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search for: home 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. 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 read
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