Casino Gambling

Casino gambling can be fun and exciting. At the same time expensive. Dependent on how much you are willing to gamble. It is important to keep in mind your specified budget. As it is very easy to get carried away when you are in the casino, you have to take care that the next thing you know, you haven’t gambled everything away and now you are down to your last penny. Before you get to this scenario, stop, think and walk away or quit casino gambling.

The first rule in casino gambling is to know the game. Casino gambling can be difficult if you are not sure about the rules of a game. For instance, if you want to play baccarat but don’t know exactly what baccarat means it is better to stand back, watch and learn the game first before you try your luck. Another golden rule that you should observe in casino gambling is to not gamble more than you can afford. Always know how much you can spend before you step foot in a casino and don’t risk any more than that.

Do not indulge in casino gambling with the aim to get rich. If you do, you will only be disappointed. And you may lose more money than you care to. Casino gambling should be for fun and entertainment. In casino gambling you should not hand a dealer the loose change. Willingly you place it in the table. If you find that your dealer is rude, then leave the table and play elsewhere. You should not put up with bad service. You can avail yourself of free casino gambling lessons. You could try casino gambling in the morning when there are less people in the casino. You could try casino gambling in the morning when there are lesser people in the casino. This way the dealer could offer you assistance when you are new to the game. In casino gambling you should not up your stakes to cover your losses. You may lose big time if you do. You can up your stakes when you are winning so you use the casino’s money instead of your own.

There are strategies you can use that can reduce the house’s edge but you can never beat the house. Another to watch out in casino gambling is the game called keno. This may be a simple game but the odds are always in favor of the house. If you are new to casino gambling, you should look for a casino that lets you play with lower stakes. This way if you commit mistakes, your losses will be smaller. The posh hotel-casinos located on the Strip in Las Vegas generally have higher minimums compared to those in the downtown area.

Casino gambling is a good way to add some exitement and break the monotony of your life. Casino gambling gives you an opportunity to engage your senses including your mental abilities to focus on the game. Casino gambling can be a good source of entertainment. You should not view casino gambling as a get-rich-quick scheme. But just like any endeavor, it should be taken in moderation. Anything that is done in extremes could be detrimental to the purpose casino gambling is aimed for- which is to provide release of stress and pleasure. Gambling, done in the extreme can become an addiction, so play in moderation and have some fun.

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).

A Closer Look At Positive Expectation

What do I mean when I refer to an over 100% machine?” An over 100% machine simply means a machine that pays back more than you put in. Fantastic, except for one thing: this is factored over a long period of time. It does not mean over 100% in every session.” In fact, an over 100% machine isn’t guaranteed to earn you a profit even over what most would consider a long period of time. And it’s certainly not graphed by a steady upward curve. The only sure thing I’ve ever found in casino gambling is streakiness, and video poker results can be as streaky as it gets.
Also, and this is a very important concept to grasp: whether or not you achieve that over 100% return depends on the number of royals you hit. A royal contributes approximately 1.7%-2% (depending on the game) to the total payback percentage, and you only hit a royal about once every 35,000- 45,000 handssome 80 hours of play. So during those other 79 hours, even if you’re playing a deuces wild machine with a 100.76% payback percentage and accruing .5% slot club cash back for your play, that 1.8% you lose for not hitting the royal pretty much wipes out your advantage during the periods in between the big jackpot. During these periods, you will most likely lose money (positive expectation is sweet, but it usually doesn’t come easily). That’s why it’s necessary to analyze situations in terms of what mathematicians call expected value” or expected return,” which assumes an infinite period of play.
Okay, with that groundwork laid, here are a couple of examples of positive expectation readily available in any number of casinos in Las Vegas at any given time.
Playing full-pay” deuces wild with computerperfect (optimal”) strategy, the return percentage is 100.76%. Another way to say this is: for every $100
you put into a full-pay deuces wild video poker machine, you’ll get back $100.76. It may look skinny,” but that’s a pretty good edge. Unfortunately, only a computer can play computer-perfect strategy. Humans make mistakes. They get tired of sitting and staring at a screen. They get a little fuzzy from the free drinks. The guys get distracted by short skirts on cocktail waitresses. I figure skilled human strategy on a full-pay deuces wild machine is more like 100.5%. In these examples, my numbers are based on that one-half-percentage-point advantage.
Playing 25 full-pay deuces, you’re making $1.25 bets (five quarters). If you play slowly (say 320 hands per hour), you’ll put about $400 through the deuces wild machine in 60 minutes. At our skilled human capability of 100.5%, over that hour your expected return is $402 (1.005 X $400 = $402). Thus, your expected return (or win) is $2 per hour. Don’t quit your day job!
Example 2. This time you’re playing $1 deuces wild with skilled human strategy, but you’re playing fast (600 hands per hour). Betting $5 per hand, you’re putting $3,000 through the machine per hour. Now your .5% positive expected return produces $3,015; over the long term you’ll take in $15 per hour. That’s like a $30,000-a-year paycheck.

A Closer Look at Negative Expectation

The flip side of positive expectation is, logically enough, negative expectation. An under 100% machine” is a machine that pays back less than you put in. Let’s say you find a 25 deuces wild machine that has only one change in the pay table from the full- pay deuces schedule. A key changeit pays only four coins for four-of-a-kind instead of five. That’s just one tiny alteration, but it gives the house a whopping 5.7% edge. This means that you’re playing a game that returns only 94.3%. Now if you play a slow 320 hands per hour, you’re losing $22.80 per hour (.057 X $400)and that’s on a 25 machine.
Does the $2-per-hour profit from full-pay deuces look better to you now? And does the $22.80-per- hour loss convince you to read pay tables carefully? The main reason for all the new video poker variations is that casino know there are a lot of players with a little bit of video poker knowledge. Many people now know that full-pay jacks or better and deuces wild are good games, but they’re not real careful about reading the pay tables to make sure that full-pay is what they’re playing. Point them toward any jacks or better or deuces machine and they assume it pays liberally. The casinos, of course, make sure that they aren’t: Play this game. It’s almost like the other one that pays a lot more.”
This occasionally backfires on a casino when it monkeys with a pay schedule of a well-known machine and the changes result in a larger payback percentage. If you become a true student of the game, you’ll be able to spot these situations, know what changes to make in the strategy, and take advantage to make a lot of money on these machines, until the casino wises up and fixes the schedule or removes the machines entirely.

Jacks or Better

Jacks or better is the basic video poker game. One of the first to come out, it’s considered something of a video poker standard. The full-pay version is known as 9/6 jacks or better, meaning the payback (with one coin in) for a full house is 9 coins and for a flush is 6 coins. Sad to say, there are not a lot of them outside of Las Vegas. Full-pay jacks or better has a return percentage of 99.5%. It’s not a positive game; as we’ve seen, the casino has a .5% advantage. But because it’s readily available in Vegas and a lot of other video poker variations are derived from it, I also consider it the standard. Often you get enough cash back from the slot club or a promotion to make jacks or better an over 100% game.The first chart is what the pay table for a 9/6 jacks or better video poker machine looks like. The second is also a jacks or better pay table, but with a crib- cal difference: it’s an 8/5 machine. Note the difference in the payouts for full house and flush; this lowers the return to 97.3%.
As I mentioned earlier, I’m not going to provide you with the strategies, which are readily available in any number of books and computer software programs. See the Appendix for recommendations.

Casino Games And Mathematics. Part 3.

After one more year Thorp published a book (I mentioned it at the beginning of the article) in which he rather in details, in the form comprehensible to any even a slightly literate and sensible person, set the rules of formation of a winning strategy. But the publication of the book did not only cause a quick growth of those willing to enrich themselves at the cost of gambling houses’ owners, as well as allowed the latter ones to understand the main reason of effectiveness of the developed by Thorp strategy.

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 t 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 Gambling: When Fun Becomes Dangerous

Summer’s here! Probably, most people are all packed-up and ready for their holiday vacation. It may be a trip to an exotic Caribbean resort, a beautiful city somewhere in Europe or any wonderful place just to get over the summer heat. Yet to us, who are so hooked up to Casino Gambling, summer is a thrilling ride for another gaming fun and adventure. So, where to this time? Vegas, Atlanta or maybe somewhere international, huh? If you’re not into traveling this time, you can also have everything at your home PC. But anyway, before you start to indulge yourself into the many luxuries of Casino Gambling, you might want to think twice about firmly setting your limits this time. All right! Maybe, you already tried before and it didn’t work. But hey! Keep on trying.

A lot of people visit different casinos all year round. Whether it be in a gambling capital such as Las Vegas or simply at their home, many Americans simply cannot do without casino games. Well, this is not surprising. Casino gambling may mean you’re risking a pot of cash. Yet the betting game and tension, plus the thought of possibly winning the jackpot prize can also be your most exciting adventure ever. Of course, if you bag the gold, the experience becomes more immense.

If you’re too stressed out or bored with your work and daily routine, you definitely need to stretch out yourself and relax. Casino gambling is a great way to release all the tensions in your mind and body. When you visit a real casino, of course, the best part is your being able to enjoy the other facilities, comforts, luxuries, and entertainment offered by the gambling place.

Each time you are enticed by the thrills and fun of casino games, you need to remind yourself though about your limits. Remember the cardinal rule for gamblers? Control, control, and control! Otherwise, you’ll end up empty handed. Worse is that you can literally get hooked with casino gambling. There’s a thin line between moderate gamblers and addicts. Often, many people are too blinded by the excitement that they fail to realize they have already crossed the line. Well, not until their life starts to crumble. For, even a single night of fun can turn into a nightmare the next morning. If you haven’t been careful enough with your bets, then don’t get surprised when you’re confronted by debts the following day.

Casino games are definitely fun and relaxing, for that is their purpose – entertainment. Yet they can also be addictive especially when they are abused. Too often, it’s difficult to tell when you start to become a Casino Gambling addict. Of course, when family members or friends begin to remind you of your gambling, then it’s probably time to check yourself. Of course, do it soon before the addiction devours you and your life. Gambling addiction is also a root of many other problems in the society such as crimes and broken families. If you think you are one or if you know somebody addicted to gambling, do your responsibility of breaking the habit before it starts to break lives and families. Casino gambling is definitely relaxing and entertaining. It eases you from all tensions and pressures. Yet remember, you must always do it with great responsibility.