The probability of winning the lottery 6 out of 45 with a deployed bet

The desires of most people are different in that for their fulfillment it takes just a huge amount of money. Buy a new car, move to a spacious apartment, or even spend your whole life in resorts and never work. Sometimes it seems that all these dreams are simply impossible to fulfill!

However, there is one completely legal way to earn the required amount, without possessing any unique talents and without too much exertion. Just win the lottery. Of course, only a few out of millions have luck smiling. Professional mathematicians strongly do not recommend participating in them, because the mathematical expectation of winning is always less than the cost of the ticket.

Let's count, what is the probability of winning the lottery 6 out of 45? It should be borne in mind that it is possible to bet immediately on many winning combinations due to the so-called deployed system.

Rules of the draw

During each draw, a special machine selects 6 balls from the drum, in which there are 45 barrels with numbers from 1 to 45. Previously, all participants try to predict the results of the experiment. The main prize is won by the players who correctly guessed all 6 dropped balls.

Often nobody succeeds. And then the jackpot either moves to the next draw, or its amount is distributed among the other winners. To receive prizes of a lower face value, it is enough to guess from 2 to 5 numbers drawn.

What is a detailed bid?

Usually a lottery participant chooses exactly 6 numbers, which, in his opinion, will fall out of the lottery drum. In this case, to win the main prize will result in the only combination of all possible. However, the rules also provide for the possibility of a so-called detailed rate.

When choosing this option, the player chooses not 6, but a larger number of numbers. They can be specified from 7 to 19. Naturally, this increases the number of combinations leading to a win. Therefore, the price of a detailed rate is much higher. Moreover, it is exactly equal to the price of a regular bet multiplied by the number of combinations leading to a jackpot win.

How to play 6 out of 45?

The lottery is held twice a day. Drawings take place at 11:00 and 23:00, Moscow time. If you wish, you can watch the broadcast of the drawing on the lottery website. It is also possible to find out the results of previous lotteries. This, by the way, allows statisticians to analyze the history of events, finding certain patterns in the formation of balls. There are 4 ways to make your bet:

• Buy a ticket at a kiosk.
• Place a bet through the Gosloto website.
• Use SMS message.
• Download a special mobile application.
• You can also use the technology of QR codes.

In addition to the deployed system, when buying, you can make a bet immediately on many runs, as well as indicate the automatic selection of the predicted numbers.

Lottery cost

The price of a ticket is determined by the number of numbers that you select with the expanded rate. If you select 6 balls, the amount is minimal and equal to 100 rubles. With an expanded rate, its price is determined by the following table:

How to calculate the probability of winning the lottery 6 out of 45 and other similar ones?

To calculate the chances of success, such a branch of mathematics as combinatorics is used. First, you should evaluate the total number of different options for falling balls. In case you need to select A balls, and in total they contain B in the lottery drum, then the number of combinations is determined by the formula:

C = B! / A! / (B-A)!

The sign “!” Means a factorial, that is, the product of all natural numbers from 1 to a given number. For example, factorial 4 is defined as 4! = 1x3x3x4 = 24. In the case of a 6 out of 45 lottery, the number of combinations will be 8,145,060. For the sake of interest, we will also give the number of options for the 5 out of 36 and 7 out of 49 lotteries. In the first case, it is 376,992, and in the second 85,900,584. It can be seen that the increase in the total number balls increases the number of possible combinations.

The number of options is inversely proportional to the chance of a jackpot. If you compare the probability of winning the lottery 6 out of 45 and 5 out of 36, it turns out that if you guess 5 balls, the hope of success is 21 times higher!

How many combinations will win with a deployed bet?

With a normal bet, victory will bring only the only combination of all possible. However, a detailed bet is advantageous in that immediately a lot of options for falling balls lead the player to receive a jackpot. How to determine the total number of such combinations? Here again it is necessary to apply combinatorics. You have the balls. In how many different ways can you choose G of them? The answer can be calculated by the formula:

D = V! / G! / (V-G)!

So, if the expanded rate is 7 numbers, then the number of options will be 7! / 6! / 1! = 7. It is not difficult to make sure that at the same time the price of the deployed rate will be exactly 7 times higher than usual, that is, there is no economic benefit here. We give in the table the number of possible winning options for different sizes of the developed bet:

Knowing the number of variations that the jackpot will bring, and their total number, it is easy to estimate the probability of winning. So, if you need to calculate the probability of winning the lottery 6 out of 45 when choosing 7 numbers, then it is equal to 7/8 145 060 = 0.000000859. The chance is less than one in a million! In the best case, when 19 numbers are selected, the probability of success will be 0.0033, which is also very small.

Lottery comparison 6 out of 45 and 7 out of 49

Gosloto holds many lotteries, the essence of which is to guess a certain number of numbers selected by the lottery drum. They differ in two parameters. The first is the total number of balls participating in the draw. The second is the number of numbers to guess. It is interesting to compare different lotteries for a chance to win them.

For example, what is higher - the probability of winning the lottery is 6 out of 45 or 7 out of 49? Formulas for calculating the number of combinations are given above. If we consider non-deployed bets, then the chance of winning 6 out of 45 is almost 10.5 times higher! Keep this in mind when choosing the lottery you want to play.

Is the game worth the candle?

What is the probability of winning a lottery 6 out of 45 with a deployed bet? Is it worthwhile to use such an expensive "pleasure" in such an unpredictable future?

The probability of winning the lottery 6 out of 45 when choosing 6 numbers is minimal and is less than 1 in 8 million. A detailed bet increases the chances of winning, but costs more. Should I use it? It all depends on the ratio of the price of the ticket to the chance to win.

Gosloto specifically sets the cost of deployed bets in such a way that it is directly proportional to the probability of victory. In other words, the application of such a strategy does not increase or decrease your projected income. Which, by the way, is negative in all lotteries. In the end, all of these lotteries are disadvantageous for the participants and in the long run only harm your wallet.

An extended bet is just a special tool invented by the lottery organizers to confuse unsuspecting participants and pump out more money from them. So if you just want to have fun playing 6 out of 45, buy the cheapest ticket for 100 rubles. And if you are interested in real money, then pass by any lotteries. Remember, free cheese only happens in a mousetrap!