# The Mathematical Theory Of Gambling Games

Despite all the obvious popularity of games of dice among the majority of social strata of various nations during several millennia and up to the XVth century, it is interesting to note the absence of any evidence of the idea of statistical correlations and probability theory. The French humanist of the XIIIth century Richard de Furnival was said to be the author of a poem in Latin, one of fragments of which contained the first of known calculations of the number of possible variants at the chuck-and luck (there are 216). Earlier in 960 Willbord the Pious invented a game, which represented 56 virtues. The player of this religious game was to improve in these virtues, according to the ways in which three dice can turn out in this game irrespective of the order (the number of such combinations of three dice is actually 56). However, neither Willbord, nor Furnival ever tried to define relative probabilities of separate combinations. It is considered that the Italian mathematician, physicist and astrologist Jerolamo Cardano was the first to conduct in 1526 the mathematical analysis of dice. He applied theoretical argumentation and his own extensive game practice for the creation of his own theory of probability. He counseled pupils how to make bets on the basis of this theory. Galileus renewed the research of dice at the end of the XVIth century. Pascal did the same in 1654. Both did it at the urgent request of hazardous players who were vexed by disappointment and big expenses at dice. Galileus’ calculations were exactly the same as those, which modern mathematics would apply. Thus, science about probabilities at last paved its way. The theory has received the huge development in the middle of the XVIIth century in manuscript of Christiaan Huygens’ «De Ratiociniis in Ludo Aleae» («Reflections Concerning Dice»). Thus the science about probabilities derives its historical origins from base problems of gambling games.Before the Reformation epoch the majority of people believed that any event of any sort is predetermined by the God’s will or, if not by the God, by any other supernatural force or a definite being. Many people, maybe even the majority, still keep to this opinion up to our days. In those times such viewpoints were predominant everywhere.And the mathematical theory entirely based on the opposite statement that some events can be casual (that is controlled by the pure case, uncontrollable, occurring without any specific purpose) had few chances to be published and approved. The mathematician M.G.Candell remarked that «the mankind needed, apparently, some centuries to get used to the idea about the world in which some events occur without the reason or are defined by the reason so remote that they could with sufficient accuracy be predicted with the help of causeless model». The idea of purely casual activity is the foundation of the concept of interrelation between accident and probability.Equally probable events or consequences have equal odds to take place in every case. Every case is completely independent in games based on the net randomness, i.e. every game has the same probability of obtaining the certain result as all others. Probabilistic statements in practice applied to a long succession of events, but not to a separate event. «The law of the big numbers» is an expression of the fact that the accuracy of correlations being expressed in probability theory increases with growing of numbers of events, but the greater is the number of iterations, the less frequently the absolute number of results of the certain type deviates from expected one. One can precisely predict only correlations, but not separate events or exact amounts.© Copyright 2006-2007 http://www.Bonus-Map.com

# Casino Gambling – The Types of Casino Bonuses

Online casinos provide several incentives to attract new players and retain existing players at their casino. The bonuses can become the major criteria for players in deciding an online casino to play at. There are various types of online casino bonuses and each has its particular advantages and conditions. You should get some understanding about the bonuses, especially the terms and conditions before you accepting the bonuses.In general, there are 2 categories of bonuses: STICKY & CASHABLE bonuses. Sticky bonuses are the free money that lent to you by the casino. You can use the sticky bonuses to play your favorite games, if you win and meet the wagering requirements, you can only withdraw the winnings and not the sticky bonuses. The casino will take back the bonus upon your withdrawal. On the other hand, cashable bonuses are the money that can be withdrawn along with your winnings after meeting the wagering requirements. Normally the online casinos won’t state their bonus offers to be the sticky or cashable in their promotion page; you need to read the terms & conditions to find out which category the bonuses are.Regardless of sticky or cashable bonuses, there are a few common casino bonuses, which can be found in casino’s promotion page. These bonuses are:No Deposit BonusesNo Deposit Bonuses are free money given by the casino. It does not require you to deposit any money. You just need to open a real-player account with the casino that offers no-deposit bonuses. Normally the bonuses will be automatically deposited into your player’s account, but some online casinos may require you to confirm your account through a confirmation email, or upon verification of your credit card before the no-deposit bonus being deposited into your account. Most no-deposit bonuses are ranging from \$10 to \$100 depending on the casinos. Some online casinos offer no-deposit bonuses in the term of free-play; this type of no-deposit bonus is normally offered for playing slots machines or video poker. Once you have sign-up a real-player account with the casino, you will be given a certain amount like \$500 free-play bonus or a number of hours such as 5-hour free-play time at the casino. There are terms & conditions of wagering requirements on the no-deposit bonuses that you need to meet before you can withdraw the winning.Welcome / Sign Up BonusesOnline casinos reward new players by offering welcome or sign up bonuses. These bonuses are offered in term of matching bonus based on the amount deposited by the new players. Normally, online casinos will match 100% to 200% for the first deposit, but some casinos may go up to 500% to attract more new players. The welcome bonuses may be matched only with the first deposit, or a few initial deposits depending on the casino’s promotion strategy. The bonuses normally have a minimum and maximum deposit limits. The player needs to deposit the amount the meet the minimum deposit in order to eligible for the bonuses. And, the casino will only match the bonuses up the maximum deposit amount.Weekly and Monthly Deposit Bonus Existing players will also be rewarded whenever they deposit the money into their account. These bonuses normally are given in term of weekly or monthly bonuses, which normally ranges from 25% to 50%.Cash-back Bonuses Some casinos will refund some of your losses during a certain period of play in term of cash-back bonuses. It may range from 5% to 15%. The more you lose the more cash-back bonus you will get. Off course, you don’t want to get more on this type of bonus because it means the more you get, the more you have lost to the casino. However, it is still an attractive bonuses offered by online casinos.Refer-A-Friend Bonuses This is the incentive given to the players who refer or invite their friends to play at the casino. You can get some money (normally \$50) for every player who register into the casino with your help.

# Slot Game Savvy Players Benefit With Slot Bonus

Casinos remind you of places like Las Vegas and also of various casino games amongst which most of these games depend on chance and one such game is the casino slots. Slot machine is known to almost everyone around the world because it is one of the easiest and most convenient games at gambling and multiplying your money. Although, the chances of winning a jackpot are not extremely high, there sure are other small wins that is won according to the combination of various colorful pictures on the reels. While decades ago our ancestors would have not been able to play the game without having a casino around things have taken a huge leap of advancement with the advent of the internet. Online slot games are much famous amongst the internet savvy individuals who fancy this intriguing game of luck and reap a lot of benefits of playing online as a result.Playing any game online has caught the interests of many young individuals off late but when it is a game that could also win you some dollars that might interest even older enthusiasts who do not mind investing some time and money and trying their luck at hand whilst also getting entertained by the excitement the online slot machine has to offer. Also, it is a game that usually needs to be played with money when played on its land-based version; however, online you also have the choice to play free slots games. A free online slots game gives you firsthand experience if you seem to be fairly new to the concept of slots without any loss of your hard earned cash. Besides, once you gain the confidence to win the game of chance with a little bit of game tactics and analysis you are ready to play them with your money. Until then you could use slot bonus to play with which is nothing but bonus allotted to you on slots.Not every online gaming site offers you slot bonus and some may even vary in the number of slot bonus offered. You could have an exhaustive research done online of all the websites that offer free slots bonus or simply click on comparison websites that give you collective information on the same and save a lot of your time in the bargain, as a result. Most of today’s online slot games have state-of-the-art graphics and designs and are pretty user friendly that even a kid can follow. Just make sure that you have gained access to a lucrative site that offers attractive slot bonus through reliable online sources and know your limits when it comes to gambling online on slot machines.