Chances of winning the lottery
Each, who buys the coveted lottery ticket, hopes to hit the jackpot. Well at least win a large sum of money. What are the real chances of winning? What is the probability of winning the lottery?
If you take such popular lotteries as 5 of 36 or 6 of 45, then the probability of winning directly depends on the number of numbers in the drawing. If the probability of guessing everything 2 number is 1 to 8 in the lottery "5 out of 36", then to get the main prize you need to guess all 5 digits. And here the probability of choosing the right combinations decreases by almost 50 thousand times and will be 1 : 376 992.
The odds of winning in various lotteries depend on the number of matched numbers and the range of numbers involved in the drawing. An increase in just one number for the drawing of the main prize immediately reduces the probability of winning tenfold.
Here is the math, showing the odds of winning combinations on the most popular lotteries.
5 of 36
| Guess numbers | Probability of winning |
| 2 | 1 to 8 |
| 3 | 1 to 81 |
| 4 | 1 to 2 432 |
| 5 | 1 to 376 992 |
6 of 45
| Guess numbers | Probability of winning |
| 2 | 1 to 7 |
| 3 | 1 to 45 |
| 4 | 1 to 733 |
| 5 | 1 to 34 808 |
| 6 | 1 to 8 145 060 |
7 of 49
| Guess numbers | Probability of winning |
| 3 | 1 to 22 |
| 4 | 1 to 214 |
| 5 | 1 to 4 757 |
| 6 | 1 to 292 179 |
| 7 | 1 to 85 900 584 |
It turns out, that the greatest chance to hit the jackpot in Gosloto is "5 out of 36", but also the prize fund is the lowest of the above. The probability of winning the 7/49 lottery in 230 times less, but the prize fund is more significant.
In order to understand which lottery is the most profitable to play, you just need to calculate the probability of winning for one ruble invested.
At the moment, the following data is available:
| Lottery | Ticket price | Grand Prize | Win for one ruble |
| 5 of 36 | 80 | 3 000 000 | 37 500 |
| 6 of 45 | 100 | 222 150 000 | 22 215 000 |
| 7 of 49 | 50 | 100 000 000 | 2 000 000 |
We received the size of the winnings for each ruble invested. But the probability of hitting the jackpot is different for everyone.. We need to equalize the chances of winning the top prize for all three lotteries. How to do it? Increase the amount of money invested in 2 other lotteries.
For example. If the chance of winning is 10% at ticket price 100 rubles, spending 200 rubles and buying 2 ticket, we increase the probability of winning to 20%, when investing in 300 rubles - up to 30% etc. Let's do the same with our examples..
The highest probability of winning in Gosloto 5 of 36 — 1 : 376 922. Respectively, we need to increase investments in other lotteries, by buying more tickets, thus leveling the probability for all three draws.
As a result, we got the following data:
| Lottery | Winnings for each ruble invested |
| 5 of 36 | 37 500 |
| 6 of 45 | 1 028 |
| 7 of 49 | 164 |
The results were quite unexpected.. With the same probability of winning, the most profitable was the lottery 5 of 36. Difference with the latter (7 of 49) nearly 230 time.
