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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. 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

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