# Blackjack Card Counting Systems, Gambling Mathematics, Cult, Fraud

## 1. Prolegomenon: Mathematics Invalidates Blackjack Card Counting Strategy

Published on August 19, 2000; later updates.

In Reply to: Ken Uston and Card Counting in Blackjack on CBS's 60 Minutes posted by Mr. T (a.k.a. Chip "Call-Me-Convict") on August 15, 2000.

• My emphasis has always been on mathematics in gambling. If there is a gambling system, I analyze it mathematically, first and foremost. It includes blackjack counting cards, the most talked about gambling system. I did practice counting for about a year, mainly as a researcher. Many gamblers fall in love with one or more systems. Sometimes they go beyond that and worship their system — I never do. BJ card-counting has become a religion sui generis for the past five decades — an undeniable cult.
• Blackjack mathematics, gambling formulae, theory of probability, combinatorics of card sequences in counting cards at casino blackjack expose deception by card counting authors, vendors, false gurus, and self-proclaimed bishops.

Mathematically, the card counting system has a minor influence today, if any at all. I showed in a previous article here that the only impact counting can have in a single deck blackjack game, only one Player against Dealer. A +2 count, generously translated into a 2% Player's advantage results in a 0.01% better chance to get a blackjack (a natural 21). Such a chance increases, at best, from 4.77% to 4.78%. Much ado about nothing!

The main mathematical aspect is the sequence of the remaining cards. Card counting does not even attempt to “predict” the card sequence. In reality, it is impossible to detect the sequence of the remaining cards. The number of blackjack sequences is staggering. They are calculated by the factorial operator (N! = 1 * 2 * 3 * ... * N).

Let's exemplify briefly in a most ideal situation. Before Edward E. Thorp's “Beat the Dealer” book (an important work, indeed) the Dealer dealt all the cards in a single deck. Therefore, the penetration was 100%. A card counter would wait up until the last quarter of the deck or so. Let's say the counter estimated that around 13 cards were remaining in the 52-card deck. The legend has it that many struck it big at the blackjack tables simply by betting huge amounts towards the end of the deck.

Mathematics, however, does not confirm such a claim — in fact, mathematics invalidates the wishful thinking. To calculate the number of possible sequences of 13 cards in blackjack, we use 13! = 1 x 2 x 3 x … x 12 x 13. The result is: 6,227,020,800 (6 billion, 227 million, 20 thousand, 800 hundred sequences). Let's be fair. There would be only 10 unique cards among 13, since 10=J=Q=K. In this case, 10! = 3,628,800 (over 6 million possible sequences)! Imagine an even better situation for Player, that the count is +3 and that there are no neutral cards remaining (i.e. 7, 8, or 9; we count Ace with Tens as high cards).

• We can use software to generate 13-card sequences in the shuffle mode. The composition would be 8 high cards (H) and 5 low cards (L). I used my probability software for the task (e.g. the old programs SHUF-5.EXE or SHUF-6.EXE; now they are functions in the Bright5 and Bright6 integrated lotto software packages). The program generated thousands of sequences, from card 1 to card 13. I considered 1-5 as L and 6-13 as H. Here are the three final sequences of the run:
L, H, L, H, H, H, L, H, L, H, H, L, L
H, L, H, H, H, L, L, H, H, H, H, L, L
H, H, L, L, L, H, H, H, L, H, L, H, H
• There are way too many sequences of cards before a favorable situation for Counter occurs — even in the highly positive counts. Big problem, though: Mr. Counter automatically bets higher in all positive-count situation! The unfavorable card sequences outnumber the favorable cases.

## 2. In-Depth Mathematical Analysis of BJ Counting Card Methodology

• Axiomatic ones, this is the most in-depth analysis of how blackjack card-counting works. We analyze a most ideal game case: One quarter of a deck, no neutral cards, a +3 count. That count figure is equivalent to a +12 count in one full deck of cards – as frequent an occurrence as once in 600 years of play (the lifespan of Biblical Noah who “played” with his daughters to save the human species!!!)

• The card-counting gambling method is founded on the premise that high cards would assure this scenario: Player receives a high-count hand of 2 cards (H + H), while causing Dealer to draw and bust (H + L + H).

It is obvious now that we work with sequences of 5 cards at a time: 2 for Player, 3 for Dealer. We simplify a great deal if we apply the numbers sets known as combinations instead of the arrangements type of sets. Combinations of (13 numbers taken 5 at a time) = 1287. We have only 8 high cards but only 5 low cards.

So, among the 13 cards left in the deck, we can only have 2 5-card sequences of HH for Player and HLH for Dealer (BUST). Each of the two cases lead directly to a Player's win. By the same token, Dealer will have a mathematically equal chance to get 2 sequences in the format HH for her, HLH for Player (BUST). Evidently, the advantage and disadvantage cancel out. No harm, no charm. But there is that big problem. The majority of the situations did not fulfill Player's Dream. The player expected wins in all those situations and bet bigger than in non-positive counts.

In fact, in this Neverland case scenario, Mrs. Dealer busts less by 8%. Meanwhile, another assumption of card counting theory is that Dealer will bust more often in positive counts. Go figure!

• Let's suppose there are 2 Aces among the 8 high cards (the same proportion Ace/Ten as in the full deck). The Player is always favored in those two situations because of the BJ natural payout (3 to 2 in Player's favor); Dealer's natural is always paid 1 to 1. That's the only mathematically undeniable advantage created by card counting for the blackjack player.
• BUT — there is always that big butt — the sequences pile up in the way to riches... again! The 2 Aces and 6 Tenners can deliver 12 blackjack naturals (Ace + 10 hands). The 13 cards in the dream-like scenario analyzed here deliver C(13, 2) = 78 2-card possibilities. The natural 21 chance is 12/78 = 0.15 = 1 in 7 — three times better than at the shoe beginning.
• Both Player and Deafer (!) have an equal chance to get the blackjack. But even IF only the Player would get the much-coveted 21, 1 in 7 is still far away from 1 in 1! The player wins 1.5 for a potential cost of 6! The natural blackjack chance should be at least 1 in 2 for the player to make a profit from a high-card count. But that 1/2 probability is not a mathematical possibility!

#### Mathematical Conclusion

Before the "favor" of counting cards comes to fruition, the card counter wrongly assumes winnings and increases his bets, drastically at times, in every positive-count situation. Mathematically, there are more losing than winning sequences for the blackjack player even in positive counts. (As you'll see below, the negative counts might be better for the player, after all!) No wonder the blackjack counters lose so much in shorter periods of time compared to straight basic strategy players. Virtually all of them counters encountered heavy losses and abandon the trade.

Inquisitively axiomatic one, I discovered one paradox regarding counting cards. I ran my special software that calculates the blackjack odds precisely mathematically. Clearly, Player would have an advantage in negative-count situations! There is a high percentage of double down sequences: 4+6, 5+5, 5+6, even 3+6, 4+5. All these situations, however, are squandered because they must occur in a low count (negative). Of course, the dealer and the player have an equal chance to get the double-down hands. You know the difference: the blackjack dealer may not double down.

### Blackjack Reversed Card Counting System

Well, now, should a reverse card counting strategy be followed instead? Let's try. We do not need the intentionally-complicated card counting of +/– (plus/minus). The traditionalists (read crooks) make card-counting hard in order to lean on a strong excuse. "Hey, you didn't learn well enough the counting system(s)! I know, it's very hard... but try again!" They add even more excuses, such as tables of indices... that look like creations of disturbed minds intent on fraud and blame.

We simply count the Ten-valued cards as 1, 2, 3... as they are dealt. We don't have to remember the previous rounds. We don't even count the Aces, as they become also 1-values (serving the purpose of doubling down). Of course, we, as the traditionalists, don't bother to count the neutral cards (7, 8, 9). The neutral cards are worthless in the traditional plus-count blackjack systems. In this reversed card counting strategy, however, the neutrals serve well the purpose of doubling down because of cases such as 9+2, 8+2/3, 7+2/3/4/A. We know that the neutrals can't hurt our mission. The 10-valued card is the only one that cannot appear in a 2-card-double-down configuration.

If our simple count tells that more than one third of the cards dealt in the previous round were Tens (10 or J, Q, K), the count is negative. That is, the next round is favorable to double down hands. Two cards in a double down configuration also increase the chance for a Ten-value card to land across our D-down hand!

• We can automate this law of the third for the reversed count by considering an average of 3 (three) cards per player in a round. That average is a fact for all intents and purposes. Say, the full blackjack table has 8 elements (playing agents): 7 players and the dealer. Total cards dealt = 8 * 3 = 24. One third of Tens is equivalent to 8. (It is easy to see that one third is equal to the number of playing agents.) A safe figure is 8 + 4 = 12 Tens out in the previous round, in my estimation. It comes close to a cutoff chance (50%) for one player to get the benefit of a double-down hand. For the heads-up case: 2 * 3 = 6; one third means 2 Tens out; a safe value to apply the reversed count is 3 Tens out; 4 is even better.
• I tell you all this because it was one of my last gambling secrets. I did apply this reversed card counting system in the late 1990s and early 2000s in Atlantic City. I was deriding the plus-count systems. "Hey, I won with a double-down in a negative count!" The witnessing pit boss called upstairs for one "expert". The "expert" took a seat at my table while he was eating his lunch (a typical American hoagie). He left the table soon because he said he had no clue what I was playing!
• I was also playing another "secret" strategy of mine. The blackjack deck (shoe) is always positive at the beginning of the game. I consider 9-value a strong card in the same category as 10 and 11 (Ace). The beginning of the shoe has a +4 true count in my book. I have done my best to start a blackjack game only at the beginning of the shoe. I kept rigorous records of my first hand: W for win, L for loss. The streaks I encountered were very close to the blackjack streak formulas. I had a streak of 5 consecutive first-hand losses, while my longest winning streak was 2. Plus 4 true count should have pocketed me a pretty good financial gain — without progressions. In truth, I martingaled after 3 consecutive losses; I also martingaled after 3 consecutive single W streaks; that way, I wiped out the losses and made a small profit.
• This blackjack system of mine should be applied to all after-shuffle situations (new shoes). That is, keep a record on the same piece of paper that shows the blackjack basic strategy tables. It is allowed at the blackjack table while you play. Just write W/L on the back side. Read also: Shoe Start Blackjack System.

Again, not all negative counts lead to double-down hands. And, again, the counter should not assume that all negative counts are winning situations and bet big all the time. All the time here means losing more often because of the prevalence of the unfavourable sequences.

Therefore, keeping track of streaks is a must and it will beat the positive-count blackjack strategy hands down! If we miss the first double down situation, we should increase the bet next time a negative count occurs. We should be mindful that there are winning streaks in addition to losing streaks. Just follow this link: The Best Casino Gambling Systems: Blackjack, Roulette, Limited Martingale Betting, Progressions.

We should also keep in mind the number of players at the table, plus the dealer. The counting traditionalists hate to hear that! The fruition rate for double down hands diminishes with an increase in the number of blackjack players at the table. The best-case scenario is heads-up play. The doubling down is equally distributed between two agents: 50-50. But the dealer is paid 1 to 1, while the player gets 2 to 1 when winning (about 60% of the time). Mathematically, the player enjoys a 10% advantage (heads-up play only; sliced by the number of players).

Now you understand why so many "traditional" card counters complain that they get mad when they witness non-counters at the same blackjack table winning big when the count is undoubtedly negative!

• In the best-case scenario of One Player versus Dealer, winning in the plus count situations is equitable to random play, which clearly favors the house (the blackjack dealer). In multiple-player cases (by far the most common), the so-called true count (TC) diminishes with the number of players. Should we apply a new concept? I coined it as the per capita true count (PCTC). The total true count is divided equally amongst all players plus the dealer. In the example above, TC = +12; PCTC = 12 / 8 = +1.5 if there are 7 players at the table (don't forget the dealer!)

• And here is the capital sin of blackjack card counting. A positive count is always considered a winning situation. The counter must increase his bet, significantly at times. But because of the staggering amount of card sequences, plus number of players, real-life winning comes to fruition for one player less than 50% of the cases; the worst situation occurs with 7 players at the same blackjack table.
• The followers of the counting-cards cult do have religiosity attached to their behavior. A card-counter blindly believes he is a "chosen one". That is, some god of blackjack will always make the card-counter a winner.
• The card-counter always disregards the existence of other players at the same table and the dealer. It's only him who wins every positive-count round — no matter how many players and the dealer's position at the table! The blackjack gods are always on card-counters' side! I was myself a card counter, but I never, ever, expected some cosmic hallucinations win the plus-count blackjack hands for me.
• It is strongly evident to every coolheaded person, especially to the axiomatics, that in the vast majority of plus-count situations, a majority of the blackjack players at the same table lose their bets. Shouldn't all players win? After all, the card-counting dogma preaches bigger bets in all positive-counts as they are automatically winning situations by "divine will"!
• The card counter finds out sooner rather than later that he lost a vast majority of his bets in plus-count situations. It is no surprise that all card counters lose large amounts of money in shorter periods of time (compared to basic strategy blackjack players). That's called mathematics. If you bet bigger in certain situations, you must be sure you win — not lose — a majority of such cases.
• Contrary to the legend, the card-counters in blackjack are big losers, not big winners. In fact, most of them lose so badly that they have no choice but end their gambling activities. The afflicted resort to alcohol or drugs, or both, and hope to find solace by mouth-foaming in forums of the same feather (cuckoo! ... cuckoo!) That's the inevitable reality, because the card-counters virulently ignore mathematics; instead, they trust cosmic hallucinations sui generis.

## 3. Card-Counting Blackjack Strategy Equates Deception, Fraud

The fraud of the card-counting blackjack system is two-pronged. It is defended by two pretexts, two absurd justifications: long run and variance.

• 1) Long run: "Why am I losing so big with card counting, while I was promised to win?" you'd hear the outcry of many card counters who spent fortunes on blackjack training materials.
• “Answer” the vendors/promoters of card counting blackjack strategy: "My gambling system failed you because you haven't reached the long run!" the skumbullows (a.k.a. gurus, bishops) of card counting mockingly and deceitfully respond (and desperately, I might add). "You must play millions... actually, billions of blackjack hands for the card counting come to fruition..." the priests of gambling conclude their sermon of deception, then asking for further "donations".
• First off, no human can live 100 times longer than Noah to play billions of blackjack hands uninterruptedly. Humans can play up to 1000 successive blackjack hands — in extreme testing. Is the long run 1000000 (one million) hands? Well, the result of card counting shows sometimes winnings, sometimes large losses — the ratio is similar to random play as calculated by mathematical formulae. Is the long run 1000000000 (one billion) blackjack hands? Well, the result of card counting shows sometimes winnings, sometimes large losses — the proportion is similar to random play as calculated by mathematical formulas.
• Not to mention that one million hands would require an impossible bankroll to prove the validity of counting cards!

• 2) Variance: "Why am I losing so big with card counting, while I was promised to win? I played lots and lots of BJ hands…" you'd hear the outcry of many card counters who spent fortunes on blackjack training materials.
• “Answer” the vendors/promoters of card counting blackjack strategy: "My blackjack counting strategy failed you because of the variance!"
• The fraudulent justification here is this: Variance is always negative from the perspective of the card counter. How about positive "variance", crooked authors/vendors of counting cards promises? Mathematically, the positive variation should be more prevalent. The counting cards “method” claims it offers the player a positive expectation — therefore the variation should be positively skewed!
• If the player must play millions of hands in order to win, why not play millions of hands without losing with card counting?! It would be more… mathematical!
• Variance itself is intentionally misused in order to obfuscate the truth. Variance is a mathematical measure calculated by the sum of squared differences between random outcomes and the average of the series. The famous standard deviation represents the square root of variance. The variance is always a positive number.
• Instead of variance, the crooks should use the term variation. But that implies fluctuation, which in turn implies positive values, not only negative values.
• The "negative variance" (sic!) represents another form of mysticism, same as the gambler's fallacy. The player is always hit by bad luck!

Some claim that blackjack simulation software always shows an advantage for card counting play. Baloney, I say. I coined this saying: Card counting authors, developers, vendors COOK THE BOOKS. The crooks do that with some simulation software applications. I experienced an interesting case in BJ Bishop Arnold Snyder's blackjack forum. One card counting system author was strikingly candid in a scrimmage the two of us had. The counting-cards developer candidly admitted that his system had failed 3 consecutive times in his attempt to create an illustrative YouTube video. He succeeded to show winning for his card-counting system in his 4th try. So, he uploaded to YouTube that fourth video that showed a success for his system!

• Evidently, the long run never reaches an end, according to the crooks of blackjack card counting desperados (read: vendors)! Theory of probability, however, applies to any situation: Any event of any probability p, any number of trials N, any degree of certainty DC.

Ion Saliu's Paradox precisely calculates the long run. Just 50 repeats of the N trials constitutes a sufficient mathematical long run. If card counting expectation is a little better than 50%, then probability p is just a little better than 1/2. Just 50 repeats of 2 gives 100 blackjack hands. 1000 BJ hands is that much better — a larger than sufficient long run. By the same standard, a sufficient long run in roulette would be 2000 spins. Every analysis of real-life casino data proves that every roulette number came out very, very close percentage-wise to formula calculations.

And, again, the reverse imposes itself upon the card-counting crooks. How about a real long run when the counters do not lose: Play billions of blackjack hands before encounter a loss!

• Take it to the bank... NOT! Because card counting has NO mathematical foundation and does NOT work. The blackjack card counters represent the largest contingent of gambling addicts and pathological liars — beating the “congregation” of old church ladies addicted to the slot machines.
• I call it the Old Florence syndrome after an elderly church lady who was telling people at work that she was always a winner in her bus trips to Atlantic City. She was winning in her hallucinating while her colleagues pitied her financial situation.
• Pathological liars can only fool themselves, but they can't lie to mathematics. "God hates mathematics while Einstein fears gambling."

No wonder the casinos are so bullish in touting and promoting counting cards at blackjack! Ever seen that failed casino movie entitled 21 dedicated to BJ card counting?

I've written this article in harsh language, indeed. It's the only language the krookoos understand. They'll jump at one's throat if one dares to critique card counting. They attacked me virulently every time and everywhere I attempted to express my opinion on counting cards at blackjack. Those with authority banished me quickly in their “public” forums. As soon as I jotted down words such as mathematics or formulas, them crooks would go beserk!

## 4. Shuffling Software Simulates Sequences of Blackjack Cards

My latest blackjack software calculates the odds of dealer busting in the most accurate mathematical fashion. We can generate all possible BJ hands mathematically — option A = Arrangements. That is, the order counts. We will notice undeniably that 10 followed by 6 occurs equally to 6 followed by 10. Even the so-called basic strategy stands on thin ice mathematically.

Let's play the first sequence now, between one Player and the Dealer.

• Player gets L, Dealer gets H. Player gets H, Dealer gets H. Player stands, Dealer stands. Dealer wins one hand. Player gets H, Dealer gets H. Player gets L and stands, Dealer gets H and wins the 2nd hand. Player gets L, Dealer gets H, Player gets H, Dealer gets L and draws L; more probably, Dealer wins the hand.
• In the 2nd sequence, Player gets H, Dealer gets L, Player gets H and stands, Dealer draws L, and must draw to LH, gets an H and busts. Player wins the 1st hand. Player gets L, Dealer gets L, Player gets H and stands, Dealer gets H and draws another H (bust). Player wins the 2nd hand.

Now, let's change the perspective from mathematics to logic. That is, instead of numerical relations, let's use words.

• The count is high. According to the blackjack card-counting gospel, high cards (H) will come out in the first round (hand); furthermore, the new count is low; accordingly, low cards (L) will be dealt in the second round (hand).
• The count is low. According to the card-counting blackjack gospel, low cards (L) will come out in the first round (hand); furthermore, the new count is high; accordingly, high cards (H) will be dealt in the second round (hand).
• What's the difference? High-low in the first case; low-high in the second!

• It is lot more effective to apply my streaks theory of gambling systems without counting cards as in those expensive training manuals for casino gambling. The blackjack player just looks at cards dealt in each round. Most importantly, the player keeps a “visual count” (!) of the cards dealt in the third hand to the players before him/her (two or three). In some cases, the player may be able to adjust the playing strategy to her/his two-card hand. For example, if the degree of certainty is high for a... high card, I don't hit 15 or 16 against dealer's pat hand. It doesn't mean I win all those situations, but I win more than blindly following the old blackjack basic strategy.

It becomes very, very complicated in a hurry. We are dealing with over three and a half million sequences. The matters are a lot more complicated when we consider the neutral cards and multiple players. The impact of card counting appears to be near negligible. I count cards sometimes up to the latest card. I call it the “real running count”. At the end of a round the count is positive, for example. When it is my turn to make a decision after my first two cards, the count turns out to be very negative. A blackjack card counter would have bet bigger at the beginning of the round. When it was his/her turn to make a decision, the count would be clearly negative. The player might expect a low card. Quite often, Player gets the opposite, a busting high card. I noticed frequently such sequences. They seem to be totally random. If you are a faithful card counter, you should expect to lose serious money for a significant number of rounds (hands).

• John Scarne, the author of Scarne's New Complete Guide to Gambling, puts jokingly the advantage of card counting. Suppose there is a one-deck blackjack game with 100% penetration (i.e. all cards are dealt). The player tracked the entire deck absolutely precisely. There are 5 cards remaining in the deck: 3 eights and 2 sevens. The player would bet the maximum immediately (actually, millions if it were possible!) There is NO way the player can lose!
• The player would always stay on two cards (it doesn't matter if it is 7+7, or 7+8 or 8+8)! On the other hand, the dealer would always bust. It doesn't matter: 7+7 (under 17); draws an 8 and busts. Or, 8+8 (still under 17); draws a 7 and busts. Or, 7+8 = 15 (under 17); either 7 or 8 as the third card would bust the dealer's hand! That's the only absolutely certain case of winning with card counting at blackjack.
• Although, we still got a problem. A card-counter is always a religiously-perfect basic strategy player. The Dealer always shows a 7 or an 8; the Player always has a stiff hand that must be hit against 7 or 8 face cards!
• Still, who could possibly find a situation like that at a real table, in any casino?! And, hey, who can possibly count all the cards, precisely, by their face value?!
Sometimes, but rarely, card counting might help in hit / stand or double-down decisions. Once, I shocked the audience when I doubled-down on 12 against dealer's 6. The blackjack dealer announced his pit boss about my play. Curiously, I won! The count was very negative — just before my third card. I did it more for showmanship… my bet was at the minimum…

## 5. Edward Thorp Fathered BJ Card Counting; Ken Uston Made it a Cult

The personal side of my previous posts on Thorp and Uston relied on blackjack and gambling books I have read. I have never claimed I experienced firsthand Thorp's or Uston's casino playing. First of all, I praise the two computer programmers who took on a very difficult challenge. Trying to discover rules in random events such as gambling represents an enormous task. Yes, the casinos did change the rules after Thorp published his book. The simple fact that the casinos added penetration to the deck diminished the effect of counting down to fractions of a percentage point. The multiple decks made it impossible to have a true count. It is impossible to divide accurately cards remaining in the deck by an approximate number of decks remaining in play — and get a true count! Contradiction in terms!

One problem I have with the two blackjack authors and researchers is the fact that they reached a point of worshipping card counting. I am sure they did a large number of computer simulations. I am sure they noticed the negligible effect of the system. Yet they continued to influence a large number of potential casino players that card counting was the road to the riches. I would like to present a few more excerpts on Edward Thorp and Ken Uston. Carl Sifakis writes in his 1990 Encyclopedia of Gambling (pg. 36-37).

• "Dr. Thorp is still in computerized mathematical research, but he is now concerned with looking for values in stocks… The late Ken Uston, author of numerous books on counting, was at the end of his life involved in computer work in the Middle East, helping Kuwait track billions of dollars in investments. He was not playing blackjack in Atlantic City, although he had won a court case that barred casinos in New Jersey from refusing to let counters play. In fact, Uston, upon winning that case, didn't hit the blackjack tables in Atlantic City but signed up to do TV commercials for Resorts International, the very target of his suit… One long time gambler, Murray Friedkin, says of Thorp in 'Big Julie of Vegas' by Edward Linn: 'Thorp is the smartest man in the world; if you don't believe me, ask him…Whatever Thorp may say, I can tell you that if he has made any money on blackjack he made it by writing a book."

The late gambling expert John Scarne derided the counters and challenged Edward Thorp to a \$100,000 match at blackjack. He later extended the challenge to other leading counting advocates. "There were some nos, then yeses, then considerably more backing and filling; the blackjack contest never came off." After long hesitation, Thorp accepted Scarne's challenge. Edward Thorp lost badly and he admitted he was a lousy blackjack player. His card-counting system didn't play any miracle!

Edward O. Thorp is associated with another gambling “system”: the Big Toe Method of beating the Wheel of Fortune (Big Six). Says Carl Sifakis in the same book I quoted above: “Is the Thorp Big Toe Method still in use? The bottom line is that the money wheels of all kinds are still in place in the casinos, something that would not be the case if there was a way they were being beaten considerably.” (page 31).

## 6. Aura and Mystique of Card Counting at Blackjack

Why this aura of legend surrounding card counting at blackjack? Even more mystique is added when considering that Las Vegas is still barring card counters from playing blackjack! Says Carl Sifakis: “And what of the casinos today? Blackjack is a much bigger game today than it was before "Beat the Dealer" appeared. More people than ever patronize the tables and casinos today make more money from the game than ever before. That's a significant bottom line.”

Roger Gros, senior editor of Casino Player Magazine writes in his 1996 “Casino Gambling the Ultimate Play-To-Win Guide”: “After all, casinos make most of the money they make at the table games via blackjack. It is great advertising when someone reports a big win at the blackjack tables. Players have been encouraged for many years to believe that blackjack can be beaten, and the casinos don't want to do anything to disrupt that message.” (page 30).

Methinks the legend of blackjack card counting plays as the most successful means of advertising for the casinos. It certainly attracts a large number of players who believe counting at blackjack is a road to riches. There are also other ways that the card counting legend favors the casinos. Read any blackjack book on card counting and virtually all of them contain the same cliché. “If you are a card counter, make some bonehead plays so that the pit bull won't ban you!” I think many card counters take the advice seriously. They do make bonehead, stupid plays from time to time just to hide their card-counting skills. What a stupid strategy for the blackjack player! What a profitable play for the casino!

It is admitted that counting cards offers no more than a 2% advantage for the blackjack player. That's a slim margin by all standards. Making bonehead plays can easily wipe out the slim, potential 2% advantage. The casinos owe big time to all authors of card-counting books. Then, in places where it is legal to ban skilled players from the blackjack action, the casinos commit downright robbery.

From what I have read, the casinos show a strong bias towards barring a blackjack player when he/she is at a serious LOSS! I read once that a known card counter was losing some \$14,000. Exactly at that point, the pit boss approached the counter and asked him to leave the blackjack game! Get it? The \$14,000 went immediately to the casino bottom line.

Meanwhile, the player was deprived of a reasonable chance to recuperate his loss. After all, they trumpet, blackjack is almost an even-odds game for a player using the basic strategy! It is fair to expect swings in the winning and losing columns of the player. Of course, the banned player is allowed to play blackjack again. The pit bosses pretend to have forgotten him/her, until another significant loss for the player. The player is thrown out again! If the known counter is winning, the rationale is that a swing in the fortune will follow. Sooner or later, the player will encounter a severe loss. That's when you ask a counter to get out! What casino would be happy if a winner does do take the money and run?!

• In conclusion, mathematics must offer the only perspective as far as gambling is concerned. By contrast, religious-like blind-faith is the life support of card-counting in blackjack; hence the widespread definition of card counting as cult. The so-called bishops of the cult — the likes of Ken Uston, Arnold Snyder, Stanford Wong (real name John Ferguson), John Patrick (Jackal), Dr. Peter Griffin — never really applied their "trade" in real life.

In fact, they work(ed) for the casinos as consultants, "card-counter catchers", spokespersons! John Patrick even shot a big TV production right inside a casino. John Patrick's casino gambling CD worshipped blackjack card counting — loudly encouraging viewers to use the counting systems!

If that is not systemic schizophrenia — I don't know what is!

You can read some shocking details (2008). It is not only about mathematics: It is about flat-out crime. If you win big, they slam you to the ground and take all your money under the "legal" pretext of BJ card-counting:

• Legal Cases Against Casino Abuse of Laws.

Read Ion Saliu's first book in print: Probability Theory, Live!
~ Founded on mathematical discoveries, also applied to casino blackjack, new BJ odds calculation, the myth of counting cards.