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.] ♠

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. ♠

© 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. ♠

Implications for Advantage, Win Rate, Betting, and Table Hopping in Blackjack Card Counting

By Arnold Snyder (with Blackjack Simulations by John Gwynn)
(From Blackjack Forum Volume II #3, September 1982)
© Blackjack Forum 1982

Brace yourself, dear card counter, because this is another one of those all-the-blackjack-experts-have-been-wrong bombshells I’ve been having so much fun dropping on my faithful followers lately. John Gwynn dropped this one on true counts on me eight months ago, and it’s taken me this long to put it all together with some coherence.

If you own a copy of the Zen Count, you will see, on page 4, that I list the various true counts at which I estimated a card counter would have a ½% advantage in various blackjack games. When Gwynn completed his first 4-deck blackjack computer simulation runs of the Zen Count, he wrote to me that my advice was only partially true. He pointed out that the player advantage using the Zen Count was, as I advised, ½% or better at a true count of +4 in the 4-deck strip game, but if 62.5% or more of the cards had been dealt out, the player would have an edge of ½% or better at a true count of only +3.

This was a revelation to me. The whole purpose of adjusting running count to true count is to obtain an accurate estimate of your advantage at any deck level. Expert opinion in blackjack has always held that a running count of +6 with one deck dealt out of a 4-deck game indicates a player advantage equivalent to that of a running count of +4 with 2 decks dealt out or +1 with 3½ decks dealt out. In all cases, the “true” count is +2 (on a count-per-deck basis.)

John Gwynn’s 23+ million hand simulations of blackjack systems indicate otherwise. Since Gwynn’s original comment to me regarding the Zen advantage, he discovered an error in his simulation program (Blackjack Forum Vol. II, #2). His corrected data show that his original observation, that a Zen player would average a ½% edge at +3 in the 4-deck Strip game with 2½ decks dealt, to be untrue (but close). However, his remark led me to examine closely the corrected data for any tendency of the true count to prove significantly “untrue”. The results, to me, are startling.

Actual Advantage for any True Count Changes with the Depth of the Deal

For instance, let’s look at the simulation results for Hi-Opt I (4 decks, no ace count, Vegas Strip rules). The depth of the deal is listed horizontally along the top of the table. The true count is listed vertically on the left. The table entries show the actual rate of win (or loss) for the player at each given true count. True counts are rounded, i.e., +2 = +1½ to +2½. The advantage shown is the cumulative advantage for all hands played up to that point:

Hi-Opt I Advantage (in %)

	50%	62.5%	75%	87.5%
-2	-1.40	-1.41	-1.38	-1.30
-1	-.85	-.86	-.84	-.84
0	-.41	-.41	-.41	-.38
+1	.10	.13	.13	.18
+2	.53	.57	.62	.66
+3	.87	.96	1.05	1.13
+4	1.36	1.52	1.70	1.8
+5	1.58	1.81	2.14	2.22

Note here that in 18 instances, the player advantage rose as depletion increased. In two instances, player advantage fell. In four instances, it remained the same.

Note how much each true point is worth with only 50% dealt out. Note how much each true point is worth with 87.5% dealt out.

Let me explain briefly how these simulations were done. Gwynn’s computer is programmed to play through 23+ million hands (or 700,000 shoes), using any inserted system. It then tallies the data for the various circumstances. Separate runs are not necessary to obtain data for the various shuffle-points and true-count values.

To obtain the player advantage at a true count of +2 with only 50% dealt, the computer is simply instructed to tally all results obtained when the true count was between +1.5 and +2.5, and to disregard the results of all hands played after two decks have been depleted. Because of this methodology, the total number of hands played at the various levels of deck depletion differ.

At the 87.5% shuffle-point, 23.6 million total hands were played. With 75%: 20.3 million. With 62.5%: 17 million. And with 50%: 13.6 million hands. This also means that these advantages in the table are cumulative, i.e., the listings at 75% do not indicate the player edge only at 75% depletion, but the average advantage of all hands up to 75% depletion.

For instance, look at the entries for a +2 true count:

	50%	62.5%	75%	87.5%
+2	.53	.57	.62	.66

What this means is that up until 50% deck depletion, the player gained .53% on all his bets placed when the true count was +2. By the time 62.5% were dealt out, the player had gained .57% on all these bets at +2 true count. By the time 75% of the cards were dealt out, he was averaging a .62% advantage, etc. This is a very important point, because…

If the player was averaging .53% on all +2 true hands up to a 50% shuffle-point, then it would take an average advantage of .73% to raise this figure to .57% by the time a 62.5% shuffle-point was reached. And, to raise the .57% to .62% (at the 75% shuffle point), it would take an average edge of .87% on those hands played between these points.

Average Point Value and Deck Depletion

Another way to analyze this Hi-Opt I data is to estimate the value of an average true point between various levels of depletion. If, as Peter Griffin tells us, the starting advantage in this game is -.48%, we can estimate the average point’s value up to the 50% shuffle-point by taking the difference between the player edge at true counts of +5 and 0, and dividing by the 5 true points. We can then calculate the value of an average point between two levels of deck depletion, according to the point value necessary to cause such a change in “average” point value.

	Up to 50%	51% to 87.5%
Average Point Value	.41%	.71%

This raises serious questions about the “truth” of the true count. Gwynn’s data for the Hi-Opt I system are generally consistent in showing notable increases in player advantage at any true count as deck depletion increases. The value of a true point appears to depend on a number of factors, one of which is the level of deck depletion. Another factor seems to be the system itself. Here is a similar table for Uston’s APC:

Uston APC (with Ace)

	50%	62.5%	75%	87.5%
-2	-1.01	-1.02	-1.01	-.97
-1	-.83	-.81	-.80	-.75
0	-.39	-.38	-.38	-.37
+1	.11	.05	.05	.07
+2	.41	.44	.41	.43
+3	.31	.42	.47	.56
+4	1.03	1.07	1.04	1.04
+5	1.50	1.37	1.48	1.52
+6	1.20	1.53	1.85	1.93
+7	2.29	2.48	2.56	2.56

Here, we’ll note that in 22 instances, player advantage rose as deck depletion increased. It fell in five instances. In three instances, it remained the same. The average point values for Uston’s APC, at various levels of deck depletion:

	Up to 50%	51% to 87.5%
Average Point Value	.40%	.51%

This data indicates that the radical change seen in the value of a true point for the Hi-Opt I system may not necessarily be expected for any system. But the difference is still significant.

Look at a similar table of player advantages for the Zen count (with 25 indices):

Zen Count Advantage (in %)

	50%	62.5%	75%	87.5%
-2	-.78	-.77	-.75	-.72
-1	-.79	-.77	-.75	-.70
0	-.38	-.36	-.35	-.32
+1	-.05	-.10	-.13	-.10
+2	.20	.18	.12	.16
+3	.35	.44	.49	.50
+4	.57	.62	.69	.76
+5	.79	.68	.76	.81
+6	1.26	1.28	1.32	1.33
+7	1.50	1.61	1.58	1.45
+8	1.70	1.82	1.72	1.84
+9	2.26	2.16	2.28	2.47

Here, in 27 instances, player advantage rose as deck depletion increased. In nine instances, player advantage fell. The average point values for the Zen Count, at various deck levels:

	Up to 50%	51% to 87.5%
Zen Average Point Value	.30%	.37%

Here again, this table as a whole shows the same tendency as Uston’s APC; the results are less consistent and more erratic.

Looking at the results for all three of these systems, it appears we cannot say with any degree of certainty what a true point is worth for any one of them. Occasionally, I get a letter asking me to clarify the precise value of a point for some system. Assigning such a value appears to be, at best, an oversimplification.

Gwynn’s Hi-Opt I results are the most consistent and dramatic. Based on this simulation, it appears that a single true point is worth twice as much (or more) deep in the shoe as shallow.

The results I used in this analysis were for player advantages up to about 2½%. Gwynn provided no data for true counts below -2. I used these results because they are the most frequently occurring true counts, thus the most significant. The data distorts radically at progressively higher true counts due to chance fluctuation.

But look at this table, which shows the Hi-Opt I advantage for all true counts from 0 through +20, with 87.5% of the cards dealt out:

True Count	Player Advantage	Point Value
0	-.38	–
+1	.18	(.56)
+2	.66	(.48)
+3	1.13	(.47)
+4	1.80	(.67)
+5	2.22	(.42)
+6	2.80	(.58)
+7	3.32	(.52)
+8	4.18	(.86)
+9	4.67	(.49)
+10	4.95	(.28)
+11	5.78	(.83)
+12	5.64	(-.14)
+13	7.37	(1.73)
+14	7.51	(.14)
+15	7.32	(-.19)
+16	9.51	(2.19)
+17	7.59	(-1.92)
+18	9.72	(2.13)
+19	10.38	(.66)
+20	10.07	(-.25)

The figure in parentheses, the “point value”, shows how much each individual true count raised the player advantage over the previous true count. For instance at +6, the win rate was 2.80%. This particular true point raised the player advantage by .58% over the player win rate at a true count of +5, which was 2.22%. Thus the “point value” of this particular true point was .58%.

The data in this table run contrary to one currently held theory that the “strategy gain” from card counting increases dramatically at higher true counts. Gwynn was employing all 201 strategy indices in this 23.6 million hand simulation.

According to The World’s Greatest Blackjack Book (Humble and Cooper), a single Hi-Opt I point is worth .515% (pp. 265-66). The formula they provide for estimating advantage at any true count is to multiply .515% times the true count, then to add both the “strategy gain” and the Starting Advantage of the game. Applying this formula to a +12 true count, we get:

(.515% x 12) + 3% – .48% = 8.7%

The -.48% is our starting advantage in this 4-deck Strip game. The 3% is the amount of “strategy gain” that Humble and Cooper explain is added at a true count of +12. (They also explain the strategy gain would be 2% at 8, and 1% at 6). Humble’s predicted 8.7% edge, at a true count of +12, is more than 3% higher than the computer simulation result.

Gwynn’s +12 advantage of only 5.64% suggests that Humble’s “strategy gain” is either virtually non-existent in the 4-deck game, at least as any highly significant factor, or that the average value of a Hi-Opt I point is quite a bit lower than .515% in the 4-deck game. This 3+% discrepancy between the Humble/Cooper estimate and Gwynn’s simulation results cannot be attributed to normal fluctuation. Gwynn’s computer played more than 52 thousand hands at this +12 true count, so one standard deviation is only .48%.

Again, these results question the validity of many currently held beliefs about true count. Gwynn’s simulation data indicates that the value of a true point for any system varies with both deck depletion and, as we shall see, with the number of decks in play.

The Hi-Opt I data indicates that a true point may be worth only .3% to .4% early in a 4-deck shoe and .7% to .9% deep in the shoe, with an average value of about .5%. From the data Gwynn has provided, it is impossible to tell how much lower these values would be without the playing strategy indices which the computer employed throughout. It appears that the total gain for the Hi-Opt I player, including the “strategy gain”, with each increase in true count, averages to about .5% by the time three decks have been depleted.

Guidelines for Card Counters

My recommendations: Since the Hi-Opt I data suggest such a radical departure from long-standing card counting theory and because the Zen and Uston APC data are more erratic, though still supportive of the “untrue” true count notion, with greater point values at deep shuffle points, I’ll be cautious in my recommendations. It may be that an entirely new method of adjusting running count to true count is needed.

The concept of true count goes back to E.O. Thorp. In his original ten-count (Beat the Dealer, 1962), Thorp described his method of estimating advantage according to the ratio of tens to non-tens. In essence, this simple ratio provided the first true count. John Gwynn has produced a body of data which leads me to question the validity of Thorp’s assumption and methodology.

Gwynn’s data does suggest certain guidelines for players. First of all, it appears to be a waste of time arguing about the actual value of a true point. This value depends not only on deck level, but also on the precise point in question. The point between +4 and +5 may be significantly more or less valuable than the point between +3 and +4.

If you are a table hopper, attempting to bet in proportion to your advantage, I would advise more conservative estimates of advantage, especially if you are in the habit of adding a “strategy gain.” None of the three systems for which Gwynn provided data indicates that true points are consistently worth more as true counts become higher. It would be interesting to see a Hi-Opt I run using no indices, but playing basic strategy. Such a run would by comparison show the actual strategy gains at the various true counts and deck levels in this 4-deck game.

I will suggest being more conservative in sizing bets early in a shoe, and somewhat more aggressive later. Table hoppers will tend to play far more hands at lower levels of deck penetration than players who keep their seats through the negative counts. Thus, the high true counts they see will more often be indicative of less of an edge than has generally been assumed by blackjack experts.

This is not an argument against table-hopping, which is still your best multi-deck count strategy. This is simply a caution to be more conservative in estimating your advantage. Essentially, Gwynn’s data show that any oversimplified methods of estimating advantage must be viewed as rough approximation techniques only.

Alas, true count, like true love, is rarely true.

Let’s look at some one-deck data for these three systems. These simulations were done in the same way, though results were tabulated at only three deck levels: 25%, 50% and 75%. A total of 20.1 million hands were played by the 75% level. Again, these results are for Vegas Strip rules, and assume that no ace side counts are being used.

Hi-Opt I

	25%	50%	75%
-2	-1.18	-.79	-.62
-1	-.51	-.63	-.63
0	-.03	.05	.23
+1	.75	.80	.80
+2	1.06	1.24	1.54
+3	1.38	1.45	1.45
+4	2.05	2.25	2.63

Complete Zen

	25%	50%	75%
-2	-.26	-.02	.13
-1	-.06	-.17	-.17
0	-.01	.02	.16
+1	.34	.45	.45
+2	.89	1.05	1.32
+3	.81	.99	.99
+4	1.10	1.27	1.53

Uston APC

	25%	50%	75%
-2	-.67	-.59	-.26
-1	-.58	-.38	-.21
0	-.03	.01	.14
+1	.54	.55	.62
+2	.71	1.01	1.33
+3	1.02	1.25	1.36
+4	1.68	1.76	2.03

Again, note that in all three systems the win rate at any given true count increases as deck depletion increases. There are a few variations from this tendency, but the overall effect of deck depletion on true point value is consistent with our 4-deck findings. In fact, in these single-deck runs, this tendency appears even stronger than in 4-deck games. A single-deck true point generally appears to be worth more than a 4-deck true point. The effect of deck depletion in single-deck games is even more radical than in 4-deck games.

For all three systems, look at the win rates at true counts of +2. Compare the win rates at 25% depletion and 75% depletion.

How can you use this knowledge at the tables? First of all, I don’t believe anyone is going to come up with a highly accurate method of adjusting running count to true count. Nor can anyone define the value of a point as specifically as most experts and writers, including myself, have been doing for years.

Nor does it appear feasible to develop a practical betting scheme that allows you to bet in proportion to your advantage with any high degree of accuracy. I’m not suggesting that you throw out your attempt to bet in proportion to your advantage, but that you realize how rough any estimate of your advantage is.

Player Advantage is not Linear

Advantage is not in any sense linear in the game of blackjack, nor does it appear to follow any pattern without variation. The value of a true point depends on the deck level. However, even at a true count of 0, the player is significantly better off in single-deck games deeper in the deck.

Although I reproduced here only the Vegas Strip results, Gwynn’s data shows the same tendency for all three count systems vs. Northern Nevada rules, to about the same degree. Although Gwynn’s printout does not show win rates at true counts below -2, it appears that you are also better off at the same negative true counts later in the deck, i.e., a true count of -2 is not so bad with 75% dealt out as with only 25% dealt out.

Strange quirks exist throughout all of the systems. The Zen Count, for instance, in the single-deck Vegas Strip game, actually indicates a player edge at a true count of -2, but a house edge at -1. This is not due to an isolated weird run of hands.

Even with Northern Nevada rules, you are better off at a true count of -2 than -1 if you are using the Zen Count. Likewise, you have a greater advantage at a true count of +10 than you do at a true count of +11, and also greater at +2 than +3, regardless of rules; and you usually have a greater advantage at +4 than at +5, depending on the penetration of the deck.

Most of these same anomalies exist to a lesser extent in 4-deck games with the Zen Count. Similar type occurrences are apparent in the other count systems, but occurring at different true counts. A precise explanation of such phenomena does not present itself.

There are undoubtedly precision system fanatics who would attempt to modify their play according to such data as Gwynn has developed. They would raise their bets at a true count of -2, lower them at -1, and raise them again at 0 (providing more than 50% of the deck was depleted). In sizing their bets, they would realize that they were always better off at a true count of +2 than +3, and better off at +4 than +5 (if 75% of the deck had been depleted), etc. However, such a betting scheme would drive most players nuts.

Precision Doesn’t Pay

Gwynn’s data indicate to me that some players are wasting a lot of time and effort with precision techniques. Gwynn programmed his computer to adjust to true count by counting the exact number of cards, “accurate to the gnat’s ass,” as he put it, and also to adjust to true count by estimating to the nearest quarter-deck (13 cards). There was no significant difference in win rates between these two methods.

Since true count isn’t true anyway, this is understandable. Why use a toothbrush to scrub the side of a barn? Such precision appears to be a waste of time.

I’m not advocating sloppy play. Most players use a quarter-deck true count approximation and should stick with it. In single-deck games, using a half-deck approximation is too sloppy. Gwynn tried this with Uston’s APC and found that it was no better than Hi-Opt I, when Hi-Opt I used a quarter-deck true count approximation.

In the next issue of Blackjack Forum I’ll continue my examination of John Gwynn’s massive body of simulation data. In particular, I’ll be comparing the single-deck win rates of various systems in single-deck games with both Vegas and Reno rules with various shuffle-points. Gwynn has already provided me with this data for Hi-Opt I, Uston’s APC, and the Zen Count. He hopes to have his single-deck runs completed for Hi-Opt II and the Hi-Lo count in time for the next issue.

This computer simulation data that John Gwynn has been making available to me for publication in these pages since Blackjack Forum Vol. I #4 is, to my knowledge, the most extensive and important computer research being done on blackjack today. Analysis of Gwynn’s extensive data answers many questions, but raises many others.

I am grateful to Dr. Gwynn for allowing me to publish his extremely valuable data with my initial analyses and commentary. I realize that this “rush to press” methodology leaves many questions unanswered, but I feel the information contained in this data is of such importance to blackjack players that they should get this information as soon as possible. Hopefully, further research on these findings, and input from other experts, will ultimately lead all of us to a better understanding of the game. ♠