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The most important book available to blackjack aficionados since Beat the Dealer by Ed Thorp, Blackjack Attack has been praised by every prominent blackjack expert.In it, Schlesinger answers virtually all of the thorny mathematical questions that have puzzled serious players for years: optimal betting, camouflage, risk analysis, team play, systems comparison, and much more.

With twice as much material as its predecessor, this third edition contains new studies bound to intrigue even the most knowledgeable pro, including a complete reexamination of the late Peter Griffin's work, and the publication of the most accurate basic strategy and effects of removal charts ever devised.

The file will be sent to your Kindle account.

It may takes up to 1-5 minutes before you received it.

Please note you need to add our NEW email km bookmail.

You can write a book review and share your experiences.

Other readers will always be interested in your opinion of the books you've read.

Whether you've loved the book or not, if you give your honest and detailed thoughts then people will find new books that are right for them.

No part of this publication may be translated, reproduced, or transmitted in any form or by any means, electronic or money android blackjack real, including photocopying and recording, or by any information storage and retrieval system, without the express written permission of the publisher, except in the case of brief excerpts for purposes of review.

Portions of this book have previously appeared in different fonn in Blackjack Forum magazine, 1984-96.

Published by: RGE Publishing 414 Santa Clara Avenue Oakland CA 94610 510 465-6452 FAX: 510 652-4330 Web site: www.

JO: The second equation, on the bottonl, to the right, is nlissing a.

DEDICATION This book is dedicated to all of my family 'members, past and present, whose love and support have encouraged me to pursue my studies ofthe game of casino twenty-one.

Their patience and understanding, throughout my career of playing, teaching, and writing about blackjack, have certainly contributed, in large measure, to any success I may have achieved in these fields.

The book is also dedicated to the memory of three dear blackjack-playing friends: Lester White, Joel Waller, and Paul Keen, whom I miss very much.

And so, I would like to thank: The one and only Stanford Wong.

He, perhaps more than any other individual, has furthered our knowledge ofthe game of blackjack and its subtleties.

I'm proud to call him my friend.

His help, throughout the years, has been invaluable to me.

In particular, Professional Blackjack and the Blackjack Count Analyzer will forever stand, in my opinion, as two ofthe most important resource tools to have ever been created for our study of the game.

I thank him, as well, for his Foreword to this book.

Arnold Snyder, who gave me a "forum" to publish my blackjack articles, and who finally convinced me, after many years of trying, to write this book.

Arnold, perhaps more than for any other individual, this one's for you!

Peter Griffin, our foremost theoretician and expert on the mathematics ofthe game.

On more than one occasion, when I was "stuck" in my pursuit ofan answer to a thorny problem, Peter came to my rescue.

I will always treasure our pages of written correspondence and our phone calls, during which I never failed to learn from the "master.

Thorp, Julian Braun, Lawrence Revere, Allan Wilson, John Gwynn, Lance Humble, and Ken Uston.

It is safe to say that I would have never become involved in the game of blackjack were it not for these gentlemen's monumental contributions to our knowledge.

In particular, it was from Revere's classic, Playing Blackjack as a Business, that I patterned my approach to the game.

Three fellow blackjack authors and experts, notably George C.

George's contributions to the game have broken ground in many areas, and his insights and innovations have opened my eyes to several new and novel approaches to playing blackjack.

Bryce Carlson, one of today's brightest authorities, whose recent work, Blackjack for Blood, and whose v software, the Omega II Blackjack Casino, have proven to be valuable reference resources; and Michael Dalton, for his quarterly, Blackjack Review, and his monumental work, Blackjack: A Professional Reference, which is truly "The Encyclopedia of Casino Twenty-One.

John's creation has unlocked the doors of blackjack research to the point where virtually all questions can now be answered, thanks to his incredible UBE; Norm Wattenberger, whose equally brilliant Casino Verite has set the standard for the ultimate in blackjack game simulation and practice software.

How I wish CVhad been around when I was practicing and learning how to count cards!

And last, but certainly not least, Karel Janecek, a relative newcomer on the blackjack scene.

Karel's Statistical Blackjack Analyzer was used to produce the simulations for Chapter 10, and it is safe to say that the SBA has fast become the most respected and reliable simulator in the industry today.

Howard Schwartz and Edna Luckman, of the fabulous Gambler's Book Club, in Las Vegas.

No trip to Vegas would ever be complete without a stop in their unique store.

The vast majority of my blackjack library was purchased at the GBC.

Their annual catalogue is a gold mine ofcasino gaming literature and software.

When the "sledding" got a bit rough, and I needed some help developing a formula or mathematical concept, they were there to furnish the crucial pieces ofthe puzzle.

My many newfound friends on the Internet, whose contributions to the various newsgroups and whose correspondence, through e-mail, have been most enlightening.

In particular, I am grateful for the wisdom of Ralph Stricker, a gentleman, a worldclass player, and truly our "elder statesman" of the game today; Steve Jacobs, whom I have anointed the "Godfather" of"rec.

All my wonderful friends and blackjack-playing buddies, too numerous to mention.

A few, of course, deserve special recognition: Kenny Feldman, a great friend, a great player, and my partner in our blackjack-teaching days.

Kenny's advice has vi proven invaluable over our thirty years of friendship, and his companionship, on many a blackjack trip, has enhanced my enjoyment ofthe game; Les Appel, another great friend and player who also taught with Kenny and me.

His easy-going approach to the.

My former teammates, see more of whom have remained wonderful friends, over the years.

For obvious reasons, no names will be mentioned; but you know who you are.

We had some great times, guys; thanks for the memories!

Last, but certainly not least, the six proofreaders ofmy manuscript who turned the tables on me and provided dozens of insightful comments, corrections, and suggestions.

This is surely a better book because ofthe remarkable attention to detail of: John Auston, Stanley Dinnelaw, Ken Feldman, Olaf Vancura, Ron James W.

Back-Counting the Shoe Game.

Betting Techniques and Win Rates 17 3.

Evaluating the New Rules and Bonuses.

The World's Greatest Blackjack Simulation.

Some Final "Words of Wisdom" from Cyberspace 252 Epilogue.

Probably because of his background as a teacher of mathematics and foreign language, he has a knack for explaining difficult concepts in a manner than can be understood by most people.

Schlesinger not only knows blackjack well enough to write about it, but he also has a long track record of big casino wins at the game.

Though he is a busy person and has a family, he manages several trips a year to Las Vegas and other casino destinations.

He generally takes his family on those trips, but he also hits the blackjack tables hard, making big bets for long hours.

For years Schlesinger has been the angel sitting on the shoulders ofblackjack experts.

He has given generously ofhis time and expertise, reading each new book carefully and sending lengthy critiques to authors and publishers.

All of my own books have benefited considerably from Schlesinger's talents.

Schlesinger also is a frequent contributor of original material to blackjack periodicals, primarily Arnold Snyder's Blackjack Forum.

Some of his articles, such as the "Illustrious 18" and "Floating Advantage," have become legendary.

On the Internet, Schlesinger has a reputation as one ofthe most helpful of blackjack experts, patiently answering questions about arcane aspects of the game.

For years, I have been telling Schlesinger that I would love to have a book that included all of his published and privately-disseminated blackjack material.

With this book, I am getting my wish.

Stanford Wong ix Publisher's Introduction I have more than a hundred books on casino blackjack in my library.

Of these, a relative handful stand out as "classics.

BlackjackAttack: Playing the Pros' Way, by Don Schlesinger, is one of those few really important books on this subject that serious players will come to revere as an indispensable classic.

I have no doubt in my mind that this will come to pass, as Don's writings on this subject are already revered by those who have been following his writing career in the pages of BlackjackForum.

Blackjack Attack is the "answer book," the book that every professional player will pack in his suitcase, the book that will solve problems, and settle arguments.

For the truly dedicated player, hitherto unfamiliar with Don Schlesinger's work, this book will be a light in the darkness, the fundamental factbook that puts a dollars-and-cents value on the fine points of play.

Don started writing this book in 1984.

He didn't know he was starting to write a book at the time, nor did I.

He was simply answering players' questions.

There was no outline for a book-tobe, no synopsis of what was to come, no formula; this book was never planned.

Blackjack players had questions, lots of questions, complicated questions that were not being answered in the myriad books on card counting.

So, for a period ofsome see more years, Don Schlesinger answered those questions, one at a time, thoughtfully, diligently, and comprehensively.

His audience was small but grateful, consisting of the true aficionados of the game, those who subscribed to Blackjack Forum magazine.

As the popularity ofcasino gambling spread across the country and throughout the world, more and more books on casino blackjack were published.

But still, these new books - many of them fine and reputable card-counting guides - continued to ignore the fine points of play.

Some years back, I noticed that these new players were asking many of the same questions that Don had already answered.

I no longer had to forward these questions to Don for his analyses; I simply referred these players to whichever x back issues of Blackjack Forum contained Don's pertinent answers.

As Don has contributed columns, letters and articles to more than 50 different issues of Blackjack Forum, this has not always been quite as simple a process as it sounds.

I don't really want to think about how many hundreds of?

Suffice it to say that the publication ofthis book makes my life easier.

Now, when a player asks me one of those complicated questions that Don has already answered in his trademark elegant and comprehensive style, I can simply refer the player to this book, knowing that should this player get bitten really seriously by the blackjack bug, then this same book will also likely answer the next 16 complicated questions that more info into his head.

Don Schlesinger is a book author by default.

He spent 13 years answering players' questions, writing by "popular request," never envisioning a book, yet, here it is, a book that is truly one of the most important texts on the game in print!

I am humbly honored to be the publisher of this work.

The amount of information contained within these pages is frankly astonishing.

I can see now why all the other blackjack experts left this stuffout oftheir books.

Aside from the fact that most had not figured out about the game much of what Don had, the fact is there wouldn't have been room for this material in any "standard" text on how to count cards.

A word of caution to the reader: this is not a book that will teach you how to play blackjack, or how to count cards.

This is the book you should read after you learn how to do those things.

Almost any dedicated player, ofaverage memory and intelligence, can learn how to count cards, but very few ultimately become successful card counters.

Ofthose who make it, you can bet a good number of them have been reading Don Schlesinger's articles for the past 13 years.

If you haven't been, you've got some catching up to do!

Now, that is not to imply, in some haughty manner, that Blackjack Attack: Playing the Pros ' Way is superior to most of the books that have been written on casino 21; it's simply that this work is substantially different from all the others.

consider, california blackjack survey something me to explain.

It might be a good idea to begin by telling you what BlackjackAttack is not.

It is not a "how to learn to count cards" book although readers will learn much about card counting.

Nor is it a work in which you will find standard basic strategy charts, the rules ofthe game, or a glossary ofits terms - all staple features of the typically thorough blackjack book.

Instead, this work assumes a more advanced reader - one who is already familiar with the above concepts and seeks a higher level of sophistication.

Indeed, were it not for the publisher's desire for a "snappy," attention-grabbing title, I might have called this book, Blackjack: The Finer Points.

For, it is my hope that even the family guy peter hit me blackjack seasoned veteran will fmd at least some new and fertile ground, while the less experienced player is apt to fmd much food for thought in Blackjack Attack.

I have often been asked, "Where did it all begin?

An avid student ofprobability theory and, especially, its applications to the field of casino gaming and sports wagering, I read, starting in my early teens, all I could get my hands on concerning gambling.

In 1962, when Professor Thorp published his seminal work on card counting, Beat the Dealer, my fascination with the game of blackjack and, at the time, simply its theoretical aspects, was kindled.

It wasn't until a full!

And, as they say, the rest is, more or less, history!

I read everything I could on the subject and, at the time, the "big names," in addition to Thorp, were Lawrence Revere, Stanford Wong, Julian Braun, and, a little later, Peter Griffm, Ken Uston, and Arnold Snyder.

Mentors all, they helped me to form a rock-solid foundation for my ensuing blackjack knowledge.

And, although playing blackjack was and remains certainly one of my great passions, it seemed that writing about it and, eventually, teaching others to play, was equally fulfilling.

Many of my early observations on the game were published in Wong's Blackjack Newsletter, but it wasn't until 1984 that my first feature article appeared in Snyder's Blackjack Forum quarterly review.

Fortunately, that initial piece was well received by Arnold's readers, and I was encouraged to continue writing.

And write I did!

The work you are about games of blackjack read is, in part, a compilation of 13 years ofarticles published in Blackjack Forum, as well as much brand-new material that has never before appeared in print.

In particular, recent improvements in our ability to simulate, not only accurately, but also at incredible speeds, have permitted the kind of hitherto impossible, exhaustive study that forms the content of our Chapter 10, "World's Greatest Blackjack Simulation.

I am indebted to all those whom I recognized in the "Acknowledgments" for, clearly, this book would have never been brought to fruition without their input and guidance.

Above all, I would like to thank Stanford Wong and Arnold Snyder who, for many years, urged me to put all of my articles in book form, and especially Snyder, who agreed to publish the finished product.

One brief technical note.

For the sake of clarity, within any given chapter, original references to other articles from BlaclgÂ·ack Forum have been changed to the appropriate chapter in the present book.

It was felt that this notation would greatly facilitate crossreferencing for the reader.

Whereas every conceivable effort has been made to assure the accuracy ofboth the link calculations and the textual expression of this book, errors in a work of this size and complexity are, nonetheless, inevitable.

Should you find any, I would be most grateful if you would convey those findings to the publisher, or to me directly.

I may be reached at Arnold Snyder's "rge21.

Don Schlesinger New York, March 1997 xiii LIST OF TABLES Table 1.

I proposed to Snyder a more formal, family guy peter hit me blackjack article on back-counting, and it appearedas "A Day in the Life ofa Table-Hopper, " in the December 1984 issue.

The response see above quotesfrom some ofthe most respected authorities in the field, was quite flattering.

And, you might say, my blackjack-writing career was officially "launched " As might be the case with a parent, who always holds a specialplace in his or her heartfor afirst-born child, thefollowing article will always be special for me.

Many who read it wrote 2 back to say that it was the best depiction of Wonging," or back-counting, that had ever appeared in print.

I'll let you be the judge.

H he adrenaline starts pumping the night before the trip down.

The dedicated perfectionist leaves no chance for sloppy or inaccurate play.

I can recite 165 index numbers in my sleep and can count down a 52-card deck starting from a face down position no scanning several clumps ofcards at once in under 14 seconds.

There is practice to be done.

Hands are dealt at lightning speed.

Cards are flipped over.

This is a discipline thing.

You either do it right or you don't do it at all.

At least that is my approach to the game.

The practice completed, I get a good night's sleep.

It's going to be a very long day.

I have eschewed the junket approach for my entire nine-year playing career.

I am very much a loner by nature and I have an infInite capacity for playing the game.

I don't care a lot about the freebies if accepting them cramps my style.

I like getting the money and doing it on my terms.

I have never uttered my real name in a casino.

I have never established credit anywhere.

Central Credit Agency doesn't know I'm alive.

I use different names in A.

Thus, Caesars Palace can't cross-reference a name with Caesars A.

It pays to be careful.

I have tried to imbue in all ofmy students that the cardinal rule in this game is not to win as much money as possible.

Rather, it is to win as much as you can consistent with being welcome back in the casino the next time.

There is a very big difference.

If improper money management is the greatest destroyer of potentially successful card counters, then certainly greed and impatience are close runners-up for that top honor.

If you can't learn to win and lose, for that matter with both style and grace, then a you probably won't last in this game, and b you will eat yourself up inside while trying.

And so, I drive down the Garden State Parkway.

Two and three-quarter hours later, I'm in my first casino, Caesars Boardwalk Regency.

It is 12 noon.

The bus would have been cheaper and much more relaxing.

Because the bus tells you when you must go home.

I like to decide 3 for myself.

Not that I'll refuse to quit if I'm losing.

You lose too often to refuse to stop playing.

It's simply that I like to be in control of as much of my own destiny as possible.

The Back-Counting Approach Readers of Blackjack Forum have questioned the practicality and feasibility of the back-counting approach.

No one promised you a rose garden!

Sure, I'd rather be in Las Vegas playing the Riviera's two-deck surrender game dealt to the 75% level.

Or at Caesars Palace or the Trop with its 85% 4-deck game.

But I live in New York and a lot of my play is going to be in A.

The game can be beaten, but probably not the way you are playing it.

Read on and follow me from casino to casino.

Warning: If you don't have a good pair of thick rubber-soled shoes, forget it.

I'm going to leave you in the dust!

Second warning: If you've come down to have fun playing lots of blackjack, stay home and play with your family.

You've come to the wrong place.

I come to win money.

I use blackjack as the vehicle to achieve that goal.

We might play 15 minutes out of the hour; we might play less.

This doesn't appeal to you?

Then you're a loser already and they haven't even dealt the first card.

The better your eyesight, the easier it is to back-count.

Of course, we're already assuming you can count seven hands and the dealer's up-card in two or three seconds.

If your concept of back-counting is literally standing two inches behind a player's back and riveting your eyes on each card as it falls, then you've got this thing all wrong.

Look, there's a dealer shuffling at the comer table, the one across the aisle from the craps table.

I position myself in between the two.

I'll be looking at the craps action almost as frequently as at the blackjack table.

And I'll seems blackjack 21 android apk something no closer to one than to the other.

I'm looking for true counts of +1 or higher to enter the game.

Zero is still a minimum bet.

Why do I want to play when they have the edge?

And zeros have a way 50% ofthe time ofturning into negative counts.

Is this any way to start a gfu-ne?

Not for me, it isn't!

I get the true of one, but there are five players at the table.

I'll be the sixth hand.

A true count of one with one deck dealt out in an 8-deck game we'll assume hi-lo even though I personally play Revere is a running count ofseven.

On the next deal, ifI play, approximately 19 cards will be used.

Can 19 cards produce a running count of -7 or lower?

Of course they can.

It happens all the time.

So where does that leave me now?

I've played one hand, the count is negative, and I have a choice: a leave atlantic city blackjack rules table and look like a 4 horse's ass!

You link like either choice?

Well, neither do I.

I have a motto: "If it's good, it'll keep.

I might miss a few advantageous https://internetbingogames.info/blackjack/100-blackjack-bankroll.html, but remember, we don't want to win every dollar possible; we want to win what we can while looking normal doing it.

You have to believe this.

And what is even harder is that you have to dedicate yourselfto playing in a manner that reflects this philosophy.

And so I wait.

Two people leave and the count gets better.

Now, a word about my style ofbetting.

It is Kelly criterion with several modifications.

You won't like most ofthe constraints because you want to win all ofthe money.

Remember - I don't.

I want to win and have them as happy with me as I am with them.

Are you getting tired of my hammering home this point?

Well then, stop being greedy and try the "right" way!

Getting back to the bet scheme: one unit from +1 to +2; two units from +2 to +3; four units from +3 to +4; six units from +4 to +5; and two hands ofsix units from +5 to anything higher.

Why two hands instead of the one-hand, eight-unit bet at +5?

Because a eight units piled up start to look a bit too conspicuous, and b two hands ofsix units thus 12 units increases my spread and thus my hourly expectation.

Yes, it also increases my standard deviation.

But it doesn't change the probability of losing.

It just makes the expected win greater with a commensurate increase in the magnitude ofthe "swings.

And you had better be, too.

I lose the first five bets.

In the process, the true count shoots up to +2.

I guess you'd double up, eh?

Well, I bet the same one unit.

In nine years ofplay, I can count the number of times I have increased my bet after a loss on the fmgers of one hand and still have several fingers left over.

I told you there would be constraints you wouldn't like.

My rationale: winners celebrate by parlaying bets.

It is the logical and acceptable thing to do.

Card counters jump bets regardless ofthe outcome ofthe previous hand.

They make the mathematically correct play.

If you want to play the single-deck drunken slob routine where the erratic betting scheme bewilders personnel, then go to Reno.

That bit doesn't get it in A.

First ofall, the cocktail service is so pathetic, you couldn't get drunk if you wanted to; second, that approach is completely unsuitable for a table-hopping, back-counting style.

This is a science, not a freak show.

I look at my watch constantly.

I go here everyone to think I'm on the verge of leaving at any moment.

In fact, I am; but if they think it's because I'm late for an appointment or because later in the day the bus is leaving, my departure from the table is expected and appears more natural.

A little common sense goes a long way.

I have no hard and fast rule for how long to play in one casino.

But I am sure of one thing.

Most amateur card counters - win or lose - overstay their welcome.

If I win a lot - say 30 units or so - I'll be out the door.

I consider it poor taste to shove it down the casinos' throats.

I won't mention it again.

And so, on the win side, I let amount rather than time dictate my departure.

However, I do have an hour or so limit.

Even if the win is meager, I don't show my face for too long.

And, on the loss side, it is naive to think that just because you've been losing, you can play forever.

I've been formally barred from one casino in my life - Bally's Park Place - back when they had the right to do so.

And do you know what?

I was losing 25 units at the time.

If someone is skillful enough to determine that you are a card counter, do you think it matters to him whether you are winning or losing?

If you think it does, you are quite simply wrong.

Round one goes to Caesars.

They beat me rather convincingly.

No time to feel sorry for myself.

Get to the next casino.

Trump Plaza is enormous.

Cut card position varies greatly.

They don't know where the hell to put it!

They'll learn, but while they're learning, I'll exploit the deep cuts.

Every little edge helps.

I go down the tubes again.

They want to offer me the casino - meals, show, everything.

I don't want to stay another hour, win back all of my loss and ruin their happiness.

I'll get the money back, but it will be at another casino.

At least, that's my plan.

You're no more than a 55% favorite to beat anyone casino during anyone playing session.

If you make it a crusade to stay until you beat them all you can't, no matter how much.

I have won 62% of the total sessions I have ever played in my life.

This is a statistical fact.

I guess I've been a little lucky!

So what am I supposed to do, cry when a casino beats me?

Technical ability comes through dedication and practice.

But most of all, this game takes an incredible amount of heart.

It takes an iron will and a fierce determination to succeed.

It takes physical stamina, nerves of 6 steel, and an inordinate amount of discipline and self-control.

Without all ofthe latter, the former technical skill is meaningless.

It's 2:30, I'm a 28-unit loser, and a bit hungry.

I grab a quick bite on the boardwalk you have to understand my aversion to lengthy, drawn-out meals and decide to honor Playboy now Atlantis with my presence.

I like the third floor posh salon prive.

Players bet fortunes up there.

Nothing I put on the table can upset them.

The tuxedoed pit bosses are accustomed to huge action.

I find a good count and, as I move in, a young man practically knocks me over getting to the table.

He hasn't even played a hand yet, but I already know he's a counter.

Suggestion: as you spot a good situation, walk to the table.

Don't you think it's a bit gauche to charge?!

I shouldn't have played because two counters at the same table is deadly.

You start orchestrating your bets in unison as the count rises and, to a skilled eye, it looks ridiculous.

But the running count goes to +20 hi-Io and I'd like to be https://internetbingogames.info/blackjack/video-blackjack-in-arizona.html part ofit.

But the guy next to me makes an ass of himself.

He also happens to win a fortune, but as you know, I'm not impressed by that because he can never play again at the Atlantis.

What was his crime?

Also, three pit bosses, two calls to the "eye in the sky," several huddles in the pit, and numerous glares.

In short, I hope the guy is satisfied with his score because that's the last money he wins on day shift at Atlantis for a.

These bosses have long memones.

When the MGM Grand in Vegas changed from four to five badly-cut decks a couple of years ago, I stopped playing there.

Then, I was told alas, erroneously that the cut card had gotten better.

After a more than two-year hiatus, I ventured back and played a couple of shoes even though the cut was mediocre.

Enter a pit boss: "Dh, hi, Mr.

Good to see you again.

It's been quite some time.

I knew him well by sight and am sure that somewhere along the line he had asked for my name, but I was really surprised.

Moral: they don't forget for a long time!

And so, you must parlay your bets when you win.

You win, the count goes up.

Eventually, you win again at a higher count and you get more 7 money on the table.

Yes, mathematically, another constraint.

But it's a necessary one.

People naturally parlay when they win.

I simply consider it very risky to raise a bet after a loss or jump a bet more than a parlay no matter what the count is.

Remember, survival is the name of the game.

The kid leaves the table and cashes out.

Of course, I stay.

There is no way in the world I'm going to leave a table at the end of the shoe with him.

I mean, you didn't need me writing this article to teach you that, did you?

I shouldn't have been at the table in the first place, but you just know I have to stay for a while nowo I pray for another high count, but the shoe is uneventful.

The French have a proverb: "Les jours se suivent mais ne se ressemblentpas" - The days follow one another but don't resemble one another.

Substitute the word "shoes" for "days" and you've got the picture.

Ifyou think there's a pattern or an exploitable rhythm to this game, if you think there are "biases" or "dumping tables" or predictable hot and cold dealers, you'd better save your blackjack playing for Disney World, for as sure as a twenty beats a twelve, you're playing in Fantasyland.

TARGET players - it's not too late to play this game properly - while you still have a bankroll.

A Narrow Escape It's 3:45, I'm still losing, but I've narrowed the gap.

On to the Tropicana where I dodge a very big bullet.

Come along with me.

The Trop is the best technical game in town, but that doesn't make it the best place to win money.

After all, if they make it very difficult to play, then what good are the 76 well-cut 6-deck games?

For a while I had a hard time playing there.

I've never claimed that with a good act it is impossible to be detected in a casino.

And there isn't a pro in the world who, sometime in his career, hasn't been spotted somewhere by somebody.

After all, if I worked for a casino, do you think that there's a counter anywhere whom I couldn't spot in five minutes flat?

Well, then, it's conceivable that if a casino wants to go to the trouble, it can hire the proper personnel to spot me.

And that's exactly what the Trop has done.

I think they have more countercatchers than the rest ofthe city combined.

On this day, however, something unexplainable happens.

They walk right by me.

They let me play.

Can it be that I've stayed away long enough only six months or so for them to forget?

I can't believe that.

Does it have anything to do with my being 35 units down?

No, as you will learn shortly.

In my system, one "session bankroll" equals 30 units and ten such "session bankrolls" 12 to 15 would be even better constitute the total bankroll.

So why have I permitted myself to lose more?

Because I reached the limit in the middle ofa very high-count shoe and there were more hands to be dealt.

You simply don't walk away from such a situation no matter how badly you're losing.

The "streak" system players will tell you you're throwing good money after bad and that there's no sense being stubborn and getting clobbered even further by finishing an obviously cold, "dealer-biased" shoe.

The streak players are full of shit!!

The count is high and so you keep on playing.

If you don't agree with this, then stop reading, close the issue, and write to Arnold for a refund.

He can't help you win and neither can I.

You don't want to win.

God bless you and I wish you luck.

You'll need plenty of it, for surely that's the only way you'll ever win.

And so I play on and finish the shoe.

I lose a little more.

I did the right thing.

In blackjack, you are right when you play correctly and wrong when you don't.

Winning and losing have absolutely nothing to do with it.

After all, if you get your brains beaten in, you have a right to move on, no?

Of course, you realize this is what I assume they'll be thinking.

It's my excuse to leave a table where I no longer have an edge.

Losing lets you get away with a few things in a casino.

Walking around is one of them.

I get the dream-corne-true situation - the ultimate in a shoe game.

We start out as five players.

And do you know what?

Two people get up and leave!

Usually, it's the other way around.

What's more, the two other remaining players are bigger bettors than I.

No matter what I put out, the pit will be more concerned with their play than with mine.

It's helpful not to be the "big shot" at the table.

Deal the cards, it's get-even time!

I win back the 35 units and 18 more.

I run this one shoe for 53 units.

Forgive me, Pit Boss in the sky, for I have sinned.

I have already told you that I don't approve ofwinning 53 units at one time.

But a I made sure the whole world knew that I was "almost even" after the bundle I had dropped at the other table, and b what's a fella to do, quit in the middle of a shoe?

I couldn't help myself.

I playa few camouflage hands offthe top ofthe next shoe and make sure I lose the last one.

The throwaway line goes something like this: "I've worked too hard to get even.

I don't want to give it all back.

I know I promised, but - it's 9 not the 18-unit win after coming back from the dead!

You guessed it: I'm welcome at the Trop again!

Nothing else matters - certainly not the money.

My feet hurt, my legs hurt, and worst of all, my eyes burn.

I don't permit it in my house or where I work.

But once inside a casino, I am helpless against it.

Call it an occupational hazard.

God, I hate it so.

Well, I'm winning a little now.

No big deal, but it's good to be in the black for the first time all day.

Unfortunately, it's not going to last.

Next stop, Golden Nugget.

The Nugget has won more money the past two months May and June than any other casino in A.

So what, you say?

Things like that can actually have an effect on your play, and I'll explain why.

They're in a good mood there these days.

They're loose and win happy.

The place is crawling with high rollers and the casino is winning tons of money.

That's a good atmosphere for playing.

Also, despite the 8-deck game, the cut is excellent - average about 1 V2 decks.

There's money to be made here - unfortunately, not by me on this night!

I walk for 45 minutes and never playa hand.

Are you capable of doing that?

You have to be.

Remember, you're in the casino to win money, not to play for the sake of playing.

I don't sit down because I can't find the right conditions.

And believe me, it's not for lack of trying.

Put a pedometer on me and I bet I've racked up a mile in the Nugget alone!

Here's the frustrating part of the A.

You fmally find a good shoe, the count is super, and you lose anyway.

I make a little comeback, but the net result is that I'm once again losing for the trip.

When this happens to many players, they have a hard time justifying their actions to their families and to themselves.

So maybe they press a little.

Maybe they increase their stakes, or play negative shoes just to have a chance at winning.

You have to watch out for this.

You're in this for the long run.

Day trips even weekends are artificial divisions oftime that have no real meaning in what is just an ongoing and continuous process.

If you are destined to win 15 units in ten hours ofplay about the average for the A.

You have to think this way or the game will drive you crazy.

I'll now describe another way that blackjack will test your mettle.

Night shift begins at 8 p.

Well, the personnel may have changed, but not the outcome.

I'm winning just enough to be even when THE HAND arrives.

Now, before I set it up for you, let's review a few mathematical facts.

The true count equals or exceeds +5 about 1.

For the Revere or Halves counts, the frequencies are slightly higher and thus, correspondingly, so are the hourly win rates.

You average around 25-27 hands played per hour based on being able to see and count about 100 rounds per hour.

If you put in six hours per day 150 hands playedyou will be placing a top bet of two hands of six units each an average of only three to four times.

And since it is at these counts that the largest contribution to your win is accomplished, they become very important.

Win your fair share of them and you'll probably be a winner for the day.

Lose them, and it's tough.

And when the two hands turn into three, or even four, that can be the whole ball of wax for the day.

Now, let's get back to the game.

The count is astronomical.

I work up to the max bet.

Dealer shows a 6.

I make twenty on the first hand and the second hand is a pair of threes.

Already, the count has gotten even higher.

I split the threes and get a six on the first.

Where are the big cards?

The double down produces 19.

I turn the other three into 18.

There blackjack card counting online 24 units on the table, and I've got 18, 19 doubledand 20.

I teach all of my students the number one tenet of the game: never celebrate early!

You know you've won a hand when the dealer pays you - not a second before.

The count is so high I can't believe it.

Normally, a dealer's six breaks about 43% of the time.

With this count, I'm sure it's closer to 50%.

She flips a three in the hole.

Although the entire process happens in a flash, I nonetheless have time to think: "I push the 19, lose the 18, win the 20.

The next card is a deuce.

Still no big cards.

The rest is history.

You're not really interested in which ten it was, are you?

I lose the 24 units I should have won.

To me, this is a 48-unit swing.

The dealer, a new young girl, actually apologizes to me: "I'm awfully sorry, sir.

On the other hand, it sure as hell isn't my fault, either!

What would a computer do now?

It would play the next hand - after all, the shoe isn't over.

If you can't do this, if you're devastated by the sad occurrence, you're not cut out for this yet.

If you do play on 11 but lose your concentration and keep returning in your mind to the "tragedy," you're not cut out for this.

Blackjack will test your soul, your character, the very fiber of your being.

You have to sit there and take it.

Otherwise, you're going to be playing this game on the funny farm!

There will be better times.

I win some back, but the final result of the trip -32 units has been sealed by the one hand.

Don't shed any tears for me.

I've got a little lead on https://internetbingogames.info/blackjack/dealer-odds-in-blackjack.html />I'm in the car by 10 and home at 1 a.

It's been a 16-hour day.

Some restful way to spend a Saturday!

When I write my first book, the title won't be Blackjackfor Fun.

And although it could very well be Blackjackfor Profit, Arnold has already beaten me to that one!

But it's late now.

I've got to get a good night's sleep.

I'm going to A.

There's just no way I'd rather spend a Saturday!

We understand he got the 32 units back.

} From "The Gospel According to Don, " Blackjack Forum, June 1990: Q.

After rereading your table-hopping article, it is clear to me that back-counting alone is a tediousprocess that takes a great deal ofpatience and discipline.

It has also occurred to me that if I were to enlist the aid ofone or more confederates who would act as tlspotters" back-counting different areas of the casino, but never playingI could certainly enhance my hourly win rate.

My question involves the calculation ofthe increase in profits these spotters wouldproduce.

I know, for example, that there would be some Hoverlapping, " but I'm not click here how to do the math.

Also, can you suggest an equitable manner for compensating the spotters for their time?

I would appreciate any help you can offer.

Although the concept of using spotters to increase backcounting hourly win rates is not new, I doubt that the kind of analysis I'm about to present, in response to our reader's question, has ever been published.

I hope it will be useful to players who are contemplating using this style of play.

First, let's define the nature of the activity.

Obviously, a spotter must walk in a separate region of the casino from where the primary player finds himself.

What good are two people if 12 they're back-counting the same tables?

The problem of"overlapping" occurs when the player is already involved in a good shoe and, simultaneously, the non-playing spotter fmds a second opportunity.

It is possible that this second positive shoe will still be playable after the first opportunity is exhausted, but until that happens, there is a temporary period of time during which the spotter's efforts cannot be exploited.

Simply put, the player can't be at two tables at the same time.

Fortunately, with only one spotter, this overlapping does not occur too frequently and the math involved in calculating the effect is relatively easy.

Let's assume, for the sake of simplicity, that a back-counter sees 100 hands per hour, of which he actually plays 25.

In practice, these are, in fact, very realistic numbers.

Here's how we alter the incorrect answer.

Multiply the probabilities that both will fmd a table simultaneously and then subtract from the 50 the number ofhands this probability implies.

The correct number of hands played per hour is 44.

Adding a second spotter can complicate the math, but I'm going to show you a short-cut that often simplifies probability calculations.

Before we consider the two-spotter problem, let's go back to the original example.

You'll like this approach.

In probability theory, the totality of all the outcomes is expressed as 100% or, in fractional form, 1.

Let's add a second spotter.

See how simple that was?!

While we're having fun, let's ~xamine one more situation, this time with three spotters.

We are now in a position to analyze the percent increase in profits that can accrue to the back-counting player who uses spotters.

With one spotter, 44 - 25, or 19 extra hands are played.

Now let's carry this one step further in an attempt to answer your second question.

How should the spotters be compensated?

Clearly, in my opinion, the actual results of play should have nothing to do with it.

Rather, the theoretical "value" ofthe spotters should be calculated.

How many extra dollars, on average, will their presence produce?

Next, how should this surplus be divided?

I suggest an equal split.

After all, the spotters who, presumably, don't have the bankroll to play themselves need the player's money.

In return, the blackjack does dealer hit on 16 needs the spotters to enhance his revenue.

I can foresee an objection.

Suppose one player is a low-stakes bettor while another is a very high roller.

A spotter who hooks up with the former will be paid much less for his efforts than if he were to team up with our well-heeled friend.

Yet, in each situation, the spotter's efforts are identical.

Permit me to digress.

If you ask a waitress to bring you a hamburger and she does, you tip her 15% ofthe bill.

Now, I've never found this to be a very rational process, but that's the way it goes.

So it really isn't unreasonable that the spotter who hooks up with the "filet mignon" will be paid more for his services than the one who works for "hamburgers.

Well, with one spotter, the extra 76% is split 50-50, so 38% goes to the player.

The extra 132% from two spotters is divided three ways, so the player gets 44% more.

With three spotters, something interesting occurs.

There is a 172% increase in profits, but a four-way split yields only an additional 43% for the player.

Obviously, "diminishing returns" have set in, and it does not pay to add the third spotter under this arrangement.

Now, I'll explain why, for practical reasons, I don't think a second spotter is worth the trouble either.

Casinos are, more often than not, noisy and crowded particularly, those in which you are most likely to back-count.

An attempt, on the part of the spotter, to get the player's attention by any kind of audio signal will undoubtedly fallon deaf ears.

So, a visual call-in family guy peter hit me blackjack be used.

Suppose the player is busy looking down at a prospective table?

Suppose he does manage to see the spotter immediately, but can't navigate his way through the casino until one or two hands have been dealt?

The bottom line is that, 14 in reality, hands will be missed.

If the idea for two spotters is to add 33 extra hands, it is not at all unreasonable to estimate that five of these hands will go unplayed.

Split three ways, it becomes 37.

Surely, compared to the one spotter 38%, it isn't worth the extra effort.

Conclusion: If you intend to share additional revenues equally, play with exactly one spotter to maximize your back-counting profits.

Of course, my profit-sharing suggestion is not the only conceivable method for compensating spotters.

Indeed, I know of a team in operation now that pays spotters a fixed, hourly wage.

Here the theoretical value to the player would be quite different.

And four getting a little crowded now!

Here again, I believe that missed opportunities would preclude the use of four spotters; but a marginal case could be made for at least three.

Obviously, there are several possible "variations on the theme," and messages blackjack oyunu nasil oynanir topic short piece is meant simply as a guideline to those who are contemplating the idea.

I have summarized the above findings in Table 1.

I hope you have found this information useful and I wish you success with your back-counting endeavors.

Postscript: It has been 12 years since this article first appeared, yet, little has changed in my approach to the shoe game.

I can't think ofany advice that I would alter.

Obviously, casino conditions are constantly changing, and many ofthe games described no longer exist in the same form as they were.

The computer age has, however, made practicing a lot more fun than it was back then.

Today, I believe the practice regimen, briefly described in the article's first paragraph, would be a lot more 15 enjoyable, thanks to the genial software, such as Norm Wattenberger's Casino Verite, that has been designedfor such purposes.

I'll be making further remarks on simulators and study aids, throughout the book.

Finally, note the casual reference, in the next-to-last paragraph ofthe "Table-Hopper," to "when I write my first book.

At the time, Schlesinger and Feldman held the New York franchise for Jerry Patterson's Blackjack Clinic.

Don expanded the article considerably with Part IL which appeared in the June 1985 Blackjack Forum.

HThe Ups and Downs of Your Bankroll, " as it was initially titled, provides the most in-depth treatment of Hbankrollj1uctuations" ever presentedfor non-mathematicians.

Though Schlesinger's work specifically analyzes the hi-lo counting system, his conclusions are applicable to all valid point-count systems played under similar conditions.

Playing for the same stakes, a student ofours one of our most successful ones just encountered a similar catastrophe when, in one week in Las Vegas, his 57 units in profits evaporated and turned into 53 units worth ofred ink.

No matter what stakes we play for, we have all experienced these incredible roller-coaster-like fluctuations in our bankroll.

The culprit is something mathematicians call "standard deviation.

How many heads do we expect?

Roll a die 600 times.

How many sixes do we expect?

What profit do we expect to show?

Thus, in layman's terms, "expected value" is nothing more than the "average" or "mean" outcome that we expect for a particular event, given a certain set of circumstances.

But rarely does the coin actually come up heads 50 times.

Rare, indeed, would be exactly 100 "sixes" in 600 tosses of a die.

And rarely do we win at blackjack for any given session the exact mathematical amount that we expected to.

We are usually a certain amount above or below "expected value.

Take our prior example of 100 hands.

How do we use this figure?

The actual outcome ofour playing session will fall somewhere within this one-s.

The whims of s.

If we are willing to expand our range to two s.

And ifwe go up or down three s.

A good weekend's worth of play will yield, roughly, 1,000 hands.

This 19 is actually an underestimate of the true s.

Now, let's get down to cases.

But it rarely turns out that way, and you've been wondering why.

And you thought you were the only one riding the roller-coaster!

Can you lose for an entire weekend?

The answer is "yes" to all ofthe above.

The greater the number of hands you play, the smaller the percentage of s.

Thus, put in everyday terms, the more you play, the closer on a % basis your actual outcome will be to your "expected" outcome.

And don't worry if it seems like just when you've reached the top, you slip back down again.

Peter Griffin estimates that we're at an all-time high only 1% of the time.

Thus, 99% of the time, we have the nagging feeling that we "once had more.

Play through the losing streaks, enjoy the winning sessions, and always remember - we have a partner in this exciting venture of ours: accept. million dollar blackjack y ken uston on blackjack think deviation.

Part II Since I wrote the above article, about two years ago, several students have asked me to be more precise about standard deviation and win-rate calculations as they applied to our specific style of back-counting and betting see Chapter One.

During the year 1983, Stanford Wong carried out the most complete set of computer simulations ever published for the hi-Io count and for the risk and return associated with four- six- and eight-deck games See Wong's BJ Newsletters, Vol.

I have used Wong's data for much ofthe work in this article, but have expanded upon it and included some original material that, to my knowledge, has never before appeared in print.

Indeed, larger risk as measured by s.

The purpose ofthis article is threefold: 1 to determine precise win rates for the back-counting and "play all decks" approaches to the game; 2 to determine accurate standard deviations for the same styles ofplay; and 3 to relate the two concepts by constructing tables that reflect the probability of being ahead after n hours of play in the various games.

Along the way, I shall explain all the mathematical principles involved so as to facilitate the reading and to justify all of my contentions.

Finally, some interesting conclusions will be drawn.

Here is a brief summary of my back-counting approach to the shoe game.

I play only true counts of +1 and higher.

I bet one unit at +1, two units at +2, four units at +3, six units at +4, and two hands of six units at +5 and higher.

Thus, my top bet is two times six units no matter how high the true count goes.

Determining how many hands per hour one actually gets to play with this technique is not a cut and dried objective calculation.

But I believe the following to be a fair and accurate approach to the problem.

First, a few empirical facts gleaned from thousands of hours of experience and observations.

Assuming four players and the dealer, it takes about 30 seconds for a competent dealer to deal one round.

During that round, 5 hands x 2.

Thus, it takes about two minutes to deal one deck.

Observation confirms the following shuffle times: 1 minute 20 seconds for 4 decks, 1 min.

Dividing each into 60 minutes, we get the following hourly figures: 8.

Next, we must interpret how many rounds per hour this translates into.

The results are as surprising as they are convenient.

When 3 decks are dealt, 156 cards are used.

But when the cut card is reached, the hand is completed; thus, on average, 13.

We subtract one 2 21 because if the cut card is poised to come out, the next hand is not dealt.

So, for the 4-deck game, 162 cards per shoe + 13.

Multiply this by 8.

Similar calculations for the 6-deck game yield 240 + 13.

Finally, for 8 decks, 318 + 13.

Will anyone mind if I call all three exactly 100 rounds per hour?

This is a great facilitator of later calculations.

Now, the question is, "Do I actually assume that, in backcounting, the number of rounds per hour actually counted is this 100 figure?

Granted, by judiciously walking away from poor counts in progress, one ought to be able to do better, in theory.

However, in practice, it is not that easy.

What good is it to count if you can't play?

Physically navigating the huge and unbelievably crowded Atlantic City casinos cuts down on mobility.

Limited availability of higherstakes tables invalidates the assumption that one can always find instantly another dealer ready to shuffle.

For all these reasons, I believe it is realistic to approach the calculation in the following manner.

Assume you actually have the right to sit at any given table and count all the rounds for the hour and that, furthermore, you may bet only the +1 and higher counts, betting, in effect, zero for the others.

If you agree to accept this premise, then all that follows should be logical and easy to understand.

Wong's frequency distributions give us 29.

Plug in the appropriate bets at the appropriate true counts, multiply horizontally by frequency and corresponding advantage, sum vertically, and you get the following hourly win rates in units for each game: 2.

I have prepared a table, for the reader's convenience, that summarizes not only these figures, but other important data.

It this web page interesting to note that ifone decides to "play all" decks of the 4-deck game and thus 100 rounds per hour, making minimum, one-unit bets 81.

And this is for the slightly inferior Las Vegas game with no double after splits.

One immediate practical application of this fmding for the A.

I am not sure that this is readily apparent to the average player.

Please note that throughout this paper, I have purposely omitted any discussion ofthe 8-deck "play all" approach.

The win rate for this game is so poor as to 22 make it totally unacceptable.

Anyone considering playing blackjack in this style is, in my opinion, wasting his time.

As for the 6-deck "play all" approach, the win rate 1.

Thus, for these reasons and others discussed later camouflagethere is little to recommend for this style ofplay where 85% ofthe wagers placed would be at one unit and where the overall edge is a mere 0.

The next part live blackjack pokerstars our discussion continues the original topic of standard deviation.

Once again, Wong's data are indispensable see, in particular, pp.

I have included detailed charts of the necessary calculations that lead to the following sobering conclusions.

For the 4-deck game, the one-round standard deviation for my back-counting approach is 5.

Remember, whereas the hourly expectation is the one-round expectation multiplied by the number of rounds per hour, the hourly s.

Six-deck figures are 4.

For the 8-deck game, we have 4.

Finally, for the "play all" decks, 4-deck approach, the one round s.

For the "play all" 4-deck game, the horizontal multiplication for counts below +1 adds only.

Thus, the new sum is 9.

Why do I call the above "sobering conclusions"?

Well, refer back to the original article on standard deviation which supposes a flat bet equal to the average bet of the 1-12 spread scheme and you will see how much greater the actual standard deviation really is.

I don't suggest that there is any brilliant way to avoid the large s.

And so, I have found blackjack setup way to relate the two crucial concepts ofexpected win and standard deviation by studying the interaction ofthe two.

Hmlm 1 5 10 20 40 50 100 200 400 500 B::da I::dsk ~ 4-deck.

The only chart of this nature I have ever seen frrst appeared in Ken Uston's Two Books on Blackjack and was reprinted in his Million Dollar Blackjack.

But Kenny's table was for a different bet scheme, a different count, and most of all, a different style of play.

For this reason, I believe that the above table provides insights into the back-counting approach that have never before appeared in print.

For those who understand the cumulative normal distribution function, the calculations are straightforward.

Simply determine for a given number of hours, what percentage of the standard deviation the corresponding expected return represents.

Then fmd, in this case, the area under the curve to the left ofthis figure.

This is the probability of being ahead after the required number of hours.

Note that, in determining the probabilities for this array, an assumption is made that one's bank is sufficiently large so as to permit play to continue for the re~uisite number ofhours, without regard for tapping out losing one s entire stake prematurely.

See Chapter 9 for a complete discussion of this phenomenon.

Now, all of the mathematics in the world goes for naught, in my opinion, if it doesn't have some practical use at the tables.

Much can be gleaned from a careful consideration of Table 2.

And many of the unbelievable frustrations that are inherent in high-level blackjack play are more readily tolerated when one understands standard deviation.

What, specifically, can we learn?

For one thing, s.

In the 4-deck back-counting game, one is playing with a 2.

But even after 200 hours at the tables, one player in ten is still going to be losing.

Will he understand why?

After 500 hours, one unfortunate soul out of 50 will still be in the red.

Try explaining to him that someone has to fall in the tail of the normal curve!

What about the 20-hour 25 weekend player?

Well, he will lose once out of every family guy peter hit me blackjack trips, while a ten-hour player loses three out of eight times.

Finally, if you subdivide your records into daily or even hourly results, you're doing just fine if you win three out of five days and five out of nine hourly sessions.

And these are all for the "best case" 4-deck back-counting approach.

You're trying to make your fortune at the 8-deck game?

Well, I hope you've got the patience and the bankroll!

God knows, it won't be easy.

For that matter, the Bishop knows it, too.

He's been telling you for four years!

In fact, after 500 hours of play, one out of ten hearty souls will actually still be losing.

You're planning a one-week, 40-hour assault on the A.

Well, you should be a winner two out ofthree times, but don't expect any more.

Finally, notice the similarity between the 6-deck back-counting figures and the 4-deck "play all" numbers.

They are almost identical.

Given my choice, which would I prefer to play?

Sedentary play is more comfortable, but it can be more risky to your cover.

I don't think it looks good to play 82 hands out of 100 at one unit and then to playa few at 6 units or two hands of 6 units.

Even with a good act, this is tough to pull off.

On the other hand, 27 quality, back-counted hands per hour will produce 86% of the "play all" approach profits and will, in my view, increase one's longevity.

Never forget: you have to be welcome back the next time.

One thing is certain.

To be successful at this game, one needs an inordinate amount of dedication.

The ravages of standard deviation will blackjack crazy hermit even the most hardened veteran.

When this happens, take a break, reread this article, and go get 'em.

I wonder how many readers would be interested in seeing the above materials expanded into a more complete work.

One could, for example, consider single-and double-deck games, rules variations, different cut-card positions, different point counts, and, of course, different betting schemes.

The combinations are almost endless.

I have the energy to collate the material and to write the text.

Perhaps someone has the interest, computer capability and know-how to generate the figures.

Any takers out there?

Give me a call!

Postscript: I'm pleased to say that the up.

I highly recommend it to all those who are interested in the statistical aspects ofblackjack, as I am.

U 26 What's more, 1 have vastly expanded upon the scope and content of this chapter with a brand-new analysis of win rates, effects of rules, penetration, and bet spreads, in this book's Chapter 10.

For simulation ufreaks, " yo~might want to take a peek now!

Bankroll required for optimal bets units 400 400 360 360 2.

Average bet size units 2.

Win per hour units Rows2x3x4 1.

Standard deviation per round units 4.

Standard deviation per hour units 20.

Hours for expected win to equal s.

My friend states that it is more mathematically correct to play one hand against the dealer with a high count versus multiple hands against the dealer with a high count.

Could you please settle this argument.

Ifyou can get more on the table with multiple hands, then multiple hands are your best strategy, provided, of course, that multiple hands do not hurt you in some other way notably, tipping off the casino that you may be a card counter.

Along the way, I trust that the reader from Utah will be satisfied with the result, which turns out to be a compromise between his approach and that of his friend.

Before considering the merits ofmultiple hands, it is important to understand the concept of optimal bet sizes.

For a given bankroll, and a given advantage at a specific true count, an optimal bet is determined by multiplying the bankroll by the edge in percent and dividing the outcome by the variance Griffin prefers the average squared result of a hand of blackjack, but the difference is slight of hands played at the particular true.

According to Stanford Wong, when one makes a bet at a true of +5 level at which most pros "max out" and place their top betthe wager should be 77% of the player's bankroll times the advantage.

For the 6-deck A.

Now, when two or three hands are played, one must consider the covariance between these hands and wager on each one of them a percentage of the one-hand bet that creates risk and profit potential commensurate table peeker the optimal one-hand play.

For two hands, one divides by the sum ofthe variance and covariance.

For 28 n hands, the general formula is to divide by the sum ofthe variance and n - 1 times the covariance.

Thus, the "trade-off' for more money on the table is more risk, in the form of higher standard deviation.

What are the optimal percentages?

For two hands, 73% ofthe one-hand bet on each ofthe free deck blackjack, and for three hands, 57% of the one-hand bet on each of the hands.

Now the question arises: "Which is the superior approach?

How do I know whether to bet the one hand, two, or three?

It is not sufficient to simply "get the most amount of money on the table" obviously, the three hands for anyone given round, thereby assuming that this strategy will get the greatest amount on the table by the time one has finished playing.

Each spot played uses up cards.

We must consider, for any given shoe, how much money will actually be put on the table with each one of the approaches.

It is only after considering the total "global" wager that one can determine the best approach.

The "correct" answer is neither obvious nor intuitive.

Let us assume that, if we play long enough Gust how long is easy to calculatewe will eventually have the opportunity to place 100 maximum bets true of +5 or above.

Now, consider the effect of playing one, two, or three hands on the number of cards used per round.

Therefore, head-on play uses 5.

Consider, also, the effect of other players at the table.

The following chart indicates exactly how many hands can be played under varying conditions, given our above scenario.

In addition, I have multiplied hands played by dollar amount of wager to produce, in each box, a total amount of money wagered.

Next determine the total number of hands being played for the box in question.

For example, playing with two other players and playing two hands equals five hands.

Multiply the number of hands by 2.

Use the result as the 29 TABLE 2.

Multiply 100 by this resulting fraction for this example, 40 hands.

On each horizontal line Table 2.

The results are most interesting.

When joined by one or two other players, we optimize potential with two hands.

Only when there are a total of four or five players at the table should three hands be played, and even here, I would strongly recommend against this.

First of all, it isn't such a great idea to be playing with three or four other players.

This cuts down too much on the hourly expectation.

Secondly, the extra amount of money gotten on the table is only marginally greater than the two-hand approach, and the price paid in possible heat and pit attention for spreading to the third hand is most defInitely not worth it.

Now, there is one instance, even when playing alone, when spreading to a second hand is a must.

If you are proficient in eyeballing the discard tray and "know" when the last hand in the shoe is about to be dealt, then by all means, spread to the second hand.

It doesn't matter any more that you are using up extra cards.

You are guaranteed the completion of the round and, therefore, you would be foolish not to get the extra money on the table.

Thank you, reader from Utah, for a thought-provoking question that, I trust, I have answered to your satisfaction.

To summarize: Play one hand if you are alone with the dealer; play two hands, each ofwhich is 73% ofyour one-hand top wager, under all other circumstances.

Finally, let's put the whole thing in perspective by considering the following: whether you back-count or "play all" in any given hour, you play the same number of top-bet hands.

Assuming 100 hands seen or played per hour, roughly 3% of them three hands are at a true of +5 or greater.

Thus, it would take, on average, 33 hours to play the 100 top-bet hands in our illustration.

As is often the case with blackjack questions, sometimes we become so enamored of the theory that we lose sight of the practical, bottom-line implications.

From "The Gospel According to Don," Blackjack Forum, December 1990: Q: I have read several texts that have indicated that the formula for determining Hexpected value" is: Average bet x Number of hands per hour x 1.

It seems to me that the https://internetbingogames.info/blackjack/blackjack-band-new-zealand.html do not consider the Hspread" and, therefore, cannot be accurate.

Can you shed some light on this topic?

This question, although relatively simple to answer, raises several interesting points that have caused a good deal of confusion for many readers.

The first item is the misconception that a particular game has some "pre-ordained" or inherent advantage associated with it.

In fact, it does not.

What it does have is a frequency distribution of true counts, each of which represents a certain advantage or disadvantage.

Until we specify a betting scheme, which associates an amount to be wagered with each true count, it is not possible to ascertain the overall advantage we will enjoy playing this game.

And that is the problem here.

The reader has assumed a fixed, 1.

In reality, each spread has associated with it its own edge, and the two advantages are not the same.

I don't claim this represents reality -just humor me!

Now, consider the two cases, A and B, in Table 2.

How can this be?

Because the advantages are not the same, as the reader had assumed.

Divide the win by the total amount wagered to yield the hourly advantage.

It has always amused me when players compare the relative merits ofdifferent games by citing advantage alone.

This reminds me of the old joke where the sportscaster has just given several final football scores and then says, "And now, a partial score: Notre Dame, 21.

If someone offered you the choice of playing a game with a 1.

Before you answer, look at Table 2.

Notice the hourly win rate 2.

Now compare this to the 1.

Taken separately, the average bet or the spreadthe number of hands played per hour, or the overall percent advantage are relatively unimportant.

It is the product that determines how much you will win, and it matters very little except for the sake of cover how that product is attained.

Of course, in this discussion, we are not considering the risk associated with the various approaches.

It goes without saying that standard deviation should always playa major role in assessing the desirability of any game.

More about this in Chapters 9 and 10.

Suppose one game yields a 2% advantage, but the table is always full.

Another has but a 1% edge, yet you can often play alone against the dealer.

Which game should you play?

I certainly hope you said the 1% one.

For, at roughly 200 hands per hour, compared to about 50 for the full table, you will win, at the 1% game, about double the amount of the 2% source />Moral of the story: Quote win rates, not edges or spreads.

September 1992 Cover Art by Judy Robertson Chapter 3 Evaluating the New Rules and Bonuses In this chapter, I combine yet another feature-length article, HLost in the Maze ofthe New Rules, "from the September 1992 Blackjack Forum, with afollow-up, companion uGospel" piece to analyze ten ofthe mostpopular uside bets, " or new ugimmick" propositions, that have been introduced to blackjack in recent years.

Whereas it's too early to tell ifthe proliferation of exotic rules, bonuses and options currently being offered at blackjack tables around the country is here to stay, one thing is certain: the "time traveler" who hasn't sat down to play for a year or two is in for culture shock!

In an effort to stimulate what appears to be sagging public interest in table games, casinos are resorting to "gimmick" side bets and propositions to keep customers happy.

But will any of these variations actually enhance the player's expectation?

Which, if any, lend themselves to a card-counting approach?

What, exactly, are the changes in basic strategy that a player should employ while tackling these games?

We shall attempt to answer all of these questions in the following article.

In addition, where feasible, the mathematical calculations needed to derive the odds will be explained.

Finally, where direct solutions prove to be cumbersome or unmanageable, we shall indicate 34 the software almost always Stanford Wong's Blackjack Count Analyzer used to obtain the answers by simulation.

This side bet on the table layout permits the player to wager on the likelihood that the total points obtained with his initial two cards will be under consider, mohegan sun pocono blackjack rules think over 13 in value.

The player loses on a total of 13 exactly.

No need to analyze this option here.

Count strategies were devised that actually offer greater profit potential than traditional blackjack approaches.

For the sake of completeness, we include the numbers here, as a reference.

Basic strategy house advantage is 6.

Quite simply, one consults a frequency distribution for initial hands Chambliss and Roginsky, Braun, Imming, etc.

Of course, one must stipulate the number of decks being shuffled I used six for the above percentages.

Likewise, the edge attainable by card-counting techniques varies, as expected, according to decks used, spread employed, and depth ofpenetration the latter, as always, being the most important.

This advantage ranges from 0.

Now, let's get on to the new proposition bets and rules.

Rule 1: Winning, Suited 6-7-8 Pays 2 to 1.

Step 1: Determine the probability ofobtaining a suited 6-7-8, given that you will automatically draw the third card regardless of the original situation your hand v.

We'll assume the TropWorld 8-deck game.

Choose one specific order of one suited sequence say, 6-7-8 spades.

But we are not confined to 6-7-8 - any order will do say, 7-8-6.

There are six possibilities or permutations.

In addition, there are four suits.

Thus, the desired probability is 6 x 4 x.

Step 2: Eliminate the percentage of starting hands that will sacrifice more than it's worth if we violate basic strategy.

For example, we hold 7-8 of hearts; dealer shows a 5.

The 2-to-l 35 bonus is not sufficient for us to draw in an attempt to find a 6 of hearts.

Wong's Blackjack Count Analyzer henceforth, Family guy peter hit me blackjack tells us that departing from basic to go for the 2-to-l bonus is correct only for the case of 6-7 v.

Note: this is a change from the advice given in the March BlackjackForum, where the dealer's 3 was included.

So, all other holdings v.

Thus, we are left with 1 .

Step 3: In their infinite gluttony and poor taste, the casinos actually require that our next-to-impossible-to-achieve suited 67-8 be a winning hand!

Thus, should the dealer reach a final total of21 7.

We're left with 1 .

Step 4: Determine our edge.

Since the payoff is 2 to 1, we win one extra unit for each unit bet.

Thus, our basic strategy advantage is simply our final probability, stated above, of.

Well, ofcourse, you're absolutely right.

On to the next rule.

But it doesn't get any better!

Rule 2: Winning 7-7-7 Pays 3 to 2.

Step 1: Determine the probability of obtaining three consecutive sevens given, once again, the assumption that, with two sevens, we will draw automatically.

Step 2: As for our 6-7-8, eliminate the percentage of starting hands pair of sevens that it would be foolish to sacrifice fail to split by trying for the bonus.

In this instance, all correct basic strategy splits should be maintained.

Since we split sevens in A.

We're left with 1 .

Step 3: Again, we get paid on only 87.

Step 4: Finally, to determine our edge, note that, for each bonus of3 to 2, we win only one-halfunit for every unit bet.

Our added advantage is, therefore, half of the number above, or.

Small errors were introduced due to my neglecting the interaction of various up-cards on final probabilities.

Nonetheless, a more precise calculation, which accounted Â·for these differences, was carried out by Peter Griffin and I'm happy to say that it yielded almost identical results.

Together, the above two bonuses will put exactly 12 extra cents per hour in the player's pocket.

Rule 3: Red-Black The Four Queens, in downtown Las Vegas, is experimenting with a side bet on the color of the dealer's up-card.

Six decks are used and the player simply chooses, in a separate betting square, the "red" or "black" designation.

The house advantage resides in the deuces.

When the deuce ofthe color you bet on appears, your bet pushes instead of winning.

Analysis of the casino's edge is straightforward.

For simplicity, assume, for the moment, a onedeck game.

Red appears 26 times, but two are red deuces, which push.

This is the house edge: 3.

It should also be obvious that this proposition lends itself admirably to card counting.

An elementary plus-minus approach is all that's needed.

FAMILY GUY - Peter Gives away Secret playing Charades #2017

## internetbingogames.info | 522: Connection timed out Family guy peter hit me blackjack

## internetbingogames.info | 522: Connection timed out Family guy peter hit me blackjack

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