this: the 2's-6's are counted as +1, the 7's-9's are 0, and the 10-valued cards and aces are counted as -1.
If you begin your count at 0, then the 20 low cards (+1) will perfectly balance out the 20 high cards (-1). The 7s, 8s, and 9s don’t change the count at all. You should start and end your count on 0 if you go all the way through a normal deck of cards.
When your count is in the positive numbers, then this means that more low cards have been removed from the deck than high cards. This is good for the player, because the deck is now rich in high cards. This means more blackjacks for the player, more 10-valued cards when the player doubles, and more busted hands for the dealer.
When there are more low cards left in the deck (a negative count), this is not good for the player. The dealer will make a good hand more often, the player won’t get as many blackjacks, and doubling down on totals of 9, 10 or 11 won’t be as profitable.
Basically all card-counting systems boil down to tracking this relationship between high cards and low cards in the deck. As I stated earlier, more high cards left in the deck is good, more low cards left in the deck is bad. When the deck is positive, the player should increase his bets, and when the deck is negative, the player should decrease his bets to the minimum, or not play at all! Incidentally, it’s no more difficult to count 2, 4, 6 or even 8 decks of cards than it is to count a single deck. Granted, it takes longer to get to the end of the shoe in multiple deck games, but the actual process of counting is no more difficult. Movies like Rainman perpetuate the myth that counting into a 6-deck shoe is a nearly impossible skill. Wrong. Anyone can learn to do it in a matter of weeks with some simple practice.
The Hi-Lo is a simple level one count. This means that none of the count numbers are higher than 1. There are level-2, level-3 and higher counting systems that have been devised. A powerful, but very difficult to play, count is the Revere Advanced Point Count. This is a level-4 count that was devised by Lawrence Revere (not his real name) and was popular amongst serious players in the 1980s and 90s.. The problem with multi-level counts is that though they are often more accurate, they are so much more difficult to play that the mistakes made with them more than make up for their increased accuracy. Most players get by just fine with a level-1 count like the Hi-Lo.
Other card-counting systems that had various degrees of popularity and success include the Hi-Opt (two versions), the Omega II (aka the Canfield Master), the Red-7 Count, the Uston APC and the previously mentioned Revere APC.
A relatively new count that was first published in 1996 is the K-O count. The K-O count is named after its inventors, Ken Fuchs and Olaf Vancura. The K-O is an excellent count for beginning counters and is almost as powerful as other level-1 counts.
The K-O count tracks cards as follows: 2s-7s are + 1, 8s and 9s are 0, and 10s and aces are -1. Notice that this is very similar to the Hi-Lo, except that 7s are now counted as low cards instead of medium cards. This small change has some interesting consequences. First of all, the K-O is not a balanced count. There are now 24 low cards, 8 medium cards, and only 20 high cards.
This means that if you start on 0 you won’t end on 0. You’ll end on -4. Or, you could begin on -4 and then you would indeed end on 0. This is called an ‘unbalanced’ count and there are several of them. If you’ll recall, the Hi-Lo had the same number of high cards as it did low cards. The Hi-Lo is an example of a balanced count.
The advantages of an unbalanced count revolve primarily around the calculation of the true count vs the running count. Let’s talk about that distinction.
Although I didn’t mention it earlier, the Hi-Lo (and other unbalanced counts) needs an adjustment before it can be used at a real table. Let’s say you’re playing in a 6-deck shoe, and the count in your head (using the Hi-Lo) is +9. Let’s also assume that 3 decks have been dealt out and 3 decks remain in the shoe. You must convert the count currently in your head, called the ‘running count,’ into what is known as the ‘true count.’ This involves dividing the running count by the number of decks remaining. In this case, 3 decks remain, so you would divide +9 by 3 to come up with a true count of 3. You would use this true count to make your betting and playing decisions, not the running count of +9. However, you would continue to count from the running count of +9 when the next hand was dealt. Making this constant conversion back and forth in your head can be difficult to do initially, but gets easier with practice and experience.
So, when using the Hi-Lo, a player must keep the running count at all times, estimate the number of decks remaining before each hand, divide the running count by the number of decks remaining to get the true count, and then bet and play according to the true count all while continuing to add to the running count! And all of this must be done in a split second, under the watchful eyes of the dealer, the floor person, and the eye in the sky.
The K-O count solves some of these problems. Like many unbalanced counts, the K-O doesn’t need a running count to true count conversion. This makes your life a bit easier at the table, since you don’t have to estimate the number of decks left, nor do you have to do mental division! The K-O does give up a bit of power and accuracy in exchange for being easier, but many players find the trade-off to be a good one.
The casinos responded to the card-counting phenomenon by changing the rules and the format of the game considerably. Gone are the days when games were dealt down to the very last card. Most current blackjack games are dealt from multi-deck shoes, with 4 and 6-deck games being the most common. Some of the playing options of the past, such as early-surrender, are now difficult to find and often don’t stick around for very long even when they are re-introduced. Although counting cards can still be used to make money at blackjack, it’s a much more difficult and involved process than it was 30 or 40 years ago. In fact, many professional advantage players have moved on to other concepts and methodologies and now only play “regular” blackjack when ideal conditions present themselves. But those are topics for another time.