After one more year Thorp published a book (I mentioned it at the beginning of the article) in which he rather in information, in the form comprehensible to any even a slightly literate and sensible person, set the guidelines of formation of a winning technique. The publication of the book did not only cause a quick growth of those ready to enhance themselves at the expense of wagering houses’ owners, as well as allowed the latter ones to understand the main factor of efficiency of the established by Thorp strategy.
Of all, gambling establishments’ owners understood at last that it was necessary to introduce the following required point into the rules of the game: cards are to be thoroughly shuffled after each video game! If this rule is rigorously observed, then a winning strategy of Thorp can not be used, considering that the computation of probabilities of removing one or another card from a pack was based upon the understanding of the fact that some cards would already not appear in the game!
But exactly what does it mean to have “thoroughly mixed” cards? Generally 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, an unique automatic device makes a particular number of more or less dull movements with a pack (the number of which varies from 10 to 20-25, as a rule). Each of these movements alters the arrangement of cards in a pack. As mathematicians state, as a result of each motion with cards a sort of “substitution” is made. Is it really so that as an outcome of such 10-25 movements a pack is thoroughly mixed, and in specific, if there are 52 cards in a pack then a possibility of the fact that, for circumstances, an upper card will appear to be a queen will be equal to 1/13? In other words, if we will, therefore, for example, shuffle cards 130 times, then the quality of our shuffling will turn out to be more “comprehensive” if the number of times of the queen’s look on leading from these 130 times will be closer to 10.
Strictly mathematically it is possible to show that in case our movements seem exactly comparable (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 variety of these motions (substitutions) after which the cards lie in the same order they were from the start of a pack shuffling. If this number equals to t, then restarting exactly comparable motions any number of times we, for all our desire, can not get more t different positioning of cards in a pack, or, utilizing mathematical terms, not more t different mixes of cards.
Certainly, in fact, shuffling of cards does not come down to recurrence of the very same motions. Even if we assume that a shuffling individual (or an automatic device) makes casual motions at which there can appear with a particular probability all possible plans of cards in a pack at each single movement, the question of “quality” of such blending turns out to be far from easy. This concern is especially interesting from the useful viewpoint that most of well-known misaligned bettors achieve remarkable success utilizing the scenario, that seemingly “careful shuffling” of cards in fact is not such!
In the work “Gaming and Likelihood Theory” A.Reni provides mathematical computations permitting him to draw the following practical conclusion:” If all movements of a shuffling individual are casual, so, essentially, while shuffling a pack there can be any replacement of cards, and if the number of such movements is huge enough, fairly it is possible to consider a pack “thoroughly reshuffled”. Evaluating these words, it is possible to notice, that, first of all, the conclusion about “quality” of shuffling has an essentially possibility character (“fairly”), and, secondly, that the number of motions should be rather huge (A.Reni likes not to consider a concern of what is understood as “rather a large number”).
Summing it all up, let’s come back to a question which has been the headline of the article. Definitely, it would be negligent to believe that knowledge of maths can help a gambler work out a winning strategy even in such an easy game like twenty-one. Thorp was successful in doing it only by utilizing flaw (momentary!) of the then utilized guidelines. We can likewise mention that one should not expect that mathematics will have the ability to offer a bettor at least with a nonlosing method. But on the other hand, understanding of mathematical elements gotten in touch with betting games will certainly assist a gambler to prevent the most unprofitable situations, in specific, not to become a victim of scams as it accompanies the issue of “cards shuffling”, for instance. Apart from that, an impossibility of production of a winning technique for all “cases” not in the least avoids “a mathematically advanced” gambler to choose whenever possible “the finest” choice in each certain video game circumstance and within the bounds enabled by “Dame Fortune” not just to enjoy the extremely process of the Video game, as well as its outcome.
Is it really so that as an outcome of such 10-25 movements a pack is thoroughly mixed, and in particular, if there are 52 cards in a pack then a probability of the truth that, for circumstances, an upper card will appear to be a queen will be equal to 1/13? At this it is still even worse if the so called “order of substitution” is less, i.e. less is the number of these motions (replacements) after which the cards are located in the exact same order they were from the start of a pack shuffling. If this number equals to t, then repeating precisely comparable motions any number of times we, for all our desire, can not get more t various positioning of cards in a pack, or, utilizing mathematical terms, not more t various combinations of cards.
Even if we presume that a shuffling individual (or an automatic device) makes casual movements at which there can appear with a particular possibility all possible plans of cards in a pack at each single motion, the question of “quality” of such blending turns out to be far from easy. In the work “Gaming and Probability Theory” A.Reni provides mathematical calculations enabling him to draw the following useful conclusion:” If all motions of a shuffling person are casual, so, essentially, while shuffling a pack there can be any replacement of cards, and if the number of such movements is big enough, reasonably it is possible to consider a pack “carefully reshuffled”.