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.

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.

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.

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).

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.