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The Four Horsemen of Blackjack

Blackjack History: Baldwin, Cantey, Maisel and McDermott and the First Accurate Blackjack Basic Strategy

By Arnold Snyder
© 1997 Blackjack Forum

[Note: This 1997 article about the Four Horsemen was written prior to our discovery that all four authors were still alive and before their subsequent induction into the Blackjack Hall of Fame. – A.S.]

Letter from F.M.:

I recently found a used copy of the 1957 classic, Playing Blackjack to Win. This is the book written by four mathematicians — Roger Baldwin, Wilbert Cantey, Herbert Maisel, and James McDermott — that contained the first accurate basic strategy for casino blackjack. As an avid follower of the blackjack scene for the past ten years, I was familiar with this book by title and reputation, though I had never before seen a copy.

I must tell you I was frankly amazed when I read it. I had no idea how far ahead of its time it was. Not only was the basic strategy nearly perfect, but the chapter on “partial casing” must be recognized as the first valid card counting system ever published, a credit that has always gone to Edward O. Thorp.

I don’t mean to discredit Thorp for his monumental Beat the Dealer (Random House, 1962), but shouldn’t we consider honoring Baldwin, Cantey, Maisel and McDermott, whose book came out five whole years earlier than Thorp’s, as the true fathers of modern card counting?

This is the 40th anniversary of this astonishing little book. I think if more card counters had actually read this impossible to find classic, these authors would be elevated in the blackjack community to a more prominent stature.

Please, Bishop, before 1997 fades away, how about a tribute to these four forgotten authors who really started it all?

Answer from Arnold Snyder:

It is a shame that this groundbreaking book is not more widely available. I do not know if the publisher, M. Barrows & Co., ever even issued a second printing. [Note: Playing Blackjack to Win has now been reissued by Cardoza Publishing, but the first edition is still a collector’s item.]

The copies of this book that have survived these 40 years are few in number, as the plastic spiral binding and the cheap pulp paper have not held up well through the decades. If you are lucky enough to find an intact copy in a used book store, grab it. Rare book dealers who know the value of this little gem will not let it go cheaply.

Expect to pay $25-$75 for an intact copy in poor to fair condition, and quite a bit more for a copy in good to excellent shape. A broken plastic binding is common , as that thin 1950s plastic is very brittle after all these years.

The First Accurate Blackjack Basic Strategy

As for your comments on the importance of this book, and its deserved place of honor in the hearts of blackjack players, I must concur. For the single-deck Vegas Strip game the authors analyzed, their basic strategy analysis was devastatingly accurate. That they conducted their research by hand on crude mechanical calculators — what used to be called “adding machines” — is truly remarkable. Their hit/stand strategies, both hard and soft, are 100% accurate, including the recommendations that hard totals of 12 should be hit against 2 and 3, and that soft totals of 18 should be hit vs. 9 and 10 only.

The only errors in their hard doubling strategy is that they failed to advise doubling down on 8 vs. 5 and 6 — borderline decisions true for single-deck games only. They missed a few more of the soft doubles, but nothing very serious in terms of dollar value.

Even on the pair split decisions, they made only three errors in their entire chart — erroneously advising that 2s and 3s be split vs. 2, and that 3s also be split vs. 3. These are also close decisions, and in double-after-splits games, are correct plays.

Any player who used their basic strategy today would not be giving up more than a few hundredths of a percent over perfect basic strategy.

The First Blackjack Card Counting System

As for their “Chapter 10: Using the Exposed Cards to Improve Your Chances,” this truly is the first valid card counting system ever published for casino blackjack, some five years prior to Thorp’s Beat the Dealer. In fact, it could be argued that this counting strategy they advised was actually the first “ten count” strategy, as they provide 16 changes to basic strategy, depending on whether or not various numbers of the last cards dealt were either ten-valued or “low cards” — which they defined as Aces, 2s, 3s, 4s, and 5s.

But, although they were undeniably the first authors to grasp and publish the concept of a card counting system, and the type of logic that must be employed for it to work, their strategy itself is very crude, and would be unlikely to add much gain to the player. They did not realize that tens and aces were more valuable to the player than the low cards, so they failed to provide any advice on proper betting strategy. Their advised technique for making use of the cards seen, though on the right track, did not even begin to take the advantage available to counters who might be watching for both tens and low cards.

I doubt the value of their strategy changes were worth more than a few tenths of a percent, if that, even in the deeply dealt single-deck games they faced. (They also acknowledged this in their book.) They did the important groundwork for card counting theory, and surely were more responsible than anyone for Thorp’s ultimate development of his truly powerful counting strategies, but their “partial casing” system simply wasn’t much of a winner.

In any case, I am glad you wrote to me, and jogged me into recognizing the anniversary of these four long-forgotten researchers, Roger Baldwin, Wilbert Cantey, Herbert Maisel, and James McDermott, who stand as giants in the field of blackjack strategies. They truly were the ones who started it all. ♠

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Articles on Using Concealed Computers

[In the early days of Blackjack Forum, I used to advertise and sell these devices. I believe they are now illegal to use in casinos throughout the world. – A.S.]

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Blackjack Computers: Your Ticket to the Big House (Part 1)
by Thomas B. Duffy, Attorney at Law

Blackjack Computers: Your Ticket to the Big House (Part 2)
by Thomas B. Duffy, Attorney at Law

The Electronic Gambler’s Fuzz-Out Syndrome
by Bob Jenkins

Interview with Keith and Marty Taft
by Richard W. Munchkin

Do Perfect Strategy Computers Play Perfect Strategy?
by Dr. Data Fehnworp

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Blackjack Computers:

Your Ticket to the Big House (Part I)

by Thomas B. Duffy, Attorney at Law

(From Blackjack Forum XIV #1, March 1994)
© Blackjack Forum 1994

[Ed. note: Eleven years ago, concealable blackjack computers were legal and growing in popularity. Then, Nevada outlawed them. New Jersey followed suit, passing laws against them, albeit with less harsh penalties. As more states legalized casino gambling, these computers were on the rise again. As we have stated in Blackjack Forum in the past, we believe these anti-computer laws are unconstitutional. That provides little comfort to the blackjack player, however, who may be caught using one of these devices. The cost of getting such a case into the federal courts would be substantial. In 1994, I asked New Jersey attorney Tom Duffy, who specializes in representing professional gamblers, to provide an update on the computer blackjack laws. Since then, California has made use of a concealable gambling computer a misdemeanor. However, some foreign countries still have no cheating statute regarding these devices. Before even considering play with a concealable computer, make sure to get reliable advice on the current legal situation where you are thinking of playing. — Arnold Snyder]

The recent flurry of states seeking to legalize casino gambling presents much opportunity for the skillful player. There is, however, also much risk as the political, legislative and judicial infrastructure of these states must acclimate themselves to the rather unique legal questions posed by legalized gambling. A case in point that has recently come to my attention is some recent Mississippi legislation.

Mississippi passed rather comprehensive anti-cheating statutes on April 20, 1993 (Laws 1993, ch. 488, formerly H.B. 507). For the most part, these statutes were badly needed. Apparently, Mississippi had been charging gambling cheats with ill-suited crimes such as theft and larceny which gave defendants too many avenues to wiggle out of the charges against them. Unfortunately for the readers of this magazine, this backlash includes a new law which relates to the use of computers at blackjack and other games. Additionally, the wording of these statutes calls into question the legality of practices long held to be legal in New Jersey and Nevada.

I will begin with this last point. Paragraph 2(b) of the new law (codified at Miss. Stat. Ann. §75-76-301(b) states, “It is unlawful for any person [t]o place, increase or decrease a bet or to determine the course of play after acquiring knowledge, not available to all players, of the outcome of the game or any event that affects the outcome of the game….” This paragraph, like all of §301, was taken word for word from Nevada §465.070 titled “Fraudulent Acts.” Obviously, the meaning of this section turns on the word “available.” I assume that this provision was not meant to outlaw card counting; in fact, one could make a good case that the highlighted words were inserted to save card counting, and similar strategies such as handicapping, from being illegal. However, §465.070(2) is extremely inappropriate for wholesale importation to Mississippi. First, in Nevada, this section was mainly meant to address the “fixing” of pari-mutual and sports betting events. Neither of these bets is legal in a Mississippi casino. Second, a 1989 amendment added the words “increase or decrease” and “to determine the course of play” to the Nevada statute. These amendments, while also covering other crimes, were primarily aimed at “spooking” at blackjack. Once again, spooking is not possible in the Mississippi casinos — hole cards cannot be checked by hand.

We must look at the general cheating statute to get a true idea of the havoc §301(b) might wreak. Both Mississippi §75-75-307 and Nevada §465.083, as amended in 1981, provide, “It is unlawful for any person, whether he is an owner or employee of or player in an establishment, to cheat at any gambling game.” “Cheat” is defined in both statutory schemes as meaning “to alter the selection of criteria which determine: (a) The result of a game; or (b) The amount or frequency of payment in a game.” While it is not clear exactly what conduct this does cover, it is clear that there are some cheating schemes not covered by this general statute. That is exactly why there is a more specific statute. There is a theory of statutory construction, especially applicable to more specific statutes such as §301, that every word must have been put there by the legislature to effect some purpose. Many of the issues, however, addressed in §301(b) are inapplicable to Mississippi gaming. What is a judge to do? Tell the truth — that the legislature was asleep at the switch when they pilfered this particular paragraph from Nevada — or give the paragraph some meaning. Most judges will, obviously, choose the latter course of action.

Giving meaning to §301(b) in a casino environment without pari-mutuel and sports wagering broadens the inquiry concerning usually unavailable information about the outcome of a casino game from whether such information was acquired by conspiracy (e.g., spooking) or “by any trick or sleight of hand performance or by fraud or fraudulent scheme” (to quote the New Jersey cheating statute §5.12-113) to whether such information is available to all — an irrelevant inquiry where, as in blackjack, the players do not compete against each other. Furthermore, this inquiry can also be irrelevant where the players do compete against each other: all poker players base their play of the game on their “hole” cards — which are unknown to the other players. A broad interpretation of §301(b), in addition to outlawing poker as we know it, would also call into question practices which are legal in Nevada, such as front loading or even adjusting one’s play to take advantage of a card the dealer exposed in error. (I assume these irregularities cannot be seen from all player positions.)

The “device” section, §75-76-303, was lifted, word for word, from Nevada §465.075, and is likewise over inclusive of unintended activities. It states:

It is unlawful for any person at a licensed gaming establishment to use, or possess with the intent to use, any device to assist:

  1. in projecting the outcome of the game;
  2. in keeping track of the cards played;
  3. in analyzing the probability of the occurrence of an event relating to the game; or
  4. in analyzing the strategy for playing or betting to be used in the game, except as permitted by the commission.

The problem here centers around the use of the words “any device.” The New Jersey “device” statute reads “an electronic, electrical or mechanical device.” The word “device” is undefined in both the Nevada and Mississippi statutes. “Gaming device” is defined and encompasses “any … contrivance, component or machine.” Webster’s, on the other hand, uses the definition, “that which is planned out or designed; contrivance; stratagem.” Card counting is a “device” within the Webster’s definition but it is not if the Mississippi courts read the “contrivance … or machine” definition into the “device” statute.

The defendant in Sheriff of Clark County v. Anderson, 746 P.2d 643 (Nev. 1987), argued that this lack of a definition of a critical word in the statute made the entire statute constitutionally unenforceable. The trial judge agreed and dismissed the charges against Anderson. The prosecution appealed to the Nevada Supreme Court which considered the case for two years. The court held that, while the statute would be unconstitutionally vague as applied to some hypothetical defendants, it was not vague with regard to Anderson’s conduct of using “computer shoes” at blackjack. Having won a theoretical victory, the prosecutor wisely decided not to proceed with the case against Anderson.

Had Anderson been convicted, it is doubtful the statute could have withstood either direct or collateral attack in the Federal Courts. The Nevada Supreme Court’s analysis was arguably correct on the issue of vagueness. The problem is that statute is so vague it is also “overbroad”‘: a special legal term meaning it infringes on the exercise of expressive and associational rights. These “device” statutes, especially when read with companion legislation making manufacturing, selling or distributing “devices”‘ intended to be used to violate the law, violate the First Amendment right to disseminate information.

As I have stated, Webster’s includes “stratagem” (such as counting) within the definition of “device.” As such, anyone using a strategy is theoretically at risk for prosecution. Furthermore, anyone who intentionally assisted in preparing the strategist for his or her bout with the casino could be liable under the companion legislation. Is Sega at risk if the strategist learned how to count from using a video game it manufactured? Probably not. Is Peter Griffin at risk for distributing the effects of removal — to two decimal places — in his book The Theory of Blackjack? Quite possibly, especially when one considers the argument that these indices must have been intended to be fed into a “device” such as a computer because they are so complicated no human could cope with them. Finally, I leave the question of whether Arnold Snyder could be prosecuted for selling Griffin’s book to the reader to ponder.

Such an overbroad law “hangs over [people’s] heads like a Sword of Damocles.” Obviously, “the value of a Sword of Damocles is that it hangs — not that it drops. See Arnett v. Kennedy, 416 U.S. 134, 231 (U.S. Supreme Court 1972). Such a law has a “chilling effect” on Professor Griffin and Book Seller Snyder, who are both within a class of persons classically protected by the First Amendment. If this chilling effect is substantial, the law is “facially invalid.” Facial invalidity can be argued by any defendant, even someone like Mr. Anderson who was engaged in an activity that clearly could be prohibited if the statute had been properly drafted. The courts use the blunt instrument of declaring laws facially invalid to force legislatures to carefully draft laws to avoid constitutional conflicts. This tool is not significantly different from the “exclusionary rule” which forces the police to obtain evidence through legal means. In sum, I believe that the Federal courts would invalidate the Mississippi and Nevada “device” statutes because the word “device” is overbroad and, at the same time, central to the meaning of the statute — eliminating any possibility the word could be overlooked to save the statute from validity. Still, the prudent course of action, obviously, would be to avoid any activity that might come within these statutes.

I also caution players from taking too much solace from the “except as permitted by the commission” language in §303. I assume the commission has absolved our pad and pencil carrying brethren at baccarat and roulette from any liability under this statute. Given the draconian penalties for violating this section (see below), I cannot make any such assumption about card counting. This is especially true given the counter’s persona non grata status in most, if not all, casinos.

For the entrepreneurs among us, as mentioned above, I note that §75-76-309 and Nevada §465.085(1) state, “It is unlawful to manufacture, sell or distribute any cards, chips, dice, game or device that is intended to be used to violate any provision of this chapter.” The above analysis notwithstanding, it would be extremely unwise to sell computer devices in or mail them to either Mississippi or Nevada. The standard disclaimers on the sale of these devices that they are “just for fun” and “for scientific research” provide no relief. The more powerful, expensive and stealthy a device is, the harder it becomes to deny that it was not “intended” to violate the law. Furthermore, given the harsh penalties involved, no lawyer, myself included, could overlook the possibility of having his or her client testify against the manufacturer in return for a lighter sentence.

Finally, the penalties exacted for violating any of the above sections are extremely harsh. Under §75-76-311(a), first offenders can be sentenced to up to 2 years in the State Penitentiary. Subsection (b) throws the book at recidivists: sentences can run up to 10 years. Both sections provide for fines of not more than $10,000 per offense. The Nevada penalty statute is similarly bifurcated. A first offender can be sentenced to “not less than 1 year nor more than 10 years, or by a fine of not more than $10,000, or by both fine and imprisonment.” A recidivist loses the benefit of the disjunctive clause and must be sentenced to at least one year in the state prison and may also be fined up to $10,000.

Compare these penalties to the New Jersey “device” statute which provides for a maximum sentence of 90 days and a $500 fine for each offense — with a presumption against incarceration for those without prior criminal records. Perhaps most importantly, the New Jersey sentence, if any, would be served in the Atlantic County jail — a reasonably pleasant facility populated by pimps, petty thieves and more serious offenders who can afford good lawyers who keep them out of state prison. The Nevada state prison may provide a slightly more interesting environment. I hear the population is just about evenly divided between death row inmates and gambling cheats. The imagination runs wild thinking about the Mississippi State Penitentiary — maybe John Grisham will enlighten us about it in his next novel. Until these laws regarding blackjack computers and other devices are clarified, either by amendment or judicial interpretation, I highly recommend that one of his stories be as close as any player of even moderate skill come to the Magnolia State.

[Ed. note: Nevada’s anti-device statute has also been copied into Illinois’ and Iowa’s lawbooks.]

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George of Georges; Bally’s crumbling; Indiana dips

Before we go any further, bravo, bravo, arcibravo to Hard Rock International to laying some serious bread on its salaried workers. As of now, the base salary for non-tipped employees at Hard Rock casinos goes from $18/hour to $21. Hard Rock didn’t have to do it, it just did, which makes it all the more laudable. True, as some are suggesting, there’s some enlightened self-interest involved: Why work for the competition if you can go to Hard Rock and make significantly more? But that doesn’t diminish Hard Rock’s generosity, summed up by CEO Jim Allen as follows: “We looked at all the starting salaries of all our line employees, certainly recognizing the economic conditions that have been going on … We’re trying to find the highest quality employees, thanking them for their efforts and recognizing that with compensation.”

Continue reading George of Georges; Bally’s crumbling; Indiana dips
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Camouflage and Comps

The Playing Habits of Imbicilicus Touristicus
by Allan Pell

Counting Cards in Comp City
by Max Rubin

Burning the Tables in Las Vegas Reviewed
by Arnold Snyder

Betting Camouflage
by Arnold Snyder

Comp Secrets for Low Rollers
by Dogass Johnny

Insurance Camouflage for Card Counters
by Jake Smallwood

Negotiate for Better Comps
by Arnold Snyder

Camouflage to the Max!
by Arnold Snyder

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The Playing Habits of Imbicilicus Touristicus

Or, Absolutely Moronic Play That Costs You Nothing

by Allan Pell
© 1992 Blackjack Forum
[From Blackjack Forum Vol. XII #3, September 1992]

Imbicilicus Touristicus, commonly (albeit perhaps cruelly) known among card counters as the Stupid Tourist, is a unique species that makes its primary habitat within the gambling establishments of Nevada’s Vegas Strip territory. Imbicilicus can also be found in northern Nevada, Stateline, Reno, and also in outlying areas of the world wherever gambling is present.

Although Imbicilici, as a species, are diverse, they all possess an important common trait — they know zip about games of chance. Imbicilicus is the preferred prey of gambling establishments, having swallowed, in a glassy-eyed manner, its natural enemy’s bait that “gambling is fun and exciting.” Imbicilicus plays only to play. This factor, combined with the total lack of game knowledge, makes survival of this species’ bankroll short-lived.

How then can our species, Predacious Cardus Counterus, benefit from the habits of Imbicilicus? We can assume some of the outrageous and stupid characteristics of Imbicilicus, however, we must not make any plays which will actually cost us money. We shall become, in effect, Predacious Imbicilicus Imposturus.

Before my stint in Japan, I made my living as a writer in television. Characters and story lines come easily to me. The real secret to it is that writers don’t make up characters; we find them on the streets and then put them on paper. My “Imbicilicus Blackjack Act” didn’t have to be invented. I only had to mimic and refine what was already there. And believe me, the idiots are abundant.

Distinctive Markings And Colors Of Imbicilicus: Cultivating That Proper Look

All varieties of this species, in fact, look like dumb tourists. Cruise the Vegas Strip in summer and you’ll see them — displaying herding instincts and migrating between Circus Circus and the volcano at the Mirage.

Gambling towns are tourist attractions, and 80% of their traffic is out-of-state. So, look like you’re from out-of-state. Appear to be on vacation. In the summer months, sport shorts, tee-shirts, a cap, and brand new tennis shoes. If you’re young, your tee-shirt should display a Michigan State, a U.C.L.A., or “I’m With Stupid” logo. Your hat should have any kind of logo but John Deere — that’s the local Reno look.

If you’re thirty to forty-ish, keep the shorts but wear an Izod Lacoste or Polo shirt – and have the collar turned up. Very important! This is no longer fashionable in Vegas and it tells everyone that you’re a hick from Armpitsville. [Note: A slight sun-burn will seal the deal that you’re a seasonal visitor.] If you’re in the autumn years, wear anything you like. Your age is your best cover — just be your crotchety self.

In the winter, delete the shorts. Bum Gear sweat-pants or jeans. Leather coats or snow boots when appropriate will be your best cover for young to forty-ish ages. Look like you’ve been skiing. This works well in Reno, Stateline, and also Vegas. It tells them you’ve been hitting the slopes.

The waist bag (fannypack) is the single most important piece of apparel worn by Imbicilicus. The waist bag is to the tourist what the woods are to the bears. The more colorful your waist bag the better. It should sport a logo like Aspen, Disneyland, New York — anything! The pit bosses and dealers notice these little details.

The key to the logo is to have it tell a story of where you’ve been, without saying where you’ve been. The Michigan State logo on your tee-shirt tells them where you’re from. The Aspen or Squaw Valley logo on your cap tells them what you are doing or how you got to the area. And the shorts, sweat pants and waist bag confirm that you are Imbicilicus. The absolute worst look would be to dress up like a character from a James Bond movie: wraparound sunglasses, black suit, etc. Dress like Imbicilicus. Your welcome will wear out slower, if at all.

Vocalizations In The Wild: Your Card Counting Camouflage Legend

In the spy trade, a “legend” is your cover background. The worst thing for you to do at a blackjack table is to sit and be an emotionless card counting machine. You must learn to converse with the indigenous Imbicilicus, the dealers and the pit bosses. Pick a simple legend — something you know about — and stick with it. The simpler the better. Make your “travel legend” fit your apparel. If you talk about skiing, make sure you know about the resort you’ve been to. Make sure it’s open. Know the conditions, etc.

Pick a personal legend using your own name, but only your first name. Never use a pseudonym. You may get called upon to provide ID. In Nevada, you must provide ID upon request, and if your pseudonym doesn’t jibe with your actual moniker, you may have to answer some uncomfortable questions. Never sign up for the Player’s Club and the like. You don’t want the casino tracking your action and having your address at the same time. Your personal legend can be anything from brain surgeon to Congressional Aide. I used the legend of civil rights attorney in Reno once. No one touched me.

Keep your legend within an area you can freely converse in. Talk to other players. Talk to the dealer. Talk to pit bosses. Crack jokes! When I get a blackjack, I lay the cards down one at a time saying, “Meet Mister Black and Mister Jack.” When you win do the tequila dance, when you loose piss and moan. Talk! Talk! Talk! If you can’t count and talk, learn. I personally keep track of my running count between rounds with chips. Many pit bosses believe that counters can’t talk and count. Play along with these foolish mortal beliefs. The trick is to hide in plain sight.

The Playing Habits of Imbicilicus: Buying Into The Game for Camouflage

Never display the extent of your bankroll. Do as Imbicilicus does. Appear to possess a short bankroll. At small stakes games of $1 to $5 minimums, buy in with 30 to 50 bucks. At larger stakes games, $10 to $25 minimums, lay no more than $200 on the table when you make your first appearance.

If you fluctuate down, pull out some more bills from the waist bag. Imbicilicus always digs deeper to chase losses. If you cash into a game with $100 or more, the pit bosses in most casinos make a note of your action on paper and track you more closely. Never use the teller machines in the casinos in which you play. Many mark their money to see if it’s drawn from their machine. And it’s simple to line up your name, bank account number, etc., with the eye-in-the-sky picture of you drawing money.

In larger clubs, purchase $40 worth of dollar slot tokens from the slot cashier’s cage. Dump them into a boob bucket (plastic containers supplied by the casino). Scout the blackjack tables with boob bucket in hand. Amble along like Imbicilicus. Wong, sit-in, whatever. The boob bucket provides lots of cover. Circus Circus boob buckets (carried from and to the casino) are tops in boob buckets.

More Card Counting Camouflage: Dogging the Game

Imbicilicus always dogs the game with lack of knowledge. To be a complete blackjack neophyte, on your first round dealt in a face-down game, hold your cards with both hands. This will merit a reprimand from which you must sincerely and quickly apologize. Do this only once per casino per session! Do not invoke the ire of the dealer!

If, on your first round, you must hit, lay the cards down behind your bet and verbally ask for a hit. The dealer will then tell you how to do it. Pretend to be intimidated and choke-up on the implementation. Now, this will earn you a crash course on playing etiquette from other players and the dealer. The dealer will physically show you how to hold the cards and scratch for a hit. More apologies are now due, but it’s worth it because you are now firmly and solidly cast as Imbicilicus.

Bust & Tuck Camouflage, Or, Standing On 22 And More!

This is my next step — and my favorite because after this they’ll think you belong in a developmentally disabled center. There are several ways to play these.

Firstly, seemingly a zillion percent of the time you will draw stiff hands. I love 8, 7 on a dealer’s 10, then hitting to get another 8 or 7 early in the session. Basic strategy dictates hitting 15 against 10. You will break more often than not, but when you do, why not make it pay?! Make them think you’re Imbicilicus. When you break, tuck your cards under your bet. Wait for the dealer to discover your mistake. Look embarrassed!

Now you’ve earned more cover. Keep your cards to yourself until the dealer exposes your first mistake. Afterwards, hold the cards looser. Either other players will tell you your totals or the dealer will to speed the game. Players who can’t count the card totals surely can’t count the cards!

The bust and tuck ploy also works with multiple-card soft hands and all hard hands of four or more cards. Note: if you stay in the game a while, appear to get up on the learning curve and let your skill progress. Tell the dealer you’re getting the “hang of it,” thanks to everyone’s help.

You may also have help from the dealers. They’ll sound out your totals so you can totally concentrate on the count. [Note: I don’t recommend this on crusty, old dealers who don’t talk, who’ve been with the casino since the lot was cleared, and who show no emotion. This type of dealer could care less if you slid under a burning gasoline tanker.]

Toss The Winners!

This is the opposite spin on bust and tuck. You will hit to 21 on three or more cards many times. Turn a winning hand into both a winning and cover-inducing hand. Thinking you busted, toss the multiple card hand and one of three things will happen.

1. Another player will catch the mistake.

2. The dealer will catch the mistake and give it back to you.

3. If neither another player nor the dealer catches it, catch it yourself at the last possible moment, showing the greatest amount of embarrassment and shock you can muster!

Use your fingers to count up the totals while moving your lips silently. Remember to always look embarrassed! You can’t lose on this move. It costs you nothing and only deepens your cover as Imbicilicus. (After doing this dozens of times, to date, I’ve never had a dealer scoop up a 21 without catching my mistake.)

The Multiple Choke Card Counting Camouflage

You will draw two small cards and then hit to get another small card, then another. This is great! If strategy dictates, hit again and prepare to choke on the total. Show your hand to the dealer asking if it’s “too many?” Either 20, 21 or bust make them work for cover. This choking technique can be used indefinitely, even after you’ve worn out some of the above moves.

Indecision, Indecision. . .

It’s just what it sounds like. Don’t know whether to hit your 16s against the 10s?! Don’t know whether to double, split or stand?! Ask advice from other players, especially one that you know knows basic strategy. If the advice is bad, ignore it. Make faces, whine, piss and moan. It only helps you. It especially helps when you need an extra few seconds to calculate a difficult true count and make that strategy decision.

Brilliantly Stupid Blackjack Play

As you can see, “stupid camouflage” without “stupid costing” camouflage will postpone casino analysis of your card counting play. Cost-free stupid play will allow you to hang in there until you are ready to strike. And when you do, there are two ways to do it. 1. Traditional parlay cover play. 2. Nuclear War, meaning whack it out when you have a big, big advantage. Remember to play the “steamer” if you choose this method. I advise playing only one short session per casino per day else they’ll get wise when they see you’re actually playing perfectly.

Remember, luck has nothing to do with this game.

Sayonara from Pell-San. ♠

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What’s the Best Card Counting System?

A Comparison of the Top 100

By Arnold Snyder
(From Blackjack Forum Volume I #3, September 1981)
© Blackjack Forum 1981

[Note to players from Arnold Snyder: This is a technical article on the way professional blackjack players and count system developers compare card counting systems. If you’re new to card counting, and are looking for your first card-counting system, I recommend you start with our Intro to Winning Blackjack article.

There are links in that article to several card counting systems, from the easiest system I’ve ever seen to a full professional-level system, as well as information for new card counters on how to choose the best system for you.]

A number of blackjack players have written me asking my opinion of the “best” card counting system. This is a loaded question.

As I mentioned in Blackjack Forum #I I have been using the Hi-Opt II count, because I like its power and simplicity for my ability and style of play. [Note from A.S.–Soon after this article was written I switched to the Zen Count for single deck play. When I began shuffle tracking, I switched to the Hi Lo Lite Count. Complete information about both counts is provided in Blackbelt in Blackjack.]

If you are using a card counting system with which you are comfortable, and you feel you can play it accurately, then stick with it. There is more money to be made by finding and exploiting lucrative table conditions than by “upgrading” your card counting strategy. Your “act” is more important than any amount of complex mental arithmetic you do at the tables.

Card counting is automatic and boring once you know your system. This is as it should be, so that you may apply your efforts to the more important work of pretending to be a non-card-counter; engaging dealers and pit-bosses in conversation; flirting with cocktail waitresses; acting engrossed in the Keno board, etc.

Some players find card counting easy, and/or are so dedicated to practice that they can accurately apply higher level card-counting strategies. By a “higher level count,” I mean a count that assigns card values other than +1, -1, or 0.

A “multi-parameter count,” on the other hand, is one that keeps separate running counts for various cards. I am of the opinion that the most difficult higher level single parameter card counting system (i.e. – no “side counts”) are easier to play with accuracy, than the “simplest” level one multi-parameter card counting systems.

Most card counters, including serious professionals, should stick with level one single-parameter card counting systems. Some players may obtain a slightly greater advantage by applying a higher level single-parameter count strategy. I’ve analyzed more than 100 different single-parameter systems, including both those that are currently available and some that are purely theoretical to determine the “best”, in terms of potential returns on the dollar.

The Search for the Best Card Counting System: Methodology

My method of comparing systems is to apply the “Blackjack Formula,” inserting the various systems’ playing efficiencies and betting correlations. If you have my book, The Blackjack Formula, see page 54 for such a comparison of eight popular card counting systems. In this comparison, I tested each system vs. Vegas Strip rules in a singledeck game with a 1 to 4 betting spread, and 60%, 70% and 80% of the cards dealt out.

I’ve similarly tested many other actual and hypothetical card counting systems in both single and multi-deck games, assuming various betting spreads. Although differences between systems are slight, this methodology allows card-counting systems to be ranked by profit potential with relative accuracy if we assume accurate strategy tables are being used.

What I’ve found is that the higher-level systems perform at a rate of profit of about .1% better than the level one systems. My method of computing the playing efficiencies and betting correlations of the various systems is explained in The Blackjack Formula (pages 85 through 90). My method is a simplification of Peter Griffin’s method in Theory of Blackjack, and for all practical purposes, is just as accurate.

The card counting systems that I analyzed in seeking the best ranged from level one through level four (i.e., I did not attempt to analyze any count system with values greater than +4). There appears to be no practical reason for employing a count system greater than a level two. I could find no significantly better count than that which applies the following values:

A23456789X
-1+1+1+2+2+2+100-2

This count, which I will dub the Zen Count, has a playing efficiency of .63 and a betting efficiency of .97. Curiously, the ace, valued at -1, is not neutralized (valued 0), but “half” neutralized. In other words, I have “taken the middle road. – a zen approach.

It is this trick that keeps the betting efficiency high, while maintaining a very respectable playing efficiency. The following table shows how various counts rank, according to the Blackjack Formula, assuming a 1-to-4 spread, single-deck game, Vegas Strip rules, dealt out 70% between shuffles:

SystemRate of Profit
Zen Count2.00
Uston APC1.98
Revere APC ’731.97
Wong Halves1.96
Hi-Opt II1.96
Canfield Master1.96
Revere Point Count1.95
Uston Adv. +/-1.89
Canfield Expert1.88
Hi-Lo1.87
Hi-Opt I1.86
Revere +/-1.86
Andersen Count1.80
DHM (Simple)1.78

The top-ranked (level two) Zen Count is simpler than any of the next three counts which are level 3, level 4, and level 3, respectively. As I noted earlier, I use the Hi-Opt II count. My reason for this is that the gain from using the Zen Count is very slight, and frankly Hi-Opt II is slightly simpler. I’m a great believer in simplicity. Nor could I say for certain that the Zen Count is undeniably superior. The Blackjack Formula indicates a negligible superiority under most conditions.

Of academic interest, the best single parameter card counting systems are those numbered #91, #92, #93 and #94. These systems represent the upper limit of single parameter systems which score high in both playing efficiency and betting correlation.

All of these systems employ the same device of not-quite-neutralizing the Ace. Although I believe it would be easier to play one of these level four single-parameter systems accurately, than it would be to play any multi-parameter system, I would not advise any player to mess with one of these monsters. The potential gain from using one of these counts, compared to that of the relatively simple Zen count, is negligible.

For instance, in the Vegas Strip game used in the prior comparison, in which the Blackjack Formula predicts the Uston APC would win at a rate of 1.98% and the Zen Count would win 2.00%, any one of the level four counts would win at a rate of only 2.02%.

The Blackiack Formula, to be fair, is not actually accurate enough to make such a fine comparison. But count #92, which has a playing efficiency of .67, and a betting correlation of .95, would undeniably rank higher than Hi-Opt II, which also has a playing efficiency of .67, but a betting correlation of only .91.

The following table lists the playing efficiencies and betting correlations of 100 selected card counting systems (with sincere thanks to Brian Gothberg for writing the computer program that generated these results).

Count23456789XAPEBC
1000100000-1.05.53
211110000-10.56.86
301111000-10.61.88
400111100-10.64.85
511111000-1-1.51.97
601111100-1-1.55.95
71111100-1-10.59.92
80111110-1-10.63.89
91111110-1-1-1.54.98
10001100000-2.05.58
1100220000-10.49.78
1200121000-10.57.83
1301121000-1-1.51.94
1400121100-1-1.53.91
150112100-1-10.57.89
160012110-1-10.59.86
1700221000-1-1.47.89
180022100-1-10.53.84
191112100-1-1-1.51.97
200112110-1-1-1.54.96
210122100-1-1-1.49.94
220022200-1-1-1.46.89
2311121000-1-2.4.96
2401121100-1-2.43.94
2501221000-1-2.4.93
2600222000-1-2.38.88
271112110-1-1-2.45.98
281122100-1-1-2.41.97
291111111-1-1-2.43.94
300122200-1-1-2.41.93
310122110-1-1-2.44.95
320022210-1-1-2.42.91
3311111111-21.61.72
3411111111-20.61.8
3511121110-20.67.88
3611221100-20.67.91
3711222000-20.63.9
3801222100-20.66.89
390222210-1-20.65.91
401122210-1-20.67.93
411222200-1-20.62.92
4211222100-2-1.63.97
4312222000-2-1.58.95
4402222100-2-1.61.94
451222210-1-2-1.62.98
462222200-1-2-1.57.97
470222220-1-2-1.62.95
481222210-2-20.63.93
4912222100-2-2.56.99
502222210-2-2-1.59.97
512222210-1-2-2.551
521222220-2-2-1.61.96
531222220-1-2-2.57.99
5422222100-2-3.48.98
5512222200-2-3.49.97
5612232100-2-3.49.98
5712332000-2-3.46.97
5812331100-2-3.48.97
5911332100-2-3.49.97
6002332100-2-3.48.96
6102333000-2-3.45.94
621223210-1-2-2.571
631233200-1-2-2.53.98
640233210-1-2-2.55.97
651233210-1-2-3.51
6612332100-30.66.92
6722232100-30.66.92
6822332000-30.63.91
6912333000-30.63.9
701233220-1-30.68.93
712233220-1-30.67.94
722233310-1-30.66.94
731233320-2-30.67.93
7412332200-3-1.65.95
7522332200-3-1.64.96
7622333100-3-1.63.96
7712332200-3-2.61.97
782233320-1-3-2.62.99
7922333200-3-3.56.99
802333320-1-3-3.571
811234210-1-30.66.93
822234210-2-30.65.94
832234220-2-3-1.64.97
842234320-2-3-2.61.99
852234320-1-3-3.581
862334320-1-3-4.531
872334320-1-40.68.93
8823343200-4-1.66.95
8922443200-4-1.66.95
903344220-1-4-1.64.96
912344320-1-4-1.66.96
922244330-1-4-1.67.95
932344330-2-4-1.66.96
943344320-2-4-1.65.97
953344330-2-4-2.63.98
9633443300-4-4.56.99
9733444200-4-4.56.99
983344430-1-4-4.571
993344330-1-4-3.6.99
1003344420-1-4-3.6.99

Any player who would like to play what may be the “best” practical card counting system ever devised, may obtain complete strategy tables for the Zen Count (developed by yours truly) in the 2005 edition of Blackbelt in Blackjack.

I used the Zen Count myself when playing deeply dealt single deck (back when such games were available at full payouts on naturals). You can find more information on the Zen Count here: Zen Count Indices. If I were still strictly counting cards, I would still be using the Zen Count.

However, when I switched to shuffle tracking, I switched to the Hi-Lo Lite count. I made that switch because I wanted an easier count (to allow for the complications added by shuffle tracking) without giving up much power. You can find a link to information on the Hi-Lo Lite at the upper left of this page, with complete information in Blackbelt in Blackjack. 

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Intro to Winning Blackjack

© Arnold Snyder

The Dream World vs. the Real World

Playing winning blackjack is often fun, but not always. Some players, including the moderators of this Web site, make a living playing blackjack and some (including some of the moderators of this site) have gotten rich playing blackjack, but to succeed takes the same hard work it takes to succeed at anything else. Don’t believe all the get rich quick spouters who claim it’s easy and anyone can do it. Read “Blackjack Reality vs. Blackjack Hype” to learn more about what to expect.

What Card Counting is Really Like

To get a realistic idea of the both the fun and frustrations of playing blackjack to win, as well as the kind of money you’ll make as a new card counter, see A First Year in the Blackjack Pits.

Blackjack Basic Strategy

The first and single most important step in learning to play winning blackjack is learning blackjack basic strategy. Read our basic Strategy articles for complete instructions and charts for every game. Then start with one of the simplified versions specifically for the types of games you’ll be playing, based on the rules and the number of decks in play. You can always make adjustments for different conditions later. Many pros learn one simplified version and never even learn all of the adjustments. But you must learn a generic version of basic staretgyso well that it’s second nature and you don’t even have to think about it. Do this before you start trying to master a counting system.

Why Card Counting Works

Card counting is not the only way professional gamblers make money playing in casinos, but it’s where you should start, because the fundamentals of card counting will prepare you for every other form of winning blackjack play.

Start off on the right foot by reading the articles in our card counting section so you fully understand the basics of card counting and why it works. Then, choose a simple counting system and start drilling.

The Easy Red 7 Count and Even Easier OPP Count

Aggression and simplicity are the keys to the money. Our articles provide complete instructions on using the super-easy OPP Count or the slightly more difficult but more powerful Red 7 count.

But don’t feel you have to start with a professional level count. It’s far important to get comfortable at the tables with an easy count than it is to start with a more powerful counting system. Your long-term success will depend on aggressive betting and remaining welcome at casinos far more than your counting system.

And you’ll be surprised how easy it will be to switch to a professional-level count down the road.

Do You Have What It Takes To Succeed?

What really separates the players who go on to win at gambling from those who never quite get started?

The guts to stick with it when you’re losing. Read the articles in our Those Damn Fluctuations section to understand. ♠

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Count per Deck with the Zen Count

Complete Zen True Count Indices

By Arnold Snyder

(From Blackbelt in Blackjack, 1983 edition)
© 1983, 2005 Arnold Snyder

[For complete information on the Zen Count, the easiest of the highest-power multi-level professional card counting systems, see Blackbelt in Blackjack : Playing 21 as a Martial Art , by Arnold Snyder.]

A number of players have asked for true count indices for the Zen Count, using the conventional count-per-deck adjustment (that is, True Count = Running Count /Number of Remaining Decks).

Complete Zen Count Indices for True Count Method (Multi-Deck)

Stand

Stand23456789XA
17SSSSSSSSS-13/-10*
16-16-18-20-24-25/-28HH8013/5
15-10-12-14-17-17/-21HH13615/8
14-6-8-9-12-12/-16HH2012H
13-2-4-5-8-7/-11HHHHH
12631-2-1/-5HHHHH
A7SSSSSSSHHS

Double Down, Hard Totals

Double23456789XA
11DDDDD-19-14-10-9111/-21
10DDDDD-14-9-47151/41
92-2-5DD7HHHH
8HH1074/4HHHHH

Double Down, Soft Totals

Soft Totals23456789TA
(A,9)SSS98/7SSSSS
(A,8)S7522/0SSSSS
(A,7)1-4-8DsDsSSHHS
(A,6)2-5DDDHHHHH
(A,5)HHDDDHHHHH
(A,4)HHDDDHHHHH
(A,3)HHDDDHHHHH
(A,2)HHDDDHHHHH

Surrender (Late)

Late Surrender23456789XA
17
1680-8-1/-12
8-8160
1512404/0
7-74
14848/4
132012

Surrender (Early)

Early Surrender23456789XA
1712Y
16120-12Y
8-816-4Y
15124-4Y
7-71680Y
141680Y
13208Y
1220-12
7-12
6-8
50



* Number before slash (/) is index for S17; number after slash is the index for H17

1 = European No Hole: Hit

S = Stand, H = Hit, D = Double Down (if doubling not available, then hit), Ds = Double Down (if doubling not available, then stand), в = Surrender

Pair Splits
With Double After Splits

Pairs23456789TA
(A,A)YYYYYYYYY-8
(T,T)171312109/8NNNNN
(9,9)-4-8-8YY4YYN4
(8,8)YYYYYYYY16**Y
(7,7)YYYYYY4NNN
(6,6)-4-8YYYNNNNN
(5,5)NNNNNNNNNN
(4,4)N1240-4NNNNN
(3,3)-8YYYYY8NNN
(2,2)-8-8YYYY12NNN

Pair Splits
No Double After Splits

Pairs23456789TA
(A,A)YYYYYYYYY-8
(T,T)171312109/8NNNNN
(9,9)-4-4-8-8-812YYN8
(8,8)YYYYYYYY8**Y/0
(7,7)YYYYYYNNNN
(6,6)40-4-8YNNNNN
(5,5)NNNNNNNNNN
(4,4)NNNNNNNNNN
(3,3)1240-8Y12**NNNN
(2,2)124-4YYYNNNN

**Split if below index number

INSURANCE: Take insurance at +5 True Count or higher

Complete Zen Count Indices for True Count Method:
Single Deck
For Depth Chargers and Serious Fanatics Only!!!
(Otherwise just use multi-deck charts)


Single Deck Stand

Stand23456789XA
17SSSSSSSSS-14/-12*
16-16-19-22-26-23/-2716129013/5
15-10-13-15-18-18/-22181614715/8
14-6-8-10-13-12/-1627H211322/15
13-1-3-5-8-7/-11HHHHH
12742-21/-4HHHHH
A7SSSSSSSHH-4/15

Single Deck Double Down, Hard Totals

Double23456789XA
11-24-26-28-32-34-18-13-9-9-2/-4
10-19-20-22-26-29-12-8-475
91-2-5-9-12714HHH
82316117626HHHH
7242020 

Single Deck Double Down, Soft Totals

Soft Totals23456789TA
(A,9)1715111110/9SSSSS
(A,8)126512/0SSSSS
(A,7)3-2-12-11-13/-18SSHHS
(A,6)1-4-11-16-25HHHHH
(A,5)H4-4-12-25HHHHH
(A,4)H8-2-9-21HHHHH
(A,3)219-3-5-12HHHHH
(A,2)1592-1-6HHHHH

Pair Splits
(For other pair splits, see multi-deck charts)

Pairs23456789TA
X,X1915131111/1026    

* Number before slash (/) is index for S17; number after slash is the index for H17

1 = European No Hole: Hit

S = Stand, H = Hit, D = Double Down (if doubling not available, then hit), Ds = Double Down (if doubling not available, then stand), ¢ = Surrender ♠