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Friends of Blackjack Insider... great sites from our authors and
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You've Got Heat
The true story of how a low stakes player beats the casino!.
You've read Barfarkel's articles in BJI, now get the book about his
wild experiences as an advantage blackjack player.
The Evolution of Card Counting
Introduction
Dan Pronovost is the owner and president of DeepNet Technologies,
makers of a wide range of advantage gambling training products and
software (blackjack, poker, craps). Their web site is: www.DeepnetTech.com,
and all products are available for free trial download. Dan is also
the creator of the easy-to-use card counting system Speed Count,
taught in the Golden Touch Blackjack course which is now available in
Frank Scoblete's new book, "Golden Touch Blackjack Revolution!":
www.GoldenTouchBlackjack.com/scbook.shtml.
Card Counting, 1950s - academic puzzler
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.
Card Counting, 1960s - mass hysteria
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.
Card Counting, 70s & 80s - keeping it away from the masses
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.
Why traditional card counting is easy
"You took a course to learn to count cards in blackjack?!
What a waste of money? I bought Mr. Geek's book
'Make Millions at Blackjack Just Like Me!' and it was easy!"
Today, there are more books on card counting in blackjack than sex (at
least on my bookshelf). The days in the 70s when card counting was a
'black-art' and the dominion of SPMBs (self-proclaimed-masters-of-
blackjack) ended a long time ago.
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?
Why traditional card counting is hard
"If card counting is so easy and works, wouldn't
the casinos get rid of the game of blackjack?"
Riding a unicycle is easy. Just climb on and peddle! And so the same
thing with card counting.
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.
Card Counting, 2000s- helping average gamblers win
Two things happened around the turn of the millenium that really
changed card counting for average gamblers. Fred Renzey, and my own
Speed Count.
Fred is the author of Blackjack Bluebook, and a long-time contributor
to Blackjack Insider. Like me, Fred understands that card counting is
hard for most gamblers to learn, and focuses on making it easier. And
in this he has succeeded wonderfully, and earns my praise. In his book
"Blackjack Bluebook II," Fred introduced The Ace/Ten Front Count and
the KISS count methods. Both represent much easier systems than High-
Low or Knock-Out, yet are backed by rigorous analysis and simulation
data that prove they work (i.e. give a player a positive edge in most
casino blackjack games). For the curious, Fred wrote an excellent
article, The World's Easiest Card Counting Systems, that discusses
both his excellent methods, as well as Speed Count, which I'll cover
shortly.
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.
Speed Count - the easiest way to win at blackjack
Ok... time to discuss Speed Count, the advantage play method I
developed in 2002 and which is taught in the Golden Touch Blackjack
course. Speed Count is also the core system in the Golden Touch
Blackjack Revolution! book by popular gaming author Frank Scoblete,
and now included in all my blackjack training software for Windows,
Palm OS and Pocket PCs.
"There must be an easier way for everyday average gamblers to learn to
count cards in blackjack and get an edge over the casino? what do you
think Dan?"
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.
So back to the end of 2002? Henry and I had been working together to
publish the Blackjack Insider, and we found a ton of common ground
when it came to blackjack instruction. Independently, we had taught
many students different card counting systems over the years,
including the popular Knock-Out and High-Low. And we both felt exactly
the same way about learning proper card counting techniques in
blackjack: it was too hard for the majority of average gamblers to
master. No matter how we taught students, or what system we used, only
a small percentage of gamblers had the skill and dedication to master
card counting sufficiently to a level that ensured them a good
positive edge in the game. Despite the plethora of blackjack books,
and even good blackjack training software (such as my own,
www.HandheldBlackjack.com), it still takes most individuals 40 to 80
hours to master High-Low, or even Knock-Out. We both frequently
encountered well-intentioned students who failed to master the
techniques required for live play, even with diligent practice.
Getting rid of subtraction and division
"So how do you get rid of subtraction when counting cards in
blackjack?"
I had known about a little discussed fact-of-blackjack for many years,
from studying thousands of computer simulations from Blackjack Audit,
my own company's software simulator.
2.7
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:
5 / 13
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:
2.7 5 / 13 = 1.038
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!
The devil is in the details
"Sounds simple? but does it really work?"
When I started my research to develop an easier count system that
could be learned by average players in minutes, instead of months, I
experimented with many different ideas. While the mathematical
blackjack logic above is great, turning it into a working count system
is another matter. I started by tracking the big cards played (10
valued cards and aces), which seemed the obvious approach. Oddly, this
failed to produce a positive player edge (my computers ran endless
simulations for days in this quest for a Better Count System). The
reason is complicated, and we cover it in detail in the Golden Touch
Blackjack Revolution! book. But here is the summary of my development
process for Speed Count.
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.
There's a lot more to the development of Speed Count. For example, I
developed the Optimal Basic Strategy (OBS), a variation on normal
fixed plays that generates most of the potential advantage of index
plays without the inevitable errors average players make with them
("when the true count hits +1 should I hit hard 16 versus 10, or is it
the other way around?"). Another mountain of simulations went into
tuning OBS specifically for Speed Counters and the recommended bet
spreads. Frank Scoblete covers all this nicely in the new book, Golden
Touch Blackjack Revolution! so the curious are directed to it. The
book also includes the results of the simulation data for just about
every blackjack game you can imagine, showing the fantastic positive
edge you can get with Speed Count.
Conclusions
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!
Insider newsletter
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BJI recommends these trusted online casinos and offers.
BJI promotions
Our Blackjack Tournament Pro and BJI columnist Kenneth R. Smith has
written his first book, How to Win More Blackjack Tournaments, which
summarizes the blackjack tournament strategies contained in his
articles from Blackjack Insider (plus three new articles not available
anywhere else!). $14.95 for the e-book, available immediately after
purchasing.
How To Win More Blackjack Tournaments
Be The Dealer online casino
$200 signup bonus! BJI recommends Be The Dealer for online blackjack.
Click here to learn why, and how to get your bonus.
play now!
(web ads above removed with paid membership. Click here for
advertisement rates)
Friends of Blackjack Insider... great sites from our authors and
partners:
You've Got Heat
The true story of how a low stakes player beats the casino!.
You've read Barfarkel's articles in BJI, now get the book about his
wild experiences as an advantage blackjack player.
The Evolution of Card Counting
Introduction
Dan Pronovost is the owner and president of DeepNet Technologies,
makers of a wide range of advantage gambling training products and
software (blackjack, poker, craps). Their web site is: www.DeepnetTech.com,
and all products are available for free trial download. Dan is also
the creator of the easy-to-use card counting system Speed Count,
taught in the Golden Touch Blackjack course which is now available in
Frank Scoblete's new book, "Golden Touch Blackjack Revolution!":
www.GoldenTouchBlackjack.com/scbook.shtml.
Card Counting, 1950s - academic puzzler
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.
Card Counting, 1960s - mass hysteria
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.
Card Counting, 70s & 80s - keeping it away from the masses
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.
Why traditional card counting is easy
"You took a course to learn to count cards in blackjack?!
What a waste of money? I bought Mr. Geek's book
'Make Millions at Blackjack Just Like Me!' and it was easy!"
Today, there are more books on card counting in blackjack than sex (at
least on my bookshelf). The days in the 70s when card counting was a
'black-art' and the dominion of SPMBs (self-proclaimed-masters-of-
blackjack) ended a long time ago.
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?
Why traditional card counting is hard
"If card counting is so easy and works, wouldn't
the casinos get rid of the game of blackjack?"
Riding a unicycle is easy. Just climb on and peddle! And so the same
thing with card counting.
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.
Card Counting, 2000s- helping average gamblers win
Two things happened around the turn of the millenium that really
changed card counting for average gamblers. Fred Renzey, and my own
Speed Count.
Fred is the author of Blackjack Bluebook, and a long-time contributor
to Blackjack Insider. Like me, Fred understands that card counting is
hard for most gamblers to learn, and focuses on making it easier. And
in this he has succeeded wonderfully, and earns my praise. In his book
"Blackjack Bluebook II," Fred introduced The Ace/Ten Front Count and
the KISS count methods. Both represent much easier systems than High-
Low or Knock-Out, yet are backed by rigorous analysis and simulation
data that prove they work (i.e. give a player a positive edge in most
casino blackjack games). For the curious, Fred wrote an excellent
article, The World's Easiest Card Counting Systems, that discusses
both his excellent methods, as well as Speed Count, which I'll cover
shortly.
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.
Speed Count - the easiest way to win at blackjack
Ok... time to discuss Speed Count, the advantage play method I
developed in 2002 and which is taught in the Golden Touch Blackjack
course. Speed Count is also the core system in the Golden Touch
Blackjack Revolution! book by popular gaming author Frank Scoblete,
and now included in all my blackjack training software for Windows,
Palm OS and Pocket PCs.
"There must be an easier way for everyday average gamblers to learn to
count cards in blackjack and get an edge over the casino? what do you
think Dan?"
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.
So back to the end of 2002? Henry and I had been working together to
publish the Blackjack Insider, and we found a ton of common ground
when it came to blackjack instruction. Independently, we had taught
many students different card counting systems over the years,
including the popular Knock-Out and High-Low. And we both felt exactly
the same way about learning proper card counting techniques in
blackjack: it was too hard for the majority of average gamblers to
master. No matter how we taught students, or what system we used, only
a small percentage of gamblers had the skill and dedication to master
card counting sufficiently to a level that ensured them a good
positive edge in the game. Despite the plethora of blackjack books,
and even good blackjack training software (such as my own,
www.HandheldBlackjack.com), it still takes most individuals 40 to 80
hours to master High-Low, or even Knock-Out. We both frequently
encountered well-intentioned students who failed to master the
techniques required for live play, even with diligent practice.
Getting rid of subtraction and division
"So how do you get rid of subtraction when counting cards in
blackjack?"
I had known about a little discussed fact-of-blackjack for many years,
from studying thousands of computer simulations from Blackjack Audit,
my own company's software simulator.
2.7
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:
5 / 13
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:
2.7 5 / 13 = 1.038
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!
The devil is in the details
"Sounds simple? but does it really work?"
When I started my research to develop an easier count system that
could be learned by average players in minutes, instead of months, I
experimented with many different ideas. While the mathematical
blackjack logic above is great, turning it into a working count system
is another matter. I started by tracking the big cards played (10
valued cards and aces), which seemed the obvious approach. Oddly, this
failed to produce a positive player edge (my computers ran endless
simulations for days in this quest for a Better Count System). The
reason is complicated, and we cover it in detail in the Golden Touch
Blackjack Revolution! book. But here is the summary of my development
process for Speed Count.
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.
There's a lot more to the development of Speed Count. For example, I
developed the Optimal Basic Strategy (OBS), a variation on normal
fixed plays that generates most of the potential advantage of index
plays without the inevitable errors average players make with them
("when the true count hits +1 should I hit hard 16 versus 10, or is it
the other way around?"). Another mountain of simulations went into
tuning OBS specifically for Speed Counters and the recommended bet
spreads. Frank Scoblete covers all this nicely in the new book, Golden
Touch Blackjack Revolution! so the curious are directed to it. The
book also includes the results of the simulation data for just about
every blackjack game you can imagine, showing the fantastic positive
edge you can get with Speed Count.
Conclusions
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!