| After one more year Thorp published a book
| |
| | the so called "order of substitution" is
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| (I mentioned it at the beginning of the
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| | less, i.e. less is the number of these
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| article) in which he rather in details, in
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| | movements (substitutions) after which the
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| the form comprehensible to any even a
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| | cards are located in the same order they
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| slightly literate and sensible person, set
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| | were from the start of a pack shuffling.
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| the rules of formation of a winning
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| | In fact, if this number equals to t, then
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| strategy. But the publication of the book
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| | repeating exactly similar movements any
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| did not only cause a quick growth of those
| |
| | number of times we, for all our wish, can
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| willing to enrich themselves at the cost
| |
| | not get more t different positioning of
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| of gambling houses' owners, as well as
| |
| | cards in a pack, or, using mathematical
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| allowed the latter ones to understand the
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| | terms, not more t different combinations
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| main reason of effectiveness of the
| |
| | of cards.
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| developed by Thorp strategy.
| |
| | Certainly, in reality, shuffling of cards
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| First of all, casinos' owners understood
| |
| | does not come down to recurrence of the
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| at last that it was necessary to introduce
| |
| | same movements. But even if we assume that
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| the following obligatory point into the
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| | a shuffling person (or an automatic
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| rules of the game: cards are to be
| |
| | device) makes casual movements at which
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| thoroughly shuffled after each game! If
| |
| | there can appear with a certain
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| this rule is rigorously observed, then a
| |
| | probability all possible arrangements of
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| winning strategy of Thorp cannot be
| |
| | cards in a pack at each single movement,
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| applied, since the calculation of
| |
| | the question of "quality" of such mixing
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| probabilities of extracting one or
| |
| | turns out to be far from simple. This
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| another card from a pack was based on the
| |
| | question is especially interesting from
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| knowledge of the fact that some cards
| |
| | the practical point of view that the
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| would already not appear in the game!
| |
| | majority of notorious crooked gamblers
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| But what does it mean to have "thoroughly
| |
| | achieve phenomenal success using the
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| shuffled" cards? Usually in gambling
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| | circumstance, that seemingly "careful
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| houses the process of "thoroughly
| |
| | shuffling" of cards actually is not such!
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| shuffling" presupposes the process when a
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| | Mathematics helps to clear a situation
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| croupier, one of the gamblers or, that is
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| | with regard to this issue as well. In the
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| still oftener seen of late, a special
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| | work "Gambling and Probability Theory"
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| automatic device makes a certain number of
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| | A.Reni presents mathematical calculations
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| more or less monotonous movements with a
| |
| | allowing him to draw the following
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| pack (the number of which varies from 10
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| | practical conclusion: " If all movements
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| to 20-25, as a rule). Each of these
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| | of a shuffling person are casual, so,
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| movements changes the arrangement of cards
| |
| | basically, while shuffling a pack there
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| in a pack. As mathematicians say, as a
| |
| | can be any substitution of cards, and if
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| result of each movement with cards a kind
| |
| | the number of such movements is large
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| of "substitution" is made. But is it
| |
| | enough, reasonably it is possible to
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| really so that as a result of such 10-25
| |
| | consider a pack "carefully reshuffled".
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| movements a pack is thoroughly shuffled,
| |
| | Analyzing these words, it is possible to
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| and in particular, if there are 52 cards
| |
| | notice, that, firstly, the conclusion
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| in a pack then a probability of the fact
| |
| | about "quality" of shuffling has an
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| that, for instance, an upper card will
| |
| | essentially likelihood character
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| appear to be a queen will be equal to 1
| |
| | ("reasonably"), and, secondly, that the
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| 13? In other words, if we will, thus, for
| |
| | number of movements should be rather large
|
| example, shuffle cards 130 times, then the
| |
| | (A.Reni prefers not to consider a question
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| quality of our shuffling will turn out to
| |
| | of what is understood as "rather a large
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| be more "thorough" if the number of
| |
| | number"). It is clear, however, that the
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| times of the queen's appearance on top out
| |
| | necessary number at least a sequence
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| of these 130 times will be closer to 10.
| |
| | higher than those 10-25 movements usually
|
| Strictly mathematically it is possible to
| |
| | applied in a real game situation. Besides,
|
| prove that in case our movements appear to
| |
| | it is not that simple "to test" movements
|
| be exactly similar (monotonous) then such
| |
| | of a shuffling person (let alone the
|
| a method of shuffling cards is not
| |
| | automatic device) for "accidence"!
|
| satisfactory. At this it is still worse if
| |
| |
|
