Internet Casinos | Online Poker | Turkish Casinos | Gambling Podcast | US Casinos | Mobile Version EternalGambling
EternalGambling QR Code Sportsbetting - Internet Casino and Online Betting
Play at Goldenpalace
> 300% Bonus now !
Play at Bovada Casino
> America's Pride !

Man's instinct to gamble is the only reason he is still not a monkey up in the trees - Mario Puzo
Gambling Articles >> Newsletter: Blackjack Strategy Software <<
Search

Home | Games


Mathematics And Casino Games III

By: Arthur Prudent

Featured Sportsbook: Famous
online sports bettingBetOnline Sports Betting company BetOnline provides you $900 in free plays if you open an account right now. Take the quick tour at America's largest online sports betting destination, and learn about casino games and internet poker. Bet nowBetOnline Sports Betting...

Great Casino: All Star Slots top online casino provides you with
a great $787 casino bonus plus unlimited free money and you will have the possibility now to play the famous and well-known cool Triple Twister video slot casino game. Play now...

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.

## End of Article

What do you want to do next ?

Play Casino Games
$4000 Cash Bonus, more than
75 games
Bet on Sports
$250 Cash Bonus, Live Lines Inferno
Play 3D Online Slots
$5000 Free Bonus, Instant Game Play
Play Internet Poker
100% Cash Bonus, $50000 Points Race
Bet on HorsesHorse Betting
$900 Free Plays, Horse Betting Toolkit
Play Online Bingo
Free $6 Bonus. Bingo Tourneys, Slots, Video Poker


Gambling Article Source: http://www.eternalgambling.com/gambling

Arthur Prudent is the developer of Casino bonus codes, web site covering gambling news on Casinos and Poker.

Please Rate this Gambling Article

 

Not yet Rated

Get Games articles via RSS by clicking the icon above !






Terms and Conditions : Privacy Policy : About and Contact

* World Series of Poker and WSOP are trademarks of Harrah's License Company, LLC ("Harrah's"). Harrah's does not sponsor or endorse, and is not associated or affiliated with the products, services or promotions presented on this website.


Powered by Article Dashboard