# Casino Games and Mathematics – Part 3

After more than one year Thorp published a book (I mentioned it at the beginning of the article), which is rather a very literate and sensible person, a winning strategy of the set of rules. But the publication of the book is not the only reason that the Growling Gambling Houses’ owners, as well as the latter, understand the main reason for the development of the Thorp strategy.

First of all, casinos’ owners understand that it is necessary to enter the following obligatory point of view of the game: the cards are to be thoroughly shuffled after each game! If this rule is rigorously observed, then a winning strategy of Thorp can be applied, since the probability of calculation is derived from one or another card based on a packed knowledge of the fact that some cards may not already appear in the game! link vào dafabet

But what does it mean to have “thoroughly shuffled” cards? A croupier, one-of-a-kind gamblers or, when the process of “thoroughly shuffling” presupposes the use of a packet with more or less monotonous movements 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, the “substitution” of a kind of cards with each movement of a result is made. But, it is really so, that a pack of 10-25 movements is perfectly shuffled, and in particular, there are 52 cards in a pack then a probability of the fact that, for instance, an upper card will appear be a queen will be equal to 1/13? In other words, if we will, for example, shuffle cards 130 times, then the quality of our shuffling will turn out to be more “thorough” than the number of times the queen’s appearance on top be closer to 10.

Strictly mathematically it is possible to prove that 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 “substitution of order” is less, ie. After less than a number of these movements (substitutions), the cards are located in the same order as the start of a pack shuffling. In fact, if this number equals to t, then repeat exactly the same number of times we can, for all our wish, we cannot get more than one tier of different positioning cards, or, using mathematical terms, not more t of cards.

Certainly, in reality, cards of shuffling do not come with the same movements of recurrence. But even if we assume that a shuffling person (or an automated device) makes casual movements at the moment, there is a certain probability that every single movement in a pack of cards, the question of “quality” of such mixing turns. out to be far from simple. This question is particularly interesting from the practical point of view that the majority of notorious crooked gamblers achieve phenomenal success, and that seemingly “careful shuffling” of cards is actually not such!

Mathematics helps to clear the situation with regard to this issue as well. In The Work “Gambling and Probability Theory” A.Reni presents the mathematical calculations that draw him to the following practical conclusion: “If all the movements of a shuffling person are casual, so, basically, there is a pack of shuffling. Analyzing these words, it is possible to notice, that, firstly, the decision about “quality” has shuffling. The likelihood character (“reasonably”), and, secondly, that the number of movements should be rather large (A. Reni prefers not to consider the question of what is a “rather large number”). Those 10-25 movements are more commonly applied in a real game situation than the required number of at least one sequence. !

Summing it all up, let’s come back to the question which article has been made. Certainly, it would be reckless to think that knowledgeable maths can help a gambler work out a winning strategy even in such an easy game as twenty-one. Thorp succeeded in doing it only by using imperfection (temporary!) Of the then used rules. We can also point to a nonlosing strategy with a gambler at the very least. But the other hand, gambling games with the mathematical aspects of understanding will undoubtedly poker.