roulette probability theory

A bit of history

In 1526, the Italian mathematician Gerolamo Cardano, in his Book of the Game of Chance, first attempted to describe the game of dice in the language of mathematics. Based on his own gaming practice, he tried to develop and theoretically substantiate a system of recommendations for managing bets. He actually formulated the definition of probability: "There is one general rule of thumb for calculating the probability: try to account for the number of possible hits and the number of ways in which these hits can appear, and then find the ratio of the last number to the number of possible hits remaining." Later, in the late 16th and early 17th centuries, the mathematical analysis of the dice game was continued by Galileo Galilei and Blaise Pascal. They started doing this at the request of friends, big fans of gambling, very dejected by the large financial costs that their hobby brought. It should be admitted that the science of probability, according to history, grew out of the mercantile problems of gamblers. It is generally accepted that it was then that a whole area of mathematics appeared, entirely devoted to probabilities. The next step in this direction was taken by the Dutch mathematician Christian Huygens, who published in the middle of the seventeenth century the book "Reflections on the game of dice" ("De Ratiociniis in Ludo Aleae"). The theory of probability was further developed in the works of the great mathematicians of the 18th-19th centuries - Jacob Bernoulli, Poisson, Laplace, Moivre and others. Very soon, the new theory found wide application in areas far from gambling.

The math of games

Coin for Determining the Probabilities of Winning How does gambling work from the point of view of probability theory? Let's see if it obeys mathematics. When a coin is tossed, any of its sides can fall out with the same probability. There are only two possibilities - heads or tails. The probability of falling heads is 1?2 (50%), that is, half of the cases will come up tails. Probability shows how often the expected result can be achieved, and can be represented as the ratio of the expected outcomes to the total number of all possible outcomes, over a sufficiently long period of time and with a large number of repetitions. The probability of an event reflects a quantitative assessment of the possibility of that event occurring. If it is equal to zero, the event cannot happen in principle. When it is equal to one (100%), the event will necessarily occur. You can find practical tips for using mathematical calculations in casinos on the next page:

How to Win Gambling Using Math?

Examples: There are 52 cards in a standard playing deck, including 4 aces. The probability of pulling one of the aces out of the deck is: (4/52) * 100 = 7.69%. There are 37 cells on the European roulette wheel: 1-36 are numbers (18 red and 18 black) and a green zero mark. It's probably not even worth talking about the theory of probability and roulette in the classical sense. For one simple reason that there is nothing to talk about. Tracking the number of red or black drops, trying to find a pattern is useless. The ball will fit into one cell, which will be impossible to predict in advance. In mathematical terms, this means that the law of distribution of random numbers is continuous and infinite. Mathematicians have fought for centuries, composing from simple and obvious truths difficult for a person to understand, unprepared rules. But, when you start to deal with the theory of probability yourself, then everything becomes obvious and simple. Knowing with certainty that Thursday is after Wednesday, with the same 100% certainty, anyone should know that if now the seven is red, then the next time any one of the thirty-seven available combinations will fall out with a probability of 1/37, that is, 0.027. But this, again, does not mean that by betting 37 times on 7 red, you will win, because any events that are related to the law of distribution of random numbers (roll of the dice, etc.), including complex events , obey all the same law. To put it very roughly and very simply, to win two bets in a row, multiply the probabilities of winning each bet. For example, the first time you bet only on black, the second time only on two blacks. The probability of success the first time is 18/37 = 0.486, and the second is 1/37 = 0.27, that is, the total probability of winning both bets is 0.013.