What You Need to Build a Winning Fantasy Football Team

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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 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 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.

Gaming Services: A Career In Gambling

It was a long time before gambling was legalized in the United States. It was not a one time legalization of all gambling games though but a very long process. The legalization process was also different and in various stages for each state. In the end, the government assessed more jobs for employment due to the legalization of gambling. Casino games such as poker, black jack, slot machines were said to be helpful in creating jobs across the United States.

Gaming or the play of various games of chance is reported to be a multi-billion industry that paved the way for the creation of a number of service professions. Gaming can include the usual casino gaming, state lotteries, horse racing, dog racing and even charitable games. The gaming industry created such an impact that it reached the status of an industry. How ironic that an industry that is supported by games of chance could sustain and provide stable jobs for the people.

Almost all workers that cater to the gaming industry are employed in the casinos. These workers have titles and responsibilities that could vary from one casino establishment to another but despite these differences in titles, all workers are basically doing the same thing. Workers could supervise, investigate and conduct surveillance while some of them will be assigned to work directly with the customers or casino players. These workers will perform various activities such as dealing cards or running games, tending the slot machines, handling money and writing or running tickets.

The Gaming Supervisor

The workers mentioned above will not be as organized as they should be without someone to oversee and supervise their day to day activities. This is the job of a gaming supervisor. A casino establishment can have more than one gaming supervisor. Gaming supervisors oversee the operations and workers assigned in a particular area of the casino. They circulate within the area, checking every table available and ensure the fluidity of the games even in the midst of shift changes.

Basically, the gaming supervisors are the workers who usually interact with guests in times of complaints or whenever guests have a hard time to understand the rules or limitations of a particular table game. These people are the ones who toy with ideas or various strategies on how to enliven the atmosphere for the guests while they are staying and playing in the casino. At the same time, they are ready for any inquiries or special requests that guests needs throughout their stay in the casino.

Other Occupations Available In The Gaming Industry

Some of the work occupations available in the gaming industry require a special level of skill. For example, black jack card dealers must be able to deal the cards smoothly and with precision, or else players might think that they are being cheated on the game. The skills indicated here are only useful and unique to casino gaming. Still, other occupations require skills that focus on being able to conduct financial transactions. All in all, these skills are mostly required by workers that are in contact with the guests and players. The workers mentioned above that deals cards or run table games, tends the slot machines, and handles money and tickets will need necessary skills helpful to their trades.

It is worth noting that workers are on shift rotation so each one will experience handling a specific work that will require a necessary skill. Casino establishment usually require their employees to undergo a specialized training that covers the whole casino gaming. In this training, attendees learn to cut a deck of cards smoothly, learn a few tricks with it and be able to deal it effectively along with other special skills.

There are slot key persons assigned in slot key machines that are responsible in overseeing its effective operation and supervising slot key workers. One job of the slot key person is to verify and handle the pay-off winnings of a lucky patron and reset the slot machine or refill its money contents. Another job is to make decisions regarding the repair of the slot machines.

A slot key person must be knowledgeable in different brands of slot machines. They must be able to detect a minor operational glitch in a slot machine and be capable of fixing it. In case of a major operational damage, the slot key person is also the person responsible to decide whether a slot machine needs to be removed from the floor for major repairs. Working in the floor as normal frontline personnel, the slot key persons are tasked to enforce the safety rules of the casino establishment and to report hazards to those concerned.

In operating games such as keno or bingo, there are gaming writers and runners that are tasked to take bets for the game and assist in its operation. These workers operates the device that issues random numbers, announce the numbers selected, pick-up and verify the tickets from the game patrons, calculate and distribute the game winnings.

The gaming dealers, on the other hand, are responsible for the card games such as poker, black jack, craps and roulette. The gaming dealers can be seen standing or sitting behind a table and facing the card game patrons. They will provide the dice and deal the cards to the patrons. During the card game, the gaming dealers will also monitor the patrons for any possible violation of the casino rules. In the card games, the gaming dealers must be highly skilled in their card games and are able to provide excellent customer service, especially in moments when a patron is losing most of his bet money.

The gaming dealers determine the winner of the card game, calculate and pay the winning bet while also collecting the bet money. It is a big advantage for a person that aspires to be a gaming dealer to be competent in at least two card games such as poker or black jack.