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Four Simultaneous Blackjacks

What Are the Odds?

by Arnold Snyder
(From Casino Player, July 1995)
© Arnold Snyder 1995

Question from a Blackjack Player:  What are the odds against three players and the dealer all getting a blackjack on the same round? This actually happened to me on my last trip to Las Vegas. The dealer was so amazed, she called the pit boss over to see it, and he said he’d never seen anything like it before. As a side note, I was the only player who took even money when the dealer asked us if we wanted to take insurance. (She had the ace up.) Both the other players declined because they thought it would be impossible for the dealer to also have a blackjack. I figured if the dealer had just dealt three naturals, she most likely dealt a fourth! I was right! Have you ever heard of anything like this?

Answer:  There are a couple of pieces of information lacking from your description of this event that are crucial to analyzing the exact probability of occurrence. First, you don’t say specifically whether or not any other players, who did not receive blackjacks, were playing hands at the same table, or if any of the three of you who received blackjacks were playing more than one hand (one of which was not a blackjack). I’m going to assume that only three players were at the table and that each player was playing only one hand.

Obviously, if four out of seven or eight hands dealt were blackjacks, it would be far less unusual than if four out of four hands dealt were blackjacks. (Or, at least, this would be obvious to anyone who’d taken an introductory course in probability and statistics. It may not be obvious to you, but take my word for it.) I’ll make the assumption that there were only four total hands in play — three players and the dealer — because you relate that the dealer was “amazed” and the pit boss stated he had “never seen anything like it before.” I’m sure most dealers and pit bosses of any experience have seen four simultaneous blackjacks dealt at a full table of players, in which three or four non-blackjack hands were also dealt, rare as even this would be.

The other pertinent fact you fail to mention is how many decks were in play. This is a crucial detail if you want to figure out the precise likelihood of occurrence. In a single-deck game, where there are only four aces in play, it would be far less likely for one of each of these aces to be dealt to each of four players than it would be in an eight-deck game where four aces represent only 12.5% of the total number of available aces in the shoe.

Technically, this is a fairly simple blackjack math problem to figure out, and you can easily do it on any pocket calculator, though it is a bit tedious. You simply calculate how many total possible ways four simultaneous blackjacks can be dealt, out of all the possible four-hand two-card combinations, and you get the odds against it occurring. Of course, it could take you a month of Sundays if you’re going to sit there and actually run through every possible two-card combination, four hands at a time, then count the totals of those which are four blackjacks vs. those which are not; and to do this for an eight-deck game, would take you multiple lifetimes. Fortunately, there are easy shortcut methods for figuring out problems like these.

In a single-deck game, the odds against being dealt four blackjacks out of four hands are about 1.8 million to 1. Most of us are unlikely to ever see such an event. A dealer who deals only single-deck games, 40 hours per week, always to three players at a time, at the average rate of 400 hands per hour, would likely see this about once every 112 weeks. Since dealers actually have constantly varying numbers of players when they deal, it’s probable that many full-time dealers would not actually experience such an occurrence as you witnessed in their careers.

In an eight-deck game, the odds against this are only about 237,000 to 1. For any number of decks between one and eight, the odds against this occurring will fall somewhere between these extremes, the fewer the number of decks in play, the greater the odds against it occurring. In any case, it’s not something that happens frequently by any means.

Regardless of the number of decks in play, if you were not counting cards, and you had not been keeping track of the ratio of tens to non-tens which had been dealt at the time these four simultaneous blackjacks had been dealt (and I assume you had not), you made a mistake when you took insurance. I realize you were the only player who made money on the hand, and that you “can’t lose” whenever you insure a natural, but the fact is, purely from the perspective of the statistician, the odds were strongly against the dealer having a ten in the hole. So, remember that the next time this happens to you! Don’t fall for that sucker insurance bet. (For some reason I feel you’re not going to take my advice on this one. . . .)  ♠

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Endorsement Retracted

Letter from Steve Forte Re: Blackjack Ace Prediction

by Steve Forte
(From Blackjack Forum XXIV #2, Spring 2005)
© 2005 Blackjack Forum

Some months back I was asked to endorse a new book on Ace Prediction by David McDowell.

Not being an active player, I first declined and suggested that the book was better reviewed by professional players. I was asked again. Given a minor business relationship with Michael Dalton (he sells my video series), and some limited, albeit enjoyable correspondence with the author, I acquiesced.

I flipped through the book quickly, noting a lengthy history of the strategy and what appeared to be an exhaustive mathematical/computer analysis. My first impressions were good. I then randomly arrived on a photo of a sorted deck with a reference to me and a related strategy. Having never talked with the author about this reference, I read this section quickly, and to be perfectly honest, the reference was taken completely out of context and I was puzzled by the author’s application.

So I then flipped to some of the endorsements and noticed a list of icons in the blackjack world. Since I really didn’t have the time to read the book carefully, I blindly jumped to the conclusion that, after 20 plus years, someone had finally written a dedicated, quality book on ace tracking.

Now, after looking over some of the analysis and comments submitted by Arnold Snyder, and going back to the book to review some of the material, I suspect that I may be guilty of (a) trying to be a nice guy and (b) falling into a common trap often seen in gambling literature: that of endorsing a product not read carefully by the endorser, or endorsing a product more strongly than it truly deserves.

Aside from my personal feelings that the author’s intentions are good, Arnold Snyder’s position is very strong. It’s also very compelling as he backs up his opinion with substance. A careful reread of Ace Prediction does reveal some oddities regarding the fundamentals of applying the strategy, some overly optimistic bet expectations, and win rates where none appear to exist. To over-rate the profit potential of a strategy or system can, of course, be very dangerous and costly to the typical player.

It’s for all of these reasons that it makes perfect sense to challenge the viability of the strategy as presented. It’s good for everyone: authors, experts, mathematicians and, most importantly, the players. After all, with any book written for the player, ultimately, only one criteria really matters: Does the strategy win?

How this notably different view of this work plays out in the blackjack community should prove to be a valuable lesson to us all. It will be especially interesting to see if any other endorsers “step up to the plate” after taking a closer look at the research. ♠

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Telephone Gambling Scams

Reach Out and Fleece Someone

by Arnold Snyder
(From Blackjack Forum XII #4, December 1992)
© 1992 Blackjack Forum

Technology continues to oblige our laziness. The latest gambling craze to sweep the country is betting over the telephone lines. Short on cash? No problem. You don’t even need a credit card. A functioning telephone will do. Just pour yourself a tall, cool one, sit back in your robe and slippers, and dial 1-900-SWINDLE.

Most states have strict laws against telephone “book-making.” The penalties for operating a betting service by phone are stiff, and often include various charges of conspiracy and racketeering. Interstate bookmaking will bring in the Feds. Anyone taking phone wagers on horse races or sporting events had better be ready to fly by night if necessary.

A better idea, however, born of modern technology, would be to take bets via the new, legal, electronic method. This allows you to run your gambling operation with impunity, advertise on TV, and even hire celebrities to promote your business. No one is using this methodology yet to book sports or horse races, but it may be only a matter of time.

I don’t know how long these legitimate(?) telephone gambling lines have been in operation because I don’t watch TV much. Until Alison and I moved into this apartment building, as temporary living quarters while our home is being rebuilt, we never had cable TV. The first ad I saw for one of these operations was on a cable station; it was called “Spelling Bee,” or something like that.

Here’s how it worked, as well as I can remember: You dial the 900 number advertised and you will be given a spelling test over the phone. If you can spell 21 words correctly in 6 minutes, you win $1000. The fine print at the bottom of the screen informs you that you will be charged a few bucks per minute for the call. So, in effect, you are wagering $20 or so (depending on how much talking before and after your spelling test is necessary to transfer name\address\etc.) for the chance to win $1000.

Are you a good speller? How fast can you correctly spell on a touchtone keypad?

Ha!

I’m willing to bet I could get out my Webster’s Unabridged and easily find hundreds of words in the English language that would rarely all be spelled correctly by anyone: kilooersted, ouananiche, stannary, craquelure, thremmatology, uintaite, vitelline, miscible, pentaerythritol, narghile, yttrotantalite, zinziberaceous, zygapophysis, quinquereme, phthalocyanine, fissiparous, lophodont, gneissoid, xenodochium, tshernosem, pneumonoultramicroscopicsilicovolcanoconiosis. That’s 21 words from my Webster’s Encyclopedic Unabridged Dictionary of the English Language. Try them on your touchtone keypad. Six minutes.

To run an operation like this for maximum profit, however, the trick would be to keep players on the line for the full 6 minutes. You want to start with easy words, but long ones, so that callers stay in the game while charges are mounting. I suspect many players never even get to the truly difficult words. No mistakes. They just run out of time.

It’s hard for me to view an operation like this as anything but a scam. Players may think they’re wagering $20 to win $1000, but anyone dumb enough to think he can spell every word in the English language is more akin to a mark in a carny game than a gambler.

One of the most sophisticated telephone gambling operations currently running is Monte Hall’s “Let’s Make A Deal.” Yes, that’s the Monty Hall of TV fame. If you haven’t seen the now white-haired Monte on TV lately, you must not be flipping through all 438 cable stations at 3 a.m. looking for hot TV gambles.

Here’s how it works:

You call up Monte’s 900 number, at a cost of $2.95 per minute, in an effort to win the $2000 grand prize. (The fine print on the TV ad informs you that the “average” call lasts 6 minutes.) Gee, thought I, for only $2.95 a minute I can play Let’s Make A Deal with Monte Hall. A dream come true! I don’t even have to dress like a gorilla in a tutu!

I couldn’t resist. As soon as the ad ended, I reached for the cordless phone.

Alison tried to hold me back. “Arnold,” she said, “Think of your reputation. You’re a respected authority on gambling. If word gets around that you’re playing Let’s Make A Deal by telephone, you’ll be ruined. This has got to be worse than keno, and it’s probably worse than the California Lottery.”

“It’s all research and development,” I defended myself, dialing 1-900-420-4544. (Yes, that’s the real number. Try it!)

I was greeted by Monte Hall’s recorded voice. There was a band playing. He was excited. It was just like TV! My first $2.95 was wasted answering personal questions – phone number, age, sex, and listening to various announcements, such as the Beverly Hills address where I could obtain a written copy of the rules of the game.

Then Monte Hall’s recorded voice came on to get down to business. First, I had to correctly answer a question: “Which president was the Lincoln Memorial named after?” Monte quizzed me. I’m not going to tell you the correct answer, only that I answered correctly. (Okay, here’s a hint: It’s not Jimmy Carter. And, yes, he was one of the choices.)

Monte then informed me that because I had answered the question correctly, I could now choose between Door Number One, Door Number Two, and Door Number Three. Wow! Just like on TV! Using the touch tone pad as directed (all questions are entered via touch tone), I chose a door… Big fanfare!

I won!

“Yes,” said Monte, “You’ve won a $15 bag of nickels, which we’ll send to you in the form of a check! Or, you can trade in that bag of nickels for a chance to win $25 by choosing what’s behind Door Number One, Door Number Two, or Door Number Three!” (Not verbatim, but you get the idea….)

I looked at my watch. I’d been on the line less than four minutes which meant that I was about three bucks to the good after subtracting my phone charges. I was tempted to quit while ahead. (I’m no gambler!) But I didn’t yet know how to collect my prize. I figured by the time I got this information, I’d just be breaking even. I chose another door…

Another big fanfare!

I’d won again!

“Yes,” said Monte, “You now have $25! Do you want to keep that $25 or go to Level Three, where behind Door Number One, Door Number Two, or Door Number Three there is $35?” He also reminded me again that if I made it all the way to Level Six, the Grand Prize would be $2000.

I looked at my watch.

Under five minutes.

I’m outta here.

As expected, another minute was wasted supplying me with my “Prize Code #” and the address where I was instructed to send a 3<$E1/2> x 5 inch postcard with my name, address, phone number, age and social security number, in order to claim my prize, which, I was informed, would take 8 to 10 weeks for delivery. Now, I must assume this operation is 100% legit, and that I will receive a check for $25 from Monte Hall in 8 to 10 weeks. This modest win, of course, will be offset by about $18 added to my phone bill.

But, let’s analyze this game mathematically, assuming it’s 100% legit. There are six levels of play, i.e., you must choose the correct door (one of three) six times in a row to win the $2000 grand prize. On the average, you will therefore win the grand prize once out of every 729 times you play (that’s 36), assuming you don’t quit early like I did.

Since the “average” call lasts 6 minutes, the cost of the average call is 6 x $2.95 = $17.70. 729 calls times $17.70 each = $12,903.30. So, in the long run you will win $2,000 for every $13,000(more or less) you spend in phone charges.

Alison was right. This is far worse than keno, and far worse than the California Lottery. Monte Hall’s “house” has about an 85% advantage (a sizeable portion of which is shared with the phone company).

It’s illegal to call a bookie and tell him you want to place a $10 bet on the 49’ers, yet it’s 100% legal for you to call up Monte Hall (or the “Spelling Bee,” or numerous other 900 number “games”) and bet your money (disguised as telephone charges) on far riskier propositions. Nor would your bookie take 8 – 10 weeks to pay you!

I asked Nelson Rose (author of Gambling and the Law) how this type of gambling operation could be legal in California. He explained to me that the operator must either offer an alternative method of playing which does not require any 900-line charges, or the game must have a “skill factor” – such as requiring the player to answer a question. Hmmm… I wonder how many contestants were stumped by that Lincoln Memorial brainteaser?

Now, I’m not opposed to legalizing phone betting, but somehow the current regulations strike me as less than fair to the player. The funny thing is that it would probably be possible to set up a sports betting or other traditional type of book-making operation if it were operated as a 900-line game with “prizes.”

In other words, if you cut the phone company in on your vigorish, then pass this charge on to your customers as part of the cost per minute for the call, and don’t forget to come up with a “skill” question to legitimize the payoff, then you’re a legal bookie! No illegal “bets” are made so long as it’s all just telephone charges!

Your customers, naturally, won’t like the lousy odds you’ll be forced to give, and many will abandon you for illegitimate bookies who offer fairer odds. But paying off the phone company is simply the price of legitimacy in today’s high-tech gambling world.

What I haven’t been able to figure out, unfortunately, is a way to offer electronic blackjack games over the phone. As soon as I iron out the bugs in this brainstorm, however, I intend to give Monte Hall a run for the money. ♠

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Blackjack Team Proposal

Business Plan for a Blackjack Team

by Bob Fisher
(From Blackjack Forum Vol. XVI #2, Summer 1996)
© 1996 Blackjack Forum

Some of my ideas regarding blackjack team play:

A major concern of most blackjack teams is being able to trust their teammates. Using people you already know well is fine; but, the problem is it takes a long time to get to know people which reduces the number of possible teammates. Then there’s the possibility of the casinos recognizing the teammates through guilt by association, plus problems such as being available, etc.

My idea for team play requires three kinds of people:

  • Type A: There are many people who have high-paying jobs or businesses that they can’t quit just to play blackjack. These people’s work, vacations, etc., take them to casino areas. They would like to supplement their income playing blackjack while they are in a casino area. They have the bankroll. Though they can be card counters, it isn’t necessary. Minimum requirements would be bankroll and blackjack basic strategy. They will only play for short periods (during their work-related trips/vacations).
  • Type B: These people will be card counters who live in a casino area. They are not bums and do have small bankrolls, but cannot play high stakes with low ruin for a decent win rate. Poker players who know how to count, or could learn, are good candidates. Minimum requirements would be blackjack basic strategy and card counting knowledge and a small bankroll.
  • Type C: These people would be middlemen to bring the other members of the blackjack team together. They would test and evaluate the prospective players. Applicants would contact the C players.

When an A player wants to go to a casino area, he calls the appropriate C player to let him know when he is coming. The C players contact the B players, trying to find 2 to 5 players that can join the A.

Prior to playing, the C player has the A and B players meet where and work out the details. Basically, the B players will play at several nearby tables, counting and making minimum bets. When they get a good count, they signal the A player who then joins that table unless playing successfully at one of the other tables.

Because the A player finds many more advantageous situations than he could if he played alone, he will except to win considerably more. Some of this extra win is shared with the B players, allowing the Bs to make more than they otherwise could with minimal risk and exposure. The B players shouldn’t expect to lose, but try to break even by leaving on very bad counts and raising their bets slightly on good counts. They should not use bet raises as signals to the A players to join the play. The B players keep their winnings and pay for their losses.

Since there is no commingling of money, honesty, though desirable, is not essential. Also, if the casino puts the A and B players together, the A player can have an entirely new set of B players on his next trip. The players can be constantly switched around, making putting them together difficult.

The B players also would not get burned out since they make minimum bets and use small spreads as they are only trying to break even or win small amounts. The casino may be further reluctant to harass B players if they give them other business such as poker or video poker. The A player would not be too concerned because he will not be a full time player and will travel a lot anyway, playing a few days here and there.

I don’t know of anyone who has suggested this idea of putting strangers together on a blackjack team before without the need to commingle money, and it’s associated problems. ♠

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The Low-stakes Professional Card Counter

Fast Action Jackson’s Distractions

by Arnold Snyder

(From Blackjack Forum Volume X #4, December 1990)
© Blackjack Forum 1990

A fixture at the blackjack tables of Las Vegas for almost a decade, Fast Action Jackson has never had much of a bankroll. Standing 5-foot-3 in his Western boots, what’s left of his hair slicked back over his tanned pate, like so many card counters I’ve met, overeducated and undercapitalized, he holds a masters degree in philosophy from some obscure east coast college. I don’t know if he’s ever been married. Every time I visit Vegas, he’s living with a different woman, always at her place. He’s not an easy guy to track down.

“I’m living proof, Bish,” he says, “that you can play your system perfectly, study your ass off, know more about fluctuations and standard deviation than most statisticians, have the persistence of Sisyphus, and still never make it into the big leagues. If you can’t take the flux, you can’t make the bucks. It’s that simple.”

I had asked him to write an article for Blackjack Forum on how a player with a small to moderate bankroll goes about surviving as a professional blackjack player.

“You don’t want that article,” he insisted. “It’s too depressing. I once went ten weeks sleeping in my car so I wouldn’t have to use my precious bankroll on such a luxury as rent money. I’ve lost two girlfriends who believed in me enough to invest in me at the wrong time. I don’t know what it is about women, Bish, but they get very irritable if you lose their paycheck a few times. Even when you finally pay ‘em back, it’s all over.”You alienate your friends. You take chances with advances on your credit cards. It’s a rotten life. Right now, I don’t owe anybody anything. The past two months have been great. I’ve dug out of yet another hole, saved my credit rating again. My bankroll is back up to six thou. Unfortunately, in this game, six thou is nothing. I could be flat broke two weeks from now.”

“The fact remains, Fast,” said I, “that you’ve been doing this for ten years. It may be a tough grind, but you’re making it. You make your living playing blackjack, and you’re not rich. My readers want to know how you do it.”Most of them aren’t wealthy, but they say they’re willing to work. What most often happens is they learn a system at home, build up their fantasies, then find out they can’t hack it in the casinos. The table conditions are lousy. They get heat when they start to win. And the casino environment is nerve-wracking—the noise, the smoke, the constant interruptions. I always tell them to play during off hours—weekdays, early mornings—in order to minimize the distractions. Am I right?”

“Wrong,” says Fast. “Casinos are designed for distraction. That’s their game. As soon as you take away the noise and the crowds and the booze, you’re not playing their game anymore, you’re letting them watch your game. You’ve got to keep in mind that what distracts you distracts them. As long as I’ve been playing in this town, my action is still welcome everywhere. That’s because I follow the crowds. That’s the only way to survive, to have staying power. But, Bish, it’s a rotten life. Believe me.”

I asked him if he had any favorite casinos. “My favorite casinos are always the busiest casinos,” he said. “Right now, in Vegas, the new stores are great. The Mirage. The Excalibur. The Rio. These places are attracting crowds. I used to like Caesars because that’s where the big money played. Money is a great distraction. Who’s going to look at my $50 bets when the george sitting next to me is betting table limit? It’s all over for Caesars now, what with the Mirage next door. Even the over/under won’t save them. Caesars is empty. You can’t play there anymore. They’re dying a slow death.

“The Rio may be off the strip, out there next to the Gold Coast, and they canned the liberal rules they opened up with. But they’ve still got good games and great crowds on the weekends. Plus they’ve got that hot double exposure.”

“Double exposure?” I asked. “At the Rio?”

“Not on the tables,” he explained. “I’m talking about the cocktail waitresses. You see, Bish, I’m a connoisseur of distractions. Just check ‘em out sometime. You’ll see what I mean. I order a lot of drinks when I play, and I spend a lot of time looking for the waitresses. It’s all part of the strategy. Drinking a lot of booze is very distracting. Counters don’t drink.”

“But doesn’t that affect your accuracy?” I asked.

“Not if you do it right,” he said. “There’s a trick to it. Always order a drink that comes with cream. Kahlua and cream. A toasted almond. You just never swizzle it. You can be damn sure the bartender doesn’t have time to stir it. The booze sits in the bottom of the glass. You drink the milk off the top. By the time you finish the milk, the waitress is bringing you a fresh drink. I’ll tell you my health has improved significantly since I started ordering so many drinks. Lots of calcium.”

“So, Fast,” says I, “Your advice to my readers who really want to enjoy that wonderfully romantic life of the professional card counter, where you lose your girlfriend only after you lose her paycheck, ever rejoicing that if you jeopardize your Diner’s Club membership, the collection agency probably won’t be able to find you since you’re sleeping in your car, all you have to do is play in the noisiest, most crowded casinos, order lots of drinks, and ogle the waitresses while playing?”

“That’s my secret,” he says. “And except for the double exposure, there’s not much fun in it.”

“Hmm…,” says I. “Have you ever stopped to consider that maybe the reason you haven’t made the big leagues is because the distractions are killing your game?”

He shrugged. “I know what I know,” he said. “And any big time pro would tell you the same thing I’m telling you. Maybe you should stop to consider that I’ve been making my living at this game for ten years, while you’ve been writing about it.”

Point well taken.

Advantage Jackson. ♠
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Fake ID for Card Counters

Fake ID: A Credit Card Under An Assumed Name

by Arnold Snyder
(From Blackjack Forum VIII #4, December 1988)
© Blackjack Forum 1988

[Note: This 1988 article is obsolete as far as the legality issues. Federal and state laws regarding identification became much stricter following 9/11 (2001). I’m including this article for historical purposes only. Loompanics Publishing, the fake ID specialists, have been out of business for decades. – A.S.]

In the last issue of Blackjack Forum, a correspondent (“Letters”) remarked that as a method of maintaining anonymity in the casinos, one might “… get a credit card under an assumed name. Some cards, such as Visa, permit this as a ‘second card’ provided the primary card holder assumes responsibility for the second user.” Blackjack Forum readers want to know:

How is this done?

Is this form of fake ID safe?

Is this form of false identification legal?

If you already have a credit card, it’s done very easily. You receive a solicitation by phone or in the mail from some out-of-state bank, offering you their Visa or Mastercard with a pre-approved line of credit. If you have a decent credit rating, you probably receive these solicitations frequently. If this is a mail solicitation, you can call the bank and say, “Gee, I’d like to thank you for preapproving me for your credit card, but I don’t realIy need another credit card right now. I was wondering if you’d send me a credit card in my nephew’s (or niece’s) name, who lives with me?”

They will answer, “Of course, if you will assume responsibility.”

You say, “I would like the card in his (or her) name, but I would like all billing and statements sent to me. I will be 100% responsible for paying the bills. But I don’t want my name on the card. I don’t want to have to co-sign for purchases. He (or she) is a student, with no credit history, and I would just like to set this up for emergencies.”

They will say, “No problem. What is your nephew’s (or niece’s) name?”

You will soon possess this credit card.

Now, as for the next two questions: is this safe, and, is this legal?

Well, the fact exists that you don’t have a nephew, or, if you do, you’re not him. The name you’ve given to the bank is phony. This may constitute fraud. You will find, however, that when you make reservations at a casino, using the card with the phony name, you will have no problem. If they run a check on the card, it’s valid. You will be known by your new name, no questions asked. In fact, you could have half a dozen valid credit cards in half a dozen different names — all, of course, from different banks — allowing you to be someone different at all of the casinos where you stay.

So long as you pay your bills, you will probably never have a problem with the bank. Even if it were somehow discovered that you had a credit card in an assumed name, it’s unlikely you’d ever be prosecuted for fraud, since no one would be able to prove any damages (again, assuming you pay your bills).

Various states have their own laws regarding fake l.D., its use, possession, etc. Most of these laws are designed to recover damages from defrauded parties. My advice, if you’re seriously considering this route, is to talk with your lawyer about possible repercussions in your state and/or other states where you may use such methods of protecting your identity for non-fraudulent purposes. There are also a couple of books in print that deal with this subject in depth — The Paper Trip I and The Paper Trip II.

The Paper Trip I was first published in 1971, then revised in 1984, and updated again in 1987. This book never mentions gambling or blackjack, but it answers many questions of importance to card counters with regards to using fictitious names, false l.D., etc. Much of this book is a “how-to” guide — i.e., how to obtain a birth certificate in a name other than your own; how to obtain a driver’s license, state l.D. card, passport, various and sundry membership cards, credit cards, university degrees, etc.

This book also discusses the issue of legality. It is not only possible, but relatively easy, for anyone to obtain multiple sets of authentic l.D., including driver’s licenses and credit cards, in various names. The Paper Trip has long been the classic “underground” reference work on this subject.

The Paper Trip II was first published in 1977, then updated in 1987. This is a companion guide to the above book for the serious paper tripper. Although the original book contains all you need to know to obtain new l.D., this book makes it a lot easier by providing state by state breakdowns of exactly where to write for vital records, the fees, etc.

There is also more information on obtaining social security cards, “counterfeit” I.D., and state by state laws regarding legal name changes. This book also contains various sample forms, a complete printout of the federal laws regarding the possession and use of identification and false identification, discussion of various state l.D. laws (including Nevada), etc. This book is recommended for authentic imposters only. Both books are published by Loompanics. ♠

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Losing Money on “Good” Rules?

Blackjack Rules: Every Rule Option is Good

by Arnold Snyder

(First published in Avery Cardoza’s Player Magazine)
© 2005 Arnold Snyder

A player recently emailed me asking if it was better if a casino allowed players to surrender, or if it was better if this was not allowed. He wrote: “Every blackjack player I know thinks this a great rule. But it seems to me that I give up a lot of hands I would have won. Now, I hardly ever surrender unless the cards are running really bad for me in a shoe. Why would casinos allow players to surrender if the house didn’t make money on it?”

Here’s something to remember: Every time a casino gives you an option, no matter what that option is, it can’t hurt your chances of winning unless you misplay the option. Let me give you a radical example. Every blackjack player has the option to hit a total of 20. Not that any of us would hit a 20, but we all have the option. Because we don’t hit our 20s, the option has no effect on us. We know how to play this option. We stand. If a casino suddenly posted signs that said, “Hitting 20s is not allowed,” no player would care.

So, hitting a 20 is an option that would hurt us if we exercised the option, since we’d bust 92% of the time, but in reality it doesn’t hurt anyone because no one exercises the right. If a casino posted a sign that said, “All players are now allowed to double down on 3-card hard 16s,” it wouldn’t matter. All intelligent players would recognize the option as an option that would be foolish to exercise. So an option can’t possibly hurt us unless we exercise it incorrectly. By definition, an option means we have the right to not exercise it.

Surrender, A Blackjack Rule with Great Value

Surrender is an option that, in fact, has real value when exercised correctly, and you don’t have to be a card counter to take advantage of it. Unfortunately for most players, it probably does hurt them more than it helps. In fact, I suspect from the email I got from the reader above that he was correct in his conclusion that he would have done better if he just didn’t surrender at all. His statement that he now only surrenders when the “cards are running really bad” is worrisome.

Surrender decisions have nothing to do with how the cards are running. The decision to play a hand or give it up, along with half the bet on it, should be based purely on math. And the major problem that many players have with this option is that they surrender way too frequently.

Some players will give up on almost any stiff total against any dealer high card. That has a huge cost to the player. Purely based on the math, do you know how often you should surrender any total of 12, 13, or 14?

Never.

It doesn’t matter if the dealer has a ten, an Ace, or any other upcard. And it doesn’t matter how the cards have been running. Purely based on the math, you will lose more money surrendering any of these hands than you’ll save by giving up half your bets.

The only hands you should ever surrender are hard 15 against a ten, or hard 16 against a ten or Ace. That’s it, as far as the math goes.

One player tried to argue with me once that if he had a hard 15, basic strategy was to hit it against any dealer 7 or higher. Since seven of the thirteen possible hit cards he could get (any 7, 8, 9, 10, J, Q, or K) would bust him, he’d be better off surrendering 15 against any dealer 7 upcard or higher. His argument: “If I’m going to bust more than half the time, then I save money by just giving the dealer half of my bet.”

That sounds logical, but it’s a twist of logic. Let me explain…

If I were to flip a coin with the understanding that if it comes up heads, I win, and if it comes up tails, I lose, this is a dead even bet. Since I know that the odds are that I’m going to lose this bet half the time, would I have the same result if I just surrendered half of my money on every bet?

No way. Without surrendering, I’ll break even on a coin-flip in the long run. If I surrender half my money on every bet, I’m losing at a 50% rate for all the money I bet! Surrender doesn’t become a break-even bet until I know I’m going to lose twice as often as I’m going to win. It takes two half-losses to make up for one win. A total of 15 against a dealer 7, 8, or 9 may be a pretty bad hand, but believe it or not, it doesn’t lose twice as often as it wins.

Good Blackjack Rules Sometimes Entice Players to Make Bad Blackjack Plays

Some years ago, a mathematician did a study of the general public’s play at casino blackjack. He literally watched players in Las Vegas and Reno and kept a record of how they played their hands.

One of his more interesting findings was that players in Reno made fewer errors than players in Las Vegas. Why was this? Because players in Las Vegas had more options.

In Reno, blackjack players were only allowed to double down on 10 or 11, while in Las Vegas they were allowed to double down on any two cards, including doubling after splits. If you are only allowed to double down on 10 or 11, you will very rarely make a double-down error, since it’s almost always correct to double down on 10 or 11. But there are lots of errors you can make if you are allowed to double down on any two cards.

In fact, the options to double down on any two cards, and to double down after splits—just like the option to surrender—are player-favorable options. If you know when to exercise the options, and when not to, these options will make money for you in the long run. But if you do not exercise the options correctly, then you’re making the options work for the house.

Surrender is one of those options that almost always makes money for the house because most players give up too many “bad” hands too often. The fact is, if it ain’t a 15 or 16, and if the dealer doesn’t have a ten or Ace showing, it just ain’t that bad. You’ve just got to be brave and hit that sucker! ♠

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Errata in McDowell’s Errata Sheet

Problems with Fundamental Math in Blackjack Ace Prediction

by Arnold Snyder

(From Blackjack Forum XXIV #2, Spring 2005)
© 2005 Blackjack Forum

I purchased my copy of David McDowell’s Blackjack Ace Prediction at the Gambler’s Book Shop in Las Vegas last month (January 2005). No errata sheet was provided and there is no instruction anywhere in the book to go to Dalton’s Web site for the errata sheet.

I have recently been alerted to the errata sheet for McDowell’s Blackjack Ace Prediction on Dalton’s Web site. Unfortunately, as ETFan has pointed out on other Web sites, the error in the page 114 formula that I addressed in my initial article is still there in the errata sheet. In fact, the situation with the errata sheet “correction” is even worse.

This math is not rocket science. It is simple, straightforward, and logical. It is based on the fundamental principles of blackjack math. David McDowell does not understand the mathematical logic of blackjack. So, I will try to explain this math. Dalton seems to think that McDowell has already addressed my concern. He has not. Please just try to follow…

According to the Errata sheet, McDowell says he made an error in his formula on page 114 (which is the formula I found fault with in my initial review of this book). The errata sheet “corrects” the formula by stating that instead of the dealer and player getting 6 additional aces each, they will be sharing a total of 6 extra aces, with only three extra aces each per 100 aces bet. The errata sheet “corrects” the player’s win rate with this assumption from 4.2% (as per the book) to 1.3% (per the errata sheet formula).

Again, McDowell is making a HUGE error. The same error with slightly different numbers.

Please follow the logic.

The errata sheet now assumes that the player and dealer will each get only 3 extra aces per 100 aces bet. Dalton’s errata sheet assumes, as per BJAP, that the ace is worth 51% when it lands on the player’s hand, and -34% when it lands on the dealer’s hand. The errata sheet now uses McDowell’s assumption that there are 7 “random” aces going to both the player and dealer per 100 aces bet, and 3 “predicted” aces going to each, for a total of 10 aces each per 100 aces bet. The errata sheet presents the math for this as follows:

E(X) = (+0.51 x 0.10) + (-0.34 x 0.10) + (-0.005 x 0.80)

= +0.051 – 0.034 – 0.004

= +.0130

Or, a 1.3% advantage when betting on an ace.

I do not know how to explain the math on this any more clearly than I did in my initial BJF article, but I will try. The MAJOR error McDowell is making is that he is assuming that the 80 hands where neither the player nor dealer get a first-card Ace are played with a house edge of only 0.50%.

This is a very important concept. Please pay attention to this: If neither the player nor the dealer are dealt a first-card Ace on any of these 80 hands, then the house edge is no longer 0.50% on these hands for the basic strategy player. That -0.50% basic strategy expectation assumes that the player and dealer will each get the random number of aces as a first card that would be expected to be dealt from a full six-deck shoe. As soon as you remove all of the random first-card aces from this set of 80 hands per 100 (which McDowell has done), then we must reconsider what the cost of these 80 hands with no first-card aces is.

Let me give an example that should clarify this error. The average number of “random” aces dealt as a first card to both the player and dealer is 1/13, or 7.7 first-card aces each per 100 hands. Exactly 1 out of every 13 cards in a six-deck shoe is an ace, so if we’re simply playing random hands, with no predictions, we would expect 7.7 aces per 100 hands since 7.7 is 1/13 of 100. The dealer would also get 7.7 aces per 100 hands.

Is this clear?

Here is how you find the error in McDowell’s formula:

McDowell estimates that the average number of aces per 100 hands is only 7, not 7.7. This is a minor error, but the math on it is so simple, I do not know why he did not just say 7.7 instead of 7. We are attempting to estimate an advantage here, so why not use the most precise number?

McDowell then says (as per the Errata sheet now) that the player and the dealer will each receive an extra 3 aces, for a total of 10 aces each. In his formula, he provides this number as a percentage (0.10) of the 100 aces bet on. He then figures out the expectation if the player and dealer each get 10 aces (0.10) per 100, and no aces are dealt on the other 80 (0.80) of the 100 aces bet on.

His mistake is in assuming that these 80 hands are played against the standard house edge of -0.50%. Note in the formula the last item: (-0.005 x 0.80), which is the notation for his mistaken calculation that 80% of the hands will be played at -0.005 (or -0.50%).

Here’s how you know the formula is WRONG.

What if we use this formula to calculate the player’s advantage when the player and dealer are each dealt exactly 7.7 aces per 100 aces bet (the exact number of aces that would occur at random with no prediction)? Here is what the formula gives us:

E(X) = (+0.51 x 0.077) + (-0.34 x 0.077) + (-0.005 x 0.846)

= +0.03927 – 0.02618 – 0.00423

= +.00886

If this were correct, it would mean that a basic strategy player, getting just the random number of aces (7.7 per 100), and with a dealer also getting 7.7 random aces, would be winning at almost a +0.9% win rate. But we’re assuming that in this game the house has a 0.50% advantage over the player. So, why isn’t our result on this completely random basic strategy game -0.50%?

The reason is because of McDowell’s incorrect assumption about the 84.6% of the hands (100% -7.7% -7.7%) that are played when neither the player nor the dealer is dealt a first-card Ace. He is making the mistake of assuming that on these other 84.6 hands per 100, the player’s expectation is the same as in a 6-deck game where those random first-card aces are included.

The house edge on hands which do not contain an ace is not the same as the edge on hands where a random ace occurs. It’s only when you combine the house edge on the ace hands with the house edge on the non-ace hands that you get an overall player expectation of -0.50%.

If we separate out our basic strategy edge on the 7.7 hands per 100 when the player is dealt a random ace (51% player expectation) and the 7.7 hands per 100 when the dealer is dealt a random ace (-34% player expectation), and we want to know the overall expectation for the basic strategy player on all 100 hands played, then we have to figure out what the player expectation is when neither the player nor the dealer is dealt an ace. This is a fairly simple calculation if we use Griffin’s numbers from Theory of Blackjack. If neither the player nor dealer is dealt an ace as a first card, the house edge is approximately 2.13%. Let’s try this number in McDowell’s expectation formula:

E(X) = (+0.51 x 0.077) + (-0.34 x 0.077) + (-0.0213 x 0.846)

= +0.03927 – 0.02618 – 0.01802

= -0.00493

Which shows the basic strategy player’s expectation to be about -0.49%, just about exactly what we expect.

You do not need a computer simulation to know this. This is long-established, fundamental blackjack math.

So, if the dealer and player are each getting 10 aces per 100 aces bet, as per McDowell’s errata sheet, then the correct math is:

E(X) = (+0.51 x 0.010) + (-0.34 x 0.010) + (-0.0213 x 0.80)

= +0.051 – 0.034 – 0.01704

= -0.00004

which is a -0.004% expectation for the player.

In other words, if the dealer and player each get 10 aces per 100 bet, instead of 7.7 aces per 100 bet, then the house no longer has a 0.50% advantage over the player, but only a 0.004% advantage.

Unfortunately, 10 aces per 100 is not quite enough aces to get the player an advantage over the house, if the dealer is also getting 10 aces per 100. The house still has a slight edge. Does this sound impossible to you? Consider what 10 aces per 100 means to the player who would normally get only 7.7 per 100.

This is an extra 2.3 aces (not 3, as McDowell claims) per 100 aces bet on. That means that for every 43 times that you bet on an ace, you will get one more ace than normal expectation. So, if you are betting on 4 aces per shoe (as per McDowell), you will get one extra ace every 11 shoes.

Unfortunately, the player advantage from getting this extra ace will be cut by the dealer also getting one extra ace every 11 shoes.

I do not know how to make the math any more clear than that.

If McDowell’s “correction” is right, and the dealer and player expect to get 10 aces each per 100 bet by the player, then there is no advantage whatsoever to the player using McDowell’s system.

McDowell then goes on in Dalton’s errata sheet to show what happens “if the dealer can be prevented from getting the ace.” This section is entirely without explanation. This is not acceptable. It is extremely important to know how the dealer is prevented from getting the ace, and an expectation cannot be calculated without specifying this information. Since the first formula shows the dealer and player splitting the 6 extra aces, then in order to prevent the dealer from getting his share of extra aces, either the player must spread to more hands in order to get the aces that would have gone to the dealer, or the aces must go to a hand played by someone else, possibly a civilian. In the first example, where the player spreads to two hands to get the ace on a big bet, we could give the player 13 aces, but we would have to show that the player is now placing 200 bets (not 100) in order to capture the dealer’s aces. In the second example, where a civilian hand is catching the dealer’s share of extra aces, then the formula should show the player is getting his 10 aces, and the dealer is getting only his 7.7 random aces.

(I want to make it clear that I am NOT saying that by spreading to two hands you can prevent the dealer getting extra aces. I am using two hands in this example only to illustrate the principle, not to provide a practical guideline.)

Unfortunately, neither of these methods are shown in the errata sheet formula. The player is shown getting all 6 extra aces, but only playing a single hand (100 hands total). The dealer is shown getting only 7 (not 7.7) aces. And the other 80 hands where no first-card aces are dealt are still being shown with a house edge of only 0.50%, not 2.13%.

I don’t even know how to correct this formula unless McDowell can describe the mechanism by which “the dealer can be prevented from getting the ace.“

If you want to put the numbers into the formula yourself, go ahead. I’ll spare you the math. If the player is spreading to two hands, placing 200 bets total to get all the extra aces, he actually does have a win rate: +0.12%.

On the other hand, if there is a convenient civilian at the table, ready to catch the dealer’s aces at no charge to the player, so the player is placing only 100 bets but still getting just a total of 10 aces to the dealer’s 7.7, the player also has a positive advantage: +0.07%.

So, in this example, spreading to two hands is the better strategy, assuming that you prefer to make +0.12% instead of +0.07%. But neither strategy is of any interest whatsoever to the player who is trying to make money by ace tracking.

Here is the problem: David McDowell didn’t go through the hard work necessary to test the theories he presented in Blackjack Ace Prediction. As a result, he never learned how to track or sequence aces. He never came to understand the techniques, the problems, or fundamental blackjack math, a problem we find with many non-players who profess to be “blackjack experts.” ♠

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An Interesting Hand in 8/5 ACE$ Bonus Poker

The cards in ACE$ Bonus Poker (ABP) are just like the ones in regular Bonus Poker (BP) except there are superimposed yellow letters on four cards: “A” on the ace of clubs, “C” on the ace of diamonds, “E” on the ace of hearts, and “$” on the ace of spades. The order of the suits is alphabetical and contract bridge players will also be familiar with this order.

If you get four aces in ACE$ order, either in positions 1-4 or 2-5, you get paid 4,000 coins instead of 400. I’ve written about this game numerous times and have usually said the only changes you make to regular 8/5 BP strategy to play 8/5 ABP perfectly are to break aces full when the aces are in proper sequence for the bonus.

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Wynn: Make mine Manhattan; Votes for sale; Mega-Jottings

There will be at least one serious push for a casino in the heart of New York City, now that Wynn Resorts has thrown in with Related Cos. on “an exposed and sunken rail yard” that some see as a gaming gold mine. The project would be near and dear to Gov. Kathy Hochul‘s heart, so Hochul + Wynn = momentum. “Wynn New York,” or whatever it would be called, would anchor a $25 billion, 28-acre mixed-use development, giving the project much needed sex appeal. On the plus side is proximity to the Jacob Javits Convention Center. Less thrilling is the fact that the casino would have to be built on a mega-platform over some train tracks. (Nothing says “the glamour of gaming” like the subterranean rumble of trains.)

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