Blackjack has always held the interest of academia. Today, basic strategy and card counting are common knowledge, and a plethora of books and other guidance is available to anyone who wants to learn how to play and win.

But at one time, playing blackjack for a long-term, mathematically proven profit was an unsolved problem. That time was not as long ago as you might think... the 1950s saw many mathematicians writing papers on the optimal way to play blackjack (lose the least money, or win the most). It is not hard to imagine that there is a best play for any given player hand and dealer upcard. And since the game is played from a fixed deck, or shoe of cards, one can easily ask if the remaining composition of unplayed cards greatly impacts the casino's edge (or player's profit). Prior to 1956, no one really knew with certainty whether blackjack was a beatable game. While it's easy to ask the question, blackjack is a more difficult game to analyze statistically than roulette, craps or other independent games of chance, where each future outcome is independent of the prior rolls or events.

In 1956 and 1957, the "Four Horsemen of Blackjack," Roger Baldwin, William Cantey, Herbert Maisel, and James McDermott, published seminal academic papers that were the culmination of 18 months of grueling manual number crunching. Their first paper, "The Optimum Strategy in Blackjack," published in September of 1956 in the Journal of the American Statistical Association, developed what we now know as basic strategy: the best way to play any combination of player and dealer up card. In 1957, they published "Playing Blackjack to Win: A New Strategy for the Game of 21," which went one step further and proved the basic concept of card counting: depending on the distribution of the remaining cards in the shoe, the player can get a positive edge over the casino.

Given everything was done by hand without the aid of computers (just math, and calculators), their achievements are all the more extraordinary. Computers and blackjack simulation software have since proven the tool of choice to study advantage play in blackjack, and have refined and improved these early works.

Beyond academic circles, not much happened with these works. The Four Horsemen apparently made less than $30 each in royalties from the publication of "Playing Blackjack to Win." Then Professor Edward O. Thorp picked up on this research, used computers to test and refine it, then tested it in casinos, and in 1962 published "Beat the Dealer," which became a best-seller with sales of over 500,000 copies. Card counting had entered the main stream.

Thorp's "Beat the Dealer" definitely changed the world of casino blackjack. The book even made the New York Time's best seller list, which really brought card counting to the attention of players and casinos alike.

Many average players bought the book to learn how to beat the casino at blackjack using card counting. And casinos reacted in kind by eliminated beatable blackjack games, by shuffling more often, by adding more decks of cards, or otherwise worsening the rules that allowed the players to get a slim edge.

But while the concept of card counting is simple, mastering it and putting it into practice in the casino is not. Thorp's Simple Point Count System, and especially the Complete Point Count System, were hard to learn effectively with the presentation in his book. While the details were accurate, and the player advantage they yielded correct, almost no attention had been paid to making card counting easy to learn by average players.

Card counting started in the world of academia where intellectual prowess, combined with hard work and study, were the primary tools of successful application of these new card counting techniques. And since the concept was so simple, no attention was paid to the successful study of card counting.

Casinos are in business to make money, and they quickly learned that with the worsened rules, their blackjack cash-cow was not bringing in players anymore. They slowly brought back the 'juicy' games with good rules, and were surprised to see their profits increase! A half million copies of a card counting book had not made 500,000 advantage players. It had simply drawn in more gamblers intent on winning, but not practicing card counting anywhere near the level required to win.

So beatable blackjack games returned, and very few players actually mastered card counting enough to play with an advantage. Card counting, in fact, proved too hard to learn for most gamblers. It remained in the hands of academics, math geniuses, and those very few hard-working professional gamblers, who truly put the time in to master it. Things stayed this way for a very long time.

During the 70s and 80s, card counting was employed by professional gamblers against the casinos, and a lot of money was made by a very small number of people, who mastered the skill. Card counting was a 'dark art,' open only to an elite inner circle of players. Why would this establishment want to help average gamblers get an edge over the casino? The answer is... they did not. So card counting stayed closed, with virtually no attempts to properly educate layman, or developing easier advantage play methods.

In 1981, professional gambler Ken Uston published his amazing book, "Million Dollar Blackjack." Ken was a brilliant Yale graduate who became the Vice President of the Pacific Stock Exchange. He left the business world to become a professional gambler and he made millions using his own advanced techniques and strategies. His book did a better job than all works up to that time at providing proper tools and guidance to master card counting, including flash cards and other tutorial methodologies. It even included two 'simplified' count systems, the Ace/Five Count and the Simple Plus/Minus. Unfortunately, the former was at best a 'toy' system, even by Ken's own account, and the latter actually added more card point values to sum-up than High-Low.

In 1998, Vancura and Fuchs wrote "Knock-Out Blackjack," introducing the KO unbalanced system. The main simplifying attribute was to eliminate the calculation of the True Count, which required dividing the running count by the number of decks remaining. But it counted the sevens as +1 (which High-Low, the base method going back to Thorp's first entries, did not), which only made tracking the count in live blackjack games harder. The main benefit of "Knock-Out Blackjack" to layman gamblers was in the clear and simple writing style, which focused almost exclusively as a training text, rather than an academic paper or personal account of fame and fortune. But KO was the best out there for simplified count systems and instructional guides, and even had the benefit of providing almost the same win rate and edge as High-Low.

The process of taking blackjack out of the ivory tower and elite crowd of professional gamblers had begun. But before we look at the next historic steps, let's take a step back and examine why card counting is so easy, yet so hard.

But the books say card counting is easy, isn’t it? Just track the count: add and subtract some numbers as the cards come out, and this single count metric is all you need to win, and the computer simulations prove it! Bet more when the count is high and you have the advantage, and bet less otherwise. Now go forth and multiply… your bankroll! What could be easier?

I get the question above from many novices (usually at parties when non-gamblers ask me what I do for living). The easy answer is that while the concept of card counting is incredibly simple, mastering the method is surprisingly difficult. And it's precisely because of this fact that many players who dabble in card counting end up losers at the tables. They think they are card counting like a pro ("It's so simple!"), when in reality their error rates are high enough to wipe out their edge, and put a smile on the pit bosses’ faces.

From years of experience teaching students, I know exactly what the 'hard part' of card counting is: adding and subtracting the card count values accurately as the dealer deals a medium to fast paced blackjack game. All effective card counting systems to date require both addition and subtraction, and it stops average players dead in their tracks, even with simple level one systems (just adding and subtracting one). The Knock-Out card counting system by Vancura and Fuchs improved the challenge of mastering card counting by eliminating true count calculations (and having to deal with negative integers), but it turned out this was one of the easiest skills to teach! Converting the run count to true count means dividing by the number of decks remaining, which is something you have plenty of time to do: before a bet, and occasionally before a play decision. Asking the dealer to stop dealing so you can keep up with your running count is obviously not an option.

The hard part of card counting is the constant up-and-down of the count as the dealer whips out the cards across the felt. Errors creep in, and before you knew it average Joes are betting on 'instinct' of what the count is. Thinking that you are tracking the count, and knowing the exact count, are two different things.

Two things happened around the turn of the millenium that really changed card counting for average gamblers. Fred Renzey, and my own Speed Count.

One caution: with all simplified card counting systems, you do pay a price, and that price is performance. You won't earn as much money as you would with a more advanced system, and the variance is greater, requiring more bankroll for the same risk. There is no way around this in blackjack, and don't be fooled by any system seller that tells you otherwise (and, there are such frauds out there). Of course, there are advantages to playing with a simpler system that can equate to greater profit. They may give you better camouflage from the casino's watchful eye ("He can't be counting! He's barely watching the cards!"). And using a complex count system like High-Low is mentally taxing after hours of play, which could lead to errors.

This innocent question from Henry Tamburin in December 2002, editor of this fine newsletter, led me to design Speed Count, a new blackjack card counting system unlike anything previously available.

Let me now switch gears and give you an introduction to Speed Count, a brief history of its development, and why it’s the easiest proven method for average players to use to get a positive edge in blackjack.

This is the average number of cards dealt per hand of blackjack, when you include all hands played (player and dealer). I had always been surprised how constant this number was… it varies little across different games. More decks, less decks, DAS, noDAS, S17/H17: it didn't really matter.

So what, you may ask? Time for another number:

This is the ratio of 'little' cards dealt out on average… the 2, 3, 4, 5 and 6 ranked cards (there are 20 of them per deck of 52 cards, which equates to the ratio of 5/13). Now… multiply the two numbers:

Still don't get it? Ask yourself this: how many 'little' cards should come out on average per hand of blackjack played? 1.038… a little over one little card per hand played!

And herein lies the secret 'trick' of Speed Count: you can eliminate 'on the fly' subtraction, the killer skill of traditional card counting systems, by tracking (ie. adding) instead only the little cards played per hand.

So how does Speed Count work in practice? Add one to the count every time a little card is dealt (to a player or dealer hand). At the end of the round, when you have plenty of time to think before you place your next bet, you subtract one for each hand dealt (don't forget the split hands too). As the count gets higher, there are more non-little cards remaining, and this equates to a positive player edge (more on this later). That's it!

Unlike High-Low, Speed Count is an unbalanced count system similar in mathematical properties to other unbalanced count systems (like Knock-Out). This means that the counting metric does not directly reflect your edge in the game, and the count tends to 'drift' upwards as the cards are played out. The latter property is essential in successful unbalanced count systems, and ideally the final average resting count (given an average penetration) should be close to the bet pivot. The bet pivot should be the count at which you have an edge, and good unbalanced counts should show a nice linear relationship to count and edge. The following graph shows this relationship very nicely with Speed Count:

You may wonder about the odd count numbers along the bottom of the chart. We established a different initial run count (IRC) after the shuffle for different number of decks so that the player's positive edge always occurs when the Speed Count reaches 31. You can see this transition from a negative (losing money) to positive (winning money) expectation in the above chart between a Speed Count of 30 and 31 in a two- deck game (where the IRC is 30). By the way, we chose these high IRC numbers to make sure players never had to deal with negative count numbers in practice when adding the count.

Now, back to the question of why counting the little cardws works better than counting the tens and aces. If you count the high cards (instead of the low cards), the edge does not drift in the right direction, nor do you get the nice correlation of edge to count. As noted earlier, it is essential in an unbalanced count system that the count metric moves toward the value the value that indicates a positive player edge (and hence larger bets), and with typical dealt penetrations ends on or slightly below that pivot value. Tracking only high-cards relative to the number of hands played fails to achieve this goal as well as with tracking little cards. Even if you invert the count meaning, and treat low counts as higher edge (as would be expected if counting the tens and aces instead of little cards), things do not work out well. Specifically, if you counted only tens and aces relative to hands played, then a players edge would improve when the count is low, meaning more tens and aces remaining )which are good for the player).The main reason is that when there are many tens and aces, the average number of counted cards per hand is no longer as high as 2.7, and the 'trick' we depend on to make Speed Count work begins to fail. Ultimately, the correlation between the low cards and average number of cards per hand is stronger when counting 2 to 6, instead of 10s and aces, since high valued hands (from 17 to 21, for example) will tend to have very few cards (and the reverse is less true with low cards).

I tried other wrinkles and twists, but in the end what worked best was simply tracking the little cards played per hand, with no exceptions. Card counting system developers look for two important characteristics when developing new methods: a nice linear correlation to count and increasing edge as shown above, and a histogram of counts centered on or near the bet pivot:

As shown above, we see that most hands occur at a count of 30 (the initial run count for a two deck game using Speed Count), with a nice bell curve on both sides.

Will Speed Count change the world of blackjack (for better or worse)? I doubt it… my experience is that most people who gamble are gamblers. Card counting is boring, and takes away the excitement of uncontrolled betting, which most regular gamblers seem to enjoy. As a mathematician, I get my kicks knowing that I'm playing with a positive edge, rather than from the groovy vibes of a wild gambling ride (ok, I do admit card counting and winning combined is no doubt the best combination). Casinos could probably have a bill board with the count and best play displayed, and players would still double that hard 12 when they feel lucky, or let winnings ride in a hot streak despite low counts, and otherwise play to gamble, instead of playing to win.

But for those astute players who want to play with a positive edge, there is finally a mathematically proven method that takes very little time to master compared to traditional counting systems, yet allows the average player to finally play with a positive, rather than a negative expectation. Yes, you can make more money with less bankroll risk with a system like High-Low, but very few people will take the time to master it properly, if they can do so at all.

You can be a winner with Speed Count, the easiest way to beat the casino at blackjack!

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