Online gambling has its roots in mathematics, and these two sciences are inextricably linked. Mathematics played an important role in the development of casino games such as blackjack and roulette, as well as slot machines. The connection between mathematics and gambling goes back centuries, with the scientist Blaise Pascal famously stating that "randomness is only a name for our ignorance of what causes randomness."
For the past decade, a group of mathematicians, psychologists, and economists have been studying what they call "non-zero-sum games," or games in which there is no clear winner and loser. The idea is to see if mathematical theories can be used to predict how people will react to a certain type of game.
The beginnings of gambling in connection with mathematics
Casinos have used mathematics since their inception to ensure fair odds in games such as roulette and craps. Today, they rely on mathematics to design slot machines that can generate billions of euros in revenue per year. Because of its importance, the use of mathematics in casinos predates the development of any other formal mathematical discipline.
Mathematics entered the field of gambling after the publication of a treatise on gambling in 1725. The treatise is known as the "Book of Chances" and was based on the reasoning of the mathematics of probability, which influenced many later works on games.
The year 1725 was marked by three important events in the study of games: the publication of the Treatise on Games of Chance, which had a significant influence on the invention of modern chess, and the first written reference to backgammon.
In 1775, James Elliott, appointed governor of Gibraltar in 1764, published a book about his trip to North Africa, in which he first mentioned in detail about backgammon and its connection with mathematics.
Mathematical principles in games
Stochastics is a discipline that helps predict how likely it is that a certain outcome will occur in a game. The higher the probability of the outcome, the higher the stochastic number, and vice versa.
A stochastic value of 1/38 means that the probability of getting a red number in roulette is 1/38. The probability of getting a black number is 17/38. For example, if the value is 500, it means that the probability of getting a red number is 1/500, and the probability of getting a black number is 490.
In this case, the events or the result of rolling the same dice are random in the sense that they do not follow a pattern or rule, while the cards are deterministic - they follow a certain rule or pattern.
Randomness refers to events that occur without order or pattern, while probability means that an event will occur within a certain period of time when it has not occurred in the past. In this case, the dice are random because they do not follow a certain pattern, but do not have a predetermined probability, while the cards are assigned fixed numbers.
In different types of gambling, the winnings depend on the chance. However, many people try to cheat this chance with math. In some games this can actually work if you use probabilities. But there's a lot to consider if you want to lend a helping hand to luck.
For example, in the lottery there are statistics of which numbers were drawn most often. As a result, these are the numbers that players prefer to use. Numbers up to 31 are not welcome due to low odds, as birthdays are often chosen here. These and other simple tips are carefully applied by some players and carried out by entire betting syndicates. Others put it on chance for fun and simply check the boxes, relying only on intuition.
Mathematics for casino
Players take the mathematical basis of casino games much more seriously than lottery games. They usually get their first experience in online games. This is due to the fact that here you can use various calculations and tricks without having to play for real money. Since many sites list popular casino free spins, newbies and pros alike can test and optimize their strategies for free.
The second most popular trick is card counting instructions in games like poker, baccarat and especially blackjack. about the how to learn how to count cards in blackjack, we will talk more about it later. In any case, it is impossible to count cards while playing online.
But there are important nuances that need to be taken into account. First, it is important to know the odds set by the casino. This shows the player how much they can expect to pay out if they win. For example, the odds in roulette are 1:1 if you bet only on color. Therefore, the rate of 50 u.o. will lead to a profit of 50 u.o.
You should also calculate the winnings and losses that you will get if you play the same bet for a long time. It is clear that in the long run you will definitely have to reckon with losses.
Therefore, the correct strategy is to make the best bet to minimize the casino advantage. Statistically calculated rates help in any situation. They depend on the specific game and often change during the game. They can be calculated, in particular, using the calculation of probabilities.
● Probability calculation
It is used to determine how likely it is that a certain number will be rolled or a certain card will be drawn, etc. In other words, the calculation of possible events.
For example, a roulette wheel has 18 red and 18 black numbers and a green field with zeros. There are 37 possible fields. The probability of getting a red square is 18/37 = 0.486, which is about 48.6%.
Or let's take a good old game of Scat. It consists of 32 cards. The probability that a queen of worms will appear is 1/32 = 0.03125, i.e. 3.125%. Thus, the various events are also linked in more complex formulas and the risk is calculated based on the odds if you bet on these numbers.
● Card counting — simplified probability calculation
The most popular and easiest way to count cards is blackjack. However, it is also possible in poker or baccarat. Dustin Hoffman was very famous and almost a role model for card counting as the autistic character in Rain Man.
For over 50 years, there have been strategies, books, and instructions on how to how to count cards correctly. All of them are about correctly predicting how many cards of the same color are still left in the deck and can be played in the near future.
Based on this, the player can assess whether he needs another card or not. If he is confident, he can even increase the bet and, if he is right, win. This can be applied to both poker and blackjack.
Different systems
There are over 20 different card counting methods. The most famous system that is used almost everywhere is Hi-Lo Count. It is also suitable for beginners.
All cards are assigned a value based on whether they are a senior or junior card. 2, 3, 4, 5 and 6 are considered low cards. If they are played, they count as +1. A 10, J, Q, K or Ace, on the other hand, counts as -1. 7, 8 and 9 are not taken into account.
As a result of such a calculation, a value is obtained that is constantly changing (running calculation). In a casino, however, not one deck of cards is used, but at least six. Therefore, the decks played are added to the current account and divided among the remaining decks. As a result, they receive a real account. For a correct bet -1 is subtracted from the true score. The result is set in units of the table minimum or 1/100 of the bankroll.
Conclusion
Casinos, of course, know that card counting is possible, even if it is not as easy as they think. However, they have no real chance of banning it. Therefore, they try to make the task as difficult as possible for the players and play with a minimum of eight decks or limit the limit at the table, and also use automatic shuffling machines.
Even if you know math well, it takes a long time to improve your counting skills. Professionals who are familiar with counting do not consider card counting to be a profitable business because the winnings are low. In Ukraine, casinos also teach how to recognize counters. Their surveillance images are sent to other casinos as a warning. This is the end of their career as a con artist.