Revere invented a new simple counting system and first described the method of reducing the current score to the real one. Stanford Wong amplified and improved Hi-Lo system, and also developed the Halves system. Lance Humble, Brison, Gordon, Harvey Dubner, – all these giants made a great contribution to the development of the methods of the game.

In late 70s the professional gambler Al Francesco, probably created the first blackjack team in history. He hired the enthusiasts, taught them Lawrence Revere’s counting system and sent them to play. He invented and put into practice the principle of “BIG PLAYER” – when the part of the team is humbly playing low and some drunken and wealthy fish makes high bets on the given signals.

Ken Uston also belonged to this team. Uston was the vice president of fund stock exchange at that time. However after meeting Revere he quitted the stock exchange and changed his strict outfit for magnificent bush of hair, golden chains and silk shirts with huge collars in the style of that time.

Uston played for Francesco’s team for quite a long time and with varied success, but his ego did stand it under the pressure of his own ego. He had a very high opinion of himself and wanted to be the first in everything. He left Francesco and wrote several books about his adventures. The books simply exploded the gambling world.

The book “BIG PLAYER” revealed the secrets of team game. The Book “Million Dollar Blackjack” is stuffed with unbelievable stories in intervals explaining the technical aspects also presents different cards counting systems. Uston made people believe that one can beat casino playing blackjack. Win a lot. Millions of dollars. Also everyone found out how casinos react to the professional gamblers – slams, insinuations, blacklists, crooked gambling, false accusations. Uston was in the blacklists all over the world, having won with his several teams about 8 million dollars.

By the way, Al Francesco and many other players are still dissatisfied with Uston’s actions who decided to publish the methods of the game which were then available only to the few. But Uston would not be himself if he had not done it.

The next outburst of his popularity was in early 80s, when Ken won the case against a casino in New Jersey (Resorts International Hotel Inc.). Since then no casino of this state (unlike, for example, Las Vegas in Nevada) is not eligible to prohibit playing to person who can count cards. On the other hand, this verdict made the rules in Nevada much worse than in Vegas.

The next wave of the struggle between the casino and counters relates to Uston’s era. The casinos understood, that well-financed team of pros can cause great losses. And then the multidecked games, frequent riffle were coming into fashion and several good rules just died away. There appeared special detective agencies who spied on the professional players, collected the necessary information about them and distributed it among the casinos.

Uston created new methods of the game, used makeup, recruited more and more people in his teams and started playing abroad. He also was writing new books, was starring on TV, was writing new articles, was developing new counting systems. By the way Ken, wrote the book on optimal game strategy for Pac-Man (arcade video game). It’s a video game not for money, he was just interested in it.

One of the most scandalous Kenny’s projects was creating the team against the casino with using the computer. They used hidden on the body and in the shoes micro chips that calculated the current situation in the game more precisely than any other “human” strategy and gave the necessary signals to the player. His teams almost broke several casinos, but in a while they were caught, arrested and accused of fraud, the computer was confiscated. However, the experts including FBI experts, proved that there was no fraud and the accusations were withdrawn. In two weeks the Supreme Court of the USA of Nevada State made the usage of computing devices in casinos illegal…

Kenny was a good guy, the heart of the company, first class jazz musician, loved by women and press. He had great plans on making a film, writing new books, arranging one more trial, and surely new projects on blackjack. His life was suddenly interrupted in 1983 and the version that casinos are privy to his death is not cast back yet.

Casino Games History Or How People Have Learnt To Count Cards Part3. is a post from: Online Casino Blog

Being a young scientist, Edward O. Thorp regularly read mathematic journals. When he was a student, he was pressed for money. The idea of outplaying the casino on the basis of calculations appealed to Thorp and he decided to check the results of the “excellent four” and see what will come out of it. The result of his activity was a phenomenal book Beat The Dealer, now its sales are approaching million of samples.

Thorp chose the other way – he did not make analytical calculations, but with powerful at that time computer IBM (they were also called mainframe) he wrote several programs on Fortran, creating quite original methods for 60s. By the way, Thorp together with his research instructor Claude Elwood Shannon, a great scientist, were also involved in solving the problem “how to outplay the roulette?”

From his calculations Thorp understood that dead cards had a considerable affect on the gambler’s chances this or that way. His main idea was about memorizing the dead cards in somewhat simplified way and when the situation is beneficial for the player, make high stakes. By the way, this system still remains the basis of any methods and counting systems of blackjack.

The counting system introduced by Thorp, was rather complicated for usage in real casinos, required great concentration and large amount of mentally arithmetic actions. However with good training there was nothing impossible in its application.

Thorp’s book immediately became a success and bestseller. Everyone understood that with quite simple actions you can get an advantage. Every reader dreamt of enormous prizes. However, the casinos also knew the score.

Panic seized them. And in 1962 after Thorp’s book, all Las Vegas Casinos without exception changed their rules being afraid of mass influx of “system players”. The quality of the rules worsened terribly and no counting system could ever help you to win. Though the effect for casino turned out to be quite unpredictable and reverse – people stopped playing blackjack. And during several months, all the casinos had to return to the former rules for their own survival.

Another interesting effect caused by Thorp’s book- incredible popularity of blackjack outrunning the favorite American craps. A lot of people, after reading the book considered themselves potential winners and rushed to the blackjack tables. However, most of them had a bad understanding of the mathematical principles of the game did not become winners but quite vice versa. Therefore, casino got more clients and moreover losing clients. Since then their number is only increasing.

The system presented in the first edition of Thorp’s book was quite difficult even for professionals and only the few could apply it under the conditions of a real game. Something should be simplified.

The power behind the throne.
Julian Braun is quite a unique personality. He had hardly ever played a deal in real blackjack. But he played millions and maybe even billions of deals on the computer. Braun was a good mathematician and programmer and he got interested in Thorp’s idea and offered him cooperation in the sphere of calculations and programming.

Braun became the person who first invented the counting system Hi-Lo. He was behind the development of all modern systems the authorship of which belongs to Revere, Humble, Wong and Uston. He wrote the only book How to Play Winning Blackjack, but what a book!

Braun upgraded Thorp’s system on FORTRAN and made considerable changes and the second edition of Thorp’s book also contained Hi-Lo system in its modern form. It was quite a revolution in gambling world. Braun worked in IBM corporation and had access to probably most powerful computers of that time. This fact helped to build simple and efficient tool in struggle with casino.

Using Braun’s calculations the gambler mostly known as Lawrence Revere developed his own counting system and presented his results in the form of convenient tables which are applied in most counters of the world. Lance Humble based his HiOpt systems on Braun’s experience.

Regardless the fact that Julian most probably had never been to the casino, he became a power behind the throne of the blackjack and all the mathematical modeling of the game fell on him.

Casino Games History Or How People Have Learnt To Count Cards Part2. is a post from: Online Casino Blog

The most famous achievement in the sphere of “system” game against the casino was the so called “card counting” at blackjack – mathematically based methods of game allowing to get some advantage over the casino. The casinos, surely, knows about the existence of “counters” and are trying to oppose them – from changing the rules to banning the game. Sometimes even exceeding the limits of reason and legality. In fact, all the history of the blackjack is the struggle between the gamblers and the casino which is more clever.

More than half a century passed since the first attempts of beating the casinos in blackjack, based not on the marked cards and intuition. There has been a peck of salt eaten since then, but the struggle is still going on…

Mammoth.
Probably the first person in history who applied mathematic analysis to the game blackjack was Jess Marcum (originally Marcovitch) was born on 30th December 1919.

It happened at the turn of 1949 and 1950, when Jess, being an excellent mathematician and physicist-theorist got to Las Vegas. Then his mathematic flair prompted him that most possibly not everything depends on intuition in blackjack.

Marcum started analyzing blackjack. First, the uniqueness of his attempt is that he performed absolutely all calculations with his pen on the paper, on principle without using any technologies whatever weak they might be at that time. Second he had found the solution!

Jess manually developed what is now called basic strategy and counting systems ten years before someone else has done that. He counted that theoretically he had an advantage over the casino of about 3% – under the conditions of that time it was quite real. Moreover, Markum had been playing blackjack in all known to him casinos- both in the USA and abroad. His name appeared on the pages of the newspapers as an example of “lucky man” who managed to hit the jackpot.

Jess Markum also went down to history as probably the first man thrown out from the casino because of cards. Though at that time casinos did not understand that such system existed. Jess lived in Las Vegas for about a year. The casino owners exchanged the information when they gathered at the general meeting. And they were terrified. After that Markum was not admitted at all Vegas casinos. He went to Reno. The same story- in half a year after unbelievable “luck” the casino owners started making inquiries about the incredible gambler. Then other states and cities. Then Cuba, the Bahamas. Nobody knows how much money he has won during that time. One thing is known for sure- in fact, Jess Markum started the war between the gamblers and casinos in blackjack, that is still going on and getting more and more strained.

He did not share his calculations with anyone, and completely gave up playing against casino after a wide public publication of blackjack methods by other authors.
Jess Markum died in 1992, at the age of 72.

The four of Neanderthals.
The next effort of great influence on the blackjack math was made in 1956 by the group of four mathematicians- Roger Baldwin, Wilbert E. Cantey, Herbert Maisel and James McDermott.

These people had never played in casino before, having spent a great number of m/hr, they created basic strategy of playing blackjack according to the most popular at that time rules and published it together with the calculation methods in the specialized math journal for statisticians – Journal of the American Statistical Association entitled “The Optimum Strategy In Blackjack”.

They made several slight mistakes in calculations which is nothing serious taking into account their enormous contribution. A year later they issued a small book Playing Blackjack to Win, which is now a bibliography rarity.

In fact their book and the article did not spark much furor, and remained almost without attention regardless of their innovative approach. However, the word almost turned out to be the key for all the gambling industry, as someone did paid close attention to the research of the excellent four.

Casino Games History Or How People Have Learnt To Count Cards Part1. is a post from: Online Casino Blog

Besides, as has been mentioned, Thorp, while building his strategy presumed that cards were not often shuffled, in particular, if after finishing of a regular game there were still cards left in a pack, a croupier did not collect the thrown-away by the gamblers cards but dealt them anew (and the next game was played), and only after complete exhaustion of a pack, an official of a gambling house collected all the cards, thoroughly shuffled them and a new “cycle” began. Naturally, if a gambler had a good memory he could change his strategy depending on the knowledge of the cards which had gone out of the game, and what cards could still be counted upon. It is important to remember that a croupier himself who was to strictly follow the directions of the casino’s owners practically without changing his strategy!

Thorp set himself a task to formulate the rules which would allow him to calculate probabilities of taking out one or another card out of an incomplete pack. Knowing these probabilities a gambler could already with reasonable assurance draw cards from the widow without being too much afraid of “a pip out”, and besides, on the basis of the knowledge of some aspects of a croupier’s strategy to make suppositions about those cards which he had, and other gamblers as well. Naturally, as a gambler was to make a decision with regard to a widow very quickly, the sought rules for calculation of probabilities were to be rather simple for a gambler to be able to use them “in mind” with the help of neither a calculator, nor a pen and paper (even if we suppose that a gambler will be given a chance to do calculation on paper, it will certainly arise suspicion). Edward Thorp managed to solve this mathematical problem having created rather simple algorithms for calculation of probabilities of taking out of one or another card from a pack, and using them to build a strategy of the game of twenty-one which would not be very complicated, allowing a gambler to considerably increase his chances of winning!

As the Hungarian mathematician A.Reni states after a few days of presenting his report on the obtained results at the meeting of the American Maths Society in 1960 in Washington “Thorp received from a businessman a letter with a check for 1 thousand dollars intended for checking of a winning strategy in practice. Thorp accepted the check and having learnt the formulated by him rules left for Nevada to try his discovery. The trial went well: less than after two hours Thorp won 17 thousand dollars.

Needless to say, the owner of a gambling house didn’t share Thorp and his companion’s delight with regard to a successful comeout of the trial and the next day did his best to prevent Thorp from joining in the game. Later on Thorp tried to penetrate into other gambling houses, but the news of him had already spread far and wide, so that the doors of all the gambling houses appeared to be closed for him. Several times having adjusted a fake beard or having got a make up of a Chinese, Thorp managed to get to the gaming-table, but in any disguise his constant gain invariably gave him away. Thorp had to refuse from further checking of the strategy developed by him”. Though “additional checks” were “necessary” only to enrich the pockets of the talented mathematician. One could hardly doubt that E.Thorp managed to create a real winning strategy!

However, since he could no longer benefit from his discovery himself, he decided to render “welfare assistance” to his colleagues having published in 1961 a small article in an American academic journal (Thorp E.O. “A favourable strategy for twenty-one”, Proc.Nat.Acad.Sci., 47, 110-112, (1961)). And despite the small size of the article and, consequently, an extremely condensed form of persentment, made it comprehensible for rather a narrow group of professionals, one can be sure that a number of American scientists and their friends certainly “improved” their material situation (owners of gambling houses were unlikely to read scientific magazines at that time).

Casino Games And Mathematics. Part Two. is a post from: Online Casino Blog

This defines what will be paid by a blow to the line of machines and what the final percentage. Traditionally, the more you go on the name in a slot, the better the rate is fixed. So, how can you win? In a machine vision due to impaired glucose tolerance, the difference is as follows. The percentages in the line of charges are much smaller than a conventional machine, since some percentage of vision added bonuses. The bonus, which is usually in the video display, can be very different. Have you ever had one picture of a cartoon looking for a cherry pie on a monitor in the top of a slot machine Cherry Pie? Or a picture of a diamond mine that is a little cartoon to see the screen flashes during playback.

If you want to play casino games, you can visit our website.

Threshing machines casino slot – How to beat the slot machines at local casinos is a post from: Online Casino Blog

Although each number has an equal chance to demonstrate at every opportunity, you will see that all 36 numbers, when the wheel rolled 36 times in a row. There will always be a number that once more and shows a pair of numbers, does not appear. Andrucha system offers a series of eight times shown, until all the numbers from 1 appears to 36. These tips are how to win at roulette requires patience and complete record so that you can know what the winning number, the eight times, until you see all the numbers appear. If you want to get information about usa online casinos, you can visit our website.

How to Win at Online Roulette – Roulette winning a system with simple strategy roulette is a post from: Online Casino Blog

First of all, casinos’ owners understood at last that it was necessary to introduce the following obligatory point into the rules of the game: cards are to be thoroughly shuffled after each game! If this rule is rigorously observed, then a winning strategy of Thorp cannot be applied, since the calculation of probabilities of extracting one or another card from a pack was based on the knowledge of the fact that some cards would already not appear in the game!

But what does it mean to have “thoroughly shuffled” cards? Usually in gambling houses the process of “thoroughly shuffling” presupposes the process when a croupier, one of the gamblers or, that is still oftener seen of late, a special automatic device makes a certain number of more or less monotonous movements with a pack (the number of which varies from 10 to 20-25, as a rule). Each of these movements changes the arrangement of cards in a pack. As mathematicians say, as a result of each movement with cards a kind of “substitution” is made. But is it really so that as a result of such 10-25 movements a pack is thoroughly shuffled, and in particular, if there are 52 cards in a pack then a probability of the fact that, for instance, an upper card will appear to be a queen will be equal to 1/13? In other words, if we will, thus, for example, shuffle cards 130 times, then the quality of our shuffling will turn out to be more “thorough” if the number of times of the queen’s appearance on top out of these 130 times will be closer to 10.

Strictly mathematically it is possible to prove that in case our movements appear to be exactly similar (monotonous) then such a method of shuffling cards is not satisfactory. At this it is still worse if the so called “order of substitution” is less, i.e. less is the number of these movements (substitutions) after which the cards are located in the same order they were from the start of a pack shuffling. In fact, if this number equals to t, then repeating exactly similar movements any number of times we, for all our wish, can not get more different positioning of cards in a pack, or, using mathematical terms, not more t different combinations of cards.

Certainly, in reality, shuffling of cards does not come down to recurrence of the same movements. But even if we assume that a shuffling person (or an automatic device) makes casual movements at which there can appear with a certain probability all possible arrangements of cards in a pack at each single movement, the question of “quality” of such mixing turns out to be far from simple. This question is especially interesting from the practical point of view that the majority of notorious crooked gamblers achieve phenomenal success using the circumstance, that seemingly “careful shuffling” of cards actually is not such!

Mathematics helps to clear a situation with regard to this issue as well. In the work “Gambling and Probability Theory” A.Reni presents mathematical calculations allowing him to draw the following practical conclusion: “If all movements of a shuffling person are casual, so, basically, while shuffling a pack there can be any substitution of cards, and if the number of such movements is large enough, reasonably it is possible to consider a pack “carefully reshuffled”. Analyzing these words, it is possible to notice, that, firstly, the conclusion about “quality” of shuffling has an essentially likelihood character (”reasonably”), and, secondly, that the number of movements should be rather large (A.Reni prefers not to consider a question of what is understood as “rather a large number”). It is clear, however, that the necessary number at least a sequence higher than those 10-25 movements usually applied in a real game situation. Besides, it is not that simple “to test” movements of a shuffling person (let alone the automatic device) for “accidence”!

Summing it all up, let’s come back to a question which has been the headline of the article. Certainly, it would be reckless to think that knowledge of maths can help a gambler work out a winning strategy even in such an easy game like twenty-one. Thorp succeeded in doing it only by using imperfection (temporary!) of the then used rules. We can also point out that one shouldn’t expect that maths will be able to provide a gambler at least with a nonlosing strategy. But on the other hand, understanding of mathematical aspects connected with gambling games will undoubtedly help a gambler to avoid the most unprofitable situations, in particular, not to become a victim of fraud as it takes place with the problem of “cards shuffling”, for example. Apart from that, an impossibility of creation of a winning strategy for all “cases” not in the least prevents “a mathematically advanced” gambler to choose whenever possible “the best” decision in each particular game situation and within the bounds allowed by “Dame Fortune” not only to enjoy the very process of the Game, as well as its result.

Casino Games And Mathematics. Part Three. is a post from: Online Casino Blog

One can often hear that the best piece of advice given by a mathematician to a lover of gambling games is an assertion which lies in the fact that the best strategy in gambling games is complete abstention from participation in them. A lot of mathematicians consider that the most which the theory of probability and the theory of games can give a gambler are the strategies following which he won’t lose too much.

It is difficult to predict whether the American mathematician Edward Thorp shared this view, when once spending winter holidays in Las-Vegas, he, having entered a casino, decided to try his luck in the game of twenty-one. As it turned out, “Dame Fortune” was extremely unkind to him. We do not know for sure what amount of money this teacher of mathematics of one of American universities lost that winter night at the end of the 50-s – the beginning of the 60-s of the last century, however, judging by the following events the amount was not small. Otherwise, how can we account for the fact that development of an optimal strategy of this game became for a number of years an “idte fixe” of our hero. Besides, the matter was not only in the quantity of money lost by the mathematician. Perhaps, Thorp was simply an extremely venturesome person, and his pride both of a gambler and an expert-mathematician was hurt. Besides, he could suspect a croupier of dishonesty, since, as he had noticed, cards were not shuffled after each game. Though, during the game itself it did not make him very uneasy. However, afterwards, having visited casinos a number of times, he noticed that as the rules did not presuppose obligatory shuffling of cards after each game, so it was difficult to accuse a croupier of anything. Anyway, he managed to develop a winning strategy in the game of twenty-one.

This strategy among other things was based on the same very aspect which had put a defeated mathematician on his guard – cards were not shuffled too often. At that, this, apparently, as a rule, was done not because of some evil design, but in order to avoid, so to say, unnecessary slowdowns in the game. The results of his studies Edward Thorp put forth in a book published in 1962 (Thorp E.O Beat the dealer. A winning strategy for the game of twenty one. – New York: Blaisdell,1962.) which made owners of gambling houses in the state of Nevada essentially change the rules of the game of twenty-one. But let’s not ride before the hounds.

In accordance with the game rules of twenty-one of that time one croupier dealt gamblers two cards each out of a thoroughly shuffled pack consisting of 52 cards. Gamblers themselves did not show their cards to a dealing croupier. At the same time out of two cards taken for himself an official of a casino showed one of them (usually the first one) to gamblers. Gamblers evaluate their cards according to the following scale. Jacks, queens and kings have a value equal to 10 points, an ace could be assigned either 1 point or 11 points, the value of the rest of the cards coincided with their numerical value (eights had 8 points, nines took 9, and etc). That gambler was considered a winner who had cards on hand with the sum of points closest to 21 from the bottom. At that, having assessed the received cards every gambler (including a croupier) had a right to take from a pack or putting it simpler, take a “widow”, any amount of cards. However, if, as a result, the total number of points after a widow, will exceed 21 points then a gambler must drop out of a game having shown his cards.

Special rules were established with regard to stakes. Initially, upper and lower bounds were set, and every gambler had a right of choice of a specific stake (within these bounds) depending on the evaluation of his position. If, as a result, it turned out that in accordance with the game rules a casino’s visitor had a “better” number of points on hand than a croupier had, he received a gain in the amount of the stake that he had made, otherwise, this gambler lost his stake. In case of an equal number of points of a gambler and a croupier, the game ended in peace, that is the result of the game is considered “harmless” both for a gambler and a casino.

Let’s point out that unlike ordinary gamblers a croupier is not obliged to open his cards in that case if the number of points in these cards exceeds 21. Moreover, after all the gamblers have opened their cards, and therefore, all the stakes go to a casino gamblers cannot practically find out what was the number of points of a croupier, in order to build their game strategy for the next game (whether to risk or not to stand pat, and etc). It goes without saying, it gives a croupier considerable advantages. Besides, all the gamblers are surely aware of this, and, … continue to play. Nothing can be done about it, who does not take risks, as is known, does not win.

Casino Games And Mathematics. Part One. is a post from: Online Casino Blog

The casino’s electronic versions of the regular games are also quirky and fun. There are serious video poker players who stake out the high-paying machines, and gamble only on them. Those who watch a serious video poker player long enough will learn some of their strategies, like the “Jacks or better” version where players favor hands, as the name implies, with a face card in it.

Casino dice games are exciting, but sometimes complicated. Variations include “street craps,” “bank craps” and what some people call “Grand Hazard”. It’s good to know what version of game is going on at the table before you lay your money down. Is the casino paying winners who roll seven or eleven? Or are you gambling, roulette style; on the numbers that come up on the dice roll?

Roulette is said to be one of the most challenging games in the casino. The roulette wheel has up to 38 numbered positions for the little ball to land in. You can start your gambling on a single number, odds or evens and other combinations. If you are a beginner, it’s best to research this one online or at your local bookstore first, as the game can be not only mesmerizing, but also expensive for a beginner.

Casino games are fun, but sometimes it’s a good idea to research first, learn the rules, and then go to the casino armed with your understanding of the rules. This insures maximum fun and a good night out. So what are you waiting for? Familiarize yourself with casino rules and get started having fun!

Casino Games – There Is Something For Everyone is a post from: Online Casino Blog

Nickel slots are by far the most inexpensive way for a newcomer to learn the ropes of casino slot machine gambling. Many of the features are the same, and there are tricks and techniques the seasoned gambling aficionado uses to increase fun and, yes, payoffs. Nickel slots may offer lower payouts, but there is still nothing like the thrill of hitting the jackpot, no matter what machines your casino offers.

Casinos feature just about everything; ‘single coin’ machines, dollar, and progressive slots. The single coin machines are just what their name implies; you are gambling one nickel, quarter, or dollar coin. The dollar slots have a feature where you can play either one coin or more until you reach the maximum bet. (Some dollar slots take up to six quarters, sometimes even more to reach the max). These slots usually have higher payouts depending on how many coins you play. Those used to gambling that maximum amount usually get the best jackpots.

Progressive slots are another type altogether. This is a machine that increases its’ big jackpot depending on how much gambling money has been inserted into the machine up to that point. Some progressive slots are tied to other machines, while others are standalone. Smart players check the readouts on progressive slots until they find the machine with the highest payout. Be sure to double-check the casino guidelines on each machine, as the big money usually doesn’t come unless you bet the maximum.

No matter which machines you prefer; take your time, read the instructions and stick with your spending limits. If you maintain financial control, you will have quite a bit of fun. In fact, you’ll have a blast!

Casino Games – Slots is a post from: Online Casino Blog