Casino Is The Temple Of Games.

An individual plays only when he is human in the full sense of the word, and he can be wholly human only when he is playing”. Friedrich Schiller

The history tells us that in 49 B.C. the famous ancient Roman commander Julius Caesar, having won brilliant victories over barbarian galls, wanted to seize supreme power in the Eternal City. Then the frightened senators forbade him and his troops to return to Italy.

Without hesitations, the commander announced about his decision regarding the senate ban by saying “Alea jacta est” (“The die has been cast”) and crossed the border river Rubicon. This led to lingering civil wars in Rome, which became one of the most significant events in ancient history.

The words of the ferocious dictator became proverbial, however, today there is hardly a person who thinks about its real meaning. As it turned out, the Great Caesar actually cast the dice. So great was his passion to gambling, that he deeply believed in the magic ability of the dice to predict the future.

The public opinion hardly favors gamble and everything connected with it. Conversely, in those times the word “player” was nearly a swearword – so huge was the contempt of the majority of people to those who gave the game its due.

But at the same time ancient people understood perfectly well that the thirst for gambling could not be eradicated. The Greeks with their characteristic rich imagination invented a myth about the goddess of the fate Tyche (the Romans called her Fortune”), who gave birth to Zeus’ daughter, and this girl was endowed with the gift of inventing various dangerous amusements, which caused the people to lose a lot of money, cheat, scuffle and committed suicides.

Tyche loved her daughter and thus winked at her cruel pranks. She even presented her with a large beautiful house, to which her daughter allured the most credulous players to make them miserable.
More than two thousand years passed since those times, and today hardly anyone believes in fortune-telling by throwing lot and myths about the goddess Tyche, but there is one thing that has not changed. It is the human need for the game. This unquenchable desire stipulated for the fact that in the course of time special premises were built for gambling as if the ancient Greek legend came true.

In these establishments visitors played with each other in these and paid a part of their winnings to the owner – or played with owner and then, if they lost, they were to pay the whole amount of the bet to the casino owner. Approximately in the 16th century such establishments came to be called by the Italian word “casino”, which has not changed its meaning up to now.

Gambling houses irrepressibly attracted people with different characters, different talents and varying financial possibilities. The list of famous casino frequenters, compiled by the largest casinos in Europe, includes such celebrities as chancellor Bismarck, composers Berlioz and Brahms, the writer Dostoyevskiy, the poet Mayakovsky and the automobile king Citroen.

Reverberating fame, however, did not prevent these people from insidious tricks of Fortune. Admittedly, some celebrities were often lucky and they won a lot. For example, Citroen was such a lucky player. He loved to play for high stakes, in order to impress other rich men. Journalists never grew tired of writing that the automobile king is as lucky on the green cloth, as in business.

Others mostly lost. For instance, Mayakovskiy was such an unlucky fellow. He loved billiards, cards and particularly the roulette. During his trips abroad the poet run into unprecedented debts, because he was lucky only at billiard table, but by no means in the roulette.

Gambling houses are known not only by their frequenters, but also by various legends that surround these establishments. The most enduring is the story how a certain Frenchman monsieur Blanchard won twice in “Casino Monte-Carlo”. When he intended to enter this casino for the first time, his hat was spoilt by the dove. Blanchard interpreted this as a good sign and was right. The player managed to win several thousands. Then he intended to go to casino once again, but on condition that a bird would spoil his hat for one more time.

He had to wait for the new dove for several days, but his expectations paid for themselves. The Frenchman was lucky that time and he won even more than before. After this, the doves displayed no interest in Blanchard and he could not win. However, all inveterate players believe that if the bird marks you before the visit to the gambling house is a true sign of good luck.

Choosing The Right Casino In Albuquerque For Gambling

Today, there are a number of casinos that are in or near Albuquerque that gamblers can play at. With so many local choices, there is little need for gamblers to go to Las Vegas in order to get exciting gambling action. Because there are so many choices in the state of New Mexico for casino gambling, it is helpful for players to figure out which casino to patronize. Choosing the right casino can make playing a lot more fun. And it can make gambling more rewarding as well. That is why it is important to choose well when looking for the right casino in Albuquerque to play at.

First of all, the casino in Albuquerque should have the games that the player wants to play. For example, a video poker player will want to make sure that the casino has a good selection of video poker machines. Those who want to play with slot machines should choose a casino with many different choices. Table players will want to make sure that their favorite games are offered. Most casinos will offer blackjack, roulette, and poker at a minimum for table players. Many also offer craps for those who like that game.

Secondly, the casino in Albuquerque should have a decent player’s reward program. A good rewards program will make it more fun to gamble at a particular casino. Although a rewards program will help enhance a gambler’s return on playing, players should also concentrate on the fun aspects of the rewards program as well. Many programs offer free show tickets, free meals, and free tournaments in order to entice players to return. High rollers often great special treatment with most casino rewards programs. Being treated like a VIP can be a great way to enhance the experience of gambling at a casino. Of course, it is also important to evaluate the cash bonuses that are offered by the program as well. Some casinos will offer more generous cash bonuses than others.

Another important criteria when choosing a casino in Albuquerque is look at the returns of the games being played. Most gamblers know that the house has an advantage at most or all of the games. However, a gambler will have more enjoyment when the house edge is lower. On a slot machine, it is usually impossible to figure out what the return is. However, it is possible to calculate the house edge on games such as craps, blackjack, poker, roulette, and video poker by looking at the payouts. Going to a casino with better payouts means the gambler’s money will last longer. That means more enjoyment. And that also means a higher chance of hitting the royal flush jackpot for video poker players.

When choosing a casino, many people prefer to stay at the casino’s hotel. That makes it easy to access the gaming over multiple days. Many gamblers prefer to stay at hotels that have higher quality rooms such as suites. In many cases, the casino’s reward program may offer free rooms to frequent gamblers and high rollers. It would be better to choose a casino with nicer hotel rooms if the casino is giving away free rooms. Other hotel amenities such as a spa and restaurant options may be important to some gamblers as well. Many gamblers find that they need a break from the gaming from time to time. Choosing a hotel casino with extra amenities can be well worth it.

There is a lot to think about when gamblers are choosing a casino to play at. If gamblers concentrate their play at a single casino, they can often get better rewards from the casino’s frequent gambler program. That is why it is beneficial to choose a single best casino at the beginning. And the best part is that there are a lot of great casino choices that are in or near the Albuquerque area.

Slot Machines For Casino Gambling People

There’s a lot of available games to play inside a casino whenever somebody wants to go Casino Gambling. A gambler could pick to play card games, roulettes, and other games that have evolved over time. But among these, slot machines remain to be one of the favorites of people who love Casino Gambling.

Slot machines have been around almost instantaneously as casinos. The very first machine was created in 1887. It featured the commonly known configuration of the machine. This one-armed bandit” was also able to feature an automated system that enabled it to simplify the payout mechanism of the machine. This became popular and soon found its way into every local bar or saloon at that time. Thus, possibly initiating the beginning of Casino Gambling.

Today, variations in the popular machine have become an act of creativity for its developers. Different machines come up with very different themes. The variations could go as creative as using pirate themes, geometric shapes, just to name a few. This is probably the reason why in Britain, slot machines are more commonly called as the fruit machines”. But whatever theme developers might come up with, the basic principle behind it still remains. The characters and the number of lines might change, but nevertheless, they still follow the original game structuring of its origin. It adds to the flavor of course, that Casino Gambling people are able to enjoy the machines they are betting on, given that they have evolved to become more fun.

The development of the slot machine did not come without myths surrounding it. Some Casino Gambling people believe that certain machines become either hot” or cold”, depending on the number hits or wins a particular machine has given. Although myths such as this have crept its way throughout different places, the odds of winning on a standard slot machine is determined by an RNG or Random Number Generator. This means that on standardized machines, the odds of winning is always the same.

There are however, some machines that are specifically programmed to increase the probability of winning. Depending on the state laws that govern a particular casino, Casino Gambling on slot machines are required to give out what is called a payout percentage. Usually, the payout percentage is somewhere between 82 to 98 percent. But in the case of Nevada where state laws are not the same as others, the baseline payout percentage of machines is set to 75. This means that supposing one spin costs $1, after 1,000,000 spins have been played, the machine should have at least returned an average of $750,000 to the players. And so goes for other machines that have a different payout percentage set.

Other machines that are commonly seen when going Casino Gambling are those that give out huge jackpot prizes. The machines that could give out as much as $7,000,000, are linked in a network of different machines. The network could also extend to other casinos, enabling a link between one casino’s slot machines and the other’s. However, because of the large jackpot prize being allotted by these systems, the usual case is that the payout percentage is smaller than the one from a single machine.

Casino Gambling is still predominantly based on probability. Although this is sometimes preset by programs that are usually required by state laws, the odds of winning on a slot machine and any other Casino Gambling endeavor still requires a certain amount of luck to pull off.

Casino Games And Mathematics. Part 1.

Can the knowledge of mathematics help a gambler to win?

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 2.

Thorp managed to find out that owners of gambling houses gave their officials rather strict directions with regard to the strategies which they should stick to in the game with visitors. Control over fulfillment of these directions had its initial aim to prevent from a frame-up of a croupier with the rest of the gamblers, a chance of which could not be excluded. Assigned for a croupier strict rules determining his game strategy really substantially reduced a probability of such a frame-up, but on the other hand, allowed an advanced” gambler to rather adequately reveal the essence of this strategy and effectively oppose it. For unlike a croupier a gambler needn’t show the first of the received cards, as well as isn’t enchained by any strict rules as regards his strategy, that is why flexibly changing his behavior he can confuse a croupier. For example, Thorp found out that practically in all gambling houses of Nevada State croupiers were strictly ordered to keep away from a widow in case the amount of points in his cards exceeded or was equal to 17, and a player, from our mathematician’s point of view did not have to miss an opportunity to make use of the knowledge of even some aspects of a croupier’s strategy for achievement of his aims. Thus, those advantages which had an official of a gambling house from the start (as we already know, he is not obliged to open his cards at the end of the game), can be compensated to a certain degree for the knowledge of a player about the strategic “tunnel vision” of a croupier.

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).