Vectors and 3D Models
Local Search - Entertainment
Weather Information
Get the App for Smartphones and Tablets

Go Back


WhmSoft Free Articles Directory
Free Articles for Reprint
Free Articles to Publish
Free Articles for Newsletters
Videos to Watch


Page Generation Date and Time:
10/23/2017 17:10:14

 
Free the Animation VR / AR
Play to reveal 3D images and 3D models!
 
Android app on Google Play
 
vlrPhone / vlrFilter
Project of very low consumption, radiation and bitrate softphones, with the support of the spatial audio, of the frequency shifts and of the ultrasonic communications / Multifunction Audio Filter with Remote Control!



 
 
Alexa Data
 

Go To Articles Directory Home Page

To get the current article, - See Below (at the bottom of the page) -.
For top news titles, see below.
Web sites and videos listed in this page are frequently updated.
If you find that this page is useful (quality of web sites, images and videos, ...), you can add it to your favorites.
Bookmark Page !

Tell a Friend:



With your mobile phone (WAP / I-Mode / iPhone / PDA), for free:
The Top News - http://www.whmsoft.net/services/wap/news.php
The Daily Files - http://www.whmsoft.net/services/wap/get.php
All the Directory Files - http://www.whmsoft.net/services/wap/choose.php

Web version of feeds:
Podcast Music - http://www.whmsoft.net/services/web/wpodcast.php
Daily Files - http://www.whmsoft.net/services/web/wget.php

You can play the Guitar Drum Revolution game (flash game) by following the link below:
Play Guitar Drum Revolution Game


You can play free online games (flash games) by following the link below:
Free Online Games

Play the samples below:
00228 Polar Rescue00102 Memory Madness0878 Canyon GliderPedestrian KillerSnowy Puzzle Islands

You can view the people (celebrities) news and the front page news (with videos, images and constant updates) by following the link below:
View Recent News
or by visiting the WhmSoft Service blog:
News Photos Slideshows


Article Keyword Videos to Watch
Entertainment
Click on the image to start the video.



Related Topics
Images - Links - Articles

New York


Related Images



Article Category Videos to Watch
Entertainment
Go to the Videos Pages


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.
© Copyright 2006-2007 www.bonus-map.com


About the Author: Arthur Prudent is the developer of Casino bonus codes , web site covering gambling news, features reviews on Casinos, Poker rooms, bingos, Sports Betting bonuses promotions and more.
Casino games and mathematics. Part 3.




Recommended Web Site(s):

Easy Articles Home Page - Articles Directory

Recommended WhmSoft Web Sites, Feeds and WAP Address:

WhmSoft Software Home Page - Software
WhmSoft Services Login Page - Music and Images
WhmSoft Moblog Home Page - Blog - Photo Gallery
WhmSoft Free Online Games Home Page - Flash Games
WhmSoft Services RSS Feed - Daily Music, Image and 3D Flash Animation
Classical Music with Drum RSS Feed - MIDI and MP3 Files
Classical Music with Drum Podcast Feed - MP3 and MP3 Files
WAP / I-Mode / PDAs - Daily Music, Image and Flash Animation

Home Pages:

WhmSoft Free Articles for Reprint Home Page
WhmSoft Services Home Page - Music and Images
Copyright (C) 2006-2017 WhmSoft - All Rights Reserved.