Participating in the lottery is a way to test your luck, intuition and, if you're lucky, break the bank by winning a significant amount. Basically, almost any lottery can be analyzed from the point of view of the theory of probability, which will allow calculating the odds of winning.
Theory and terms
A lot of lotteries are constantly held in the world with a variety of rules, winning conditions, prizes, however, there are general principles for calculating the probability of winning, which can be adapted to the conditions of a particular lottery. But first, it is advisable to define the terminology.
So, probability is a calculated estimate of the probability that a certain event will occur, which is most often expressed in the form of the ratio of the number of desired events to the total number of outcomes. For example, the probability of getting heads on a coin toss is one in two.
Based on this, it is obvious that the probability of winning is the ratio of the number of winning combinations to the number of all possible ones. However, we must not forget that the criteria and definitions of the concept of "winning" can also be different. For example, most lotteries use the definition of "win class". The requirements for winning the third class are lower than the requirements for winning the first class, so the probability of winning the first class is the lowest. As a rule, such a prize is the jackpot.
Another significant point in the calculations is that the probability of two related events is calculated by multiplying the probabilities of each of them. Simply put, if you flip a coin twice, the probability of getting heads each time will be equal to one in two, but the chance of getting heads both times is only one in four. In the case of three tosses, the chance generally drops to one in eight.
Calculating odds
Thus, to calculate the chance of winning a jackpot in an abstract lottery, where you need to correctly guess several dropped values from a certain number of balls (for example, 6 out of 36), you need to calculate the probability of each of the six balls falling out and multiply them together. Please note that as the number of balls remaining in the reel decreases, the probability of getting the desired ball changes. If for the first ball the probability that the desired ball will fall out is 6 to 36, that is, 1 to 6, then for the second the chance will be 5 to 35, and so on. In this example, the probability that the ticket will be winning is 6x5x4x3x2x1 to 36x35x34x33x32x31, that is, 720 to 1402410240, which is 1 in 1947792.
Despite such frightening numbers, people regularly win lotteries around the world. Do not forget that even if you do not take the main prize, there are still second and third class wins, which are much more likely to receive. It is also clear that the best strategy is to buy multiple tickets of the same draw, as each additional ticket multiplies your chances. For example, if you buy not one ticket, but two, then the probability of winning will be twice as high: two out of 1.95 million, that is, approximately 1 in 950 thousand.
