This article is about calculating lottery probabilities or odds. to suit me better I decided to play Grandlotto 6/55 which is the biggest lottery game in Philippines. Two different cases are mentioned: the probability of winning the game when all six numbers match; and the probability that n numbers match
Lottery Game Rules
It is always important to know the rules of any game before entering Grandlotto 6/55 to win the jackpot. You have to match six numbers from a group of 55 numbers from 1-55. The minimum start-up fee is P20 (or approx. $0.47). You can also win money if you can match three. Four or five numbers in a winning combination. Note that the order of the winning combinations doesn’t matter here.
before we start the calculations i want to talk about permutations and combinations. This is one of the basic concepts of probability theory. The main difference is that permutation assumes that order matters. Although sorting is not a problem.
in a Permutation lottery ticket must be used if the numbers on the ticket must match the winning number serial image. In Grandlotto 6/55, the order doesn’t matter as long as you have the winning numbers. You can also win prizes.
The following formula only applies to numbers without repeating them. This means that if you draw an x number, you can’t draw any more. If numbers drawn from one set are returned before the next draw, this indicates that there are duplicates
Note that according to the given formula, C(n,k) is always less than or equal to P(n,k) .
How to calculate lottery probabilities for six matching numbers
Now we know the basic concepts of permutations and combinations. Let’s go back to the Grandlotto example game 6/55 n = 55 total number of possible choices k = 6 number of choices to choose from. because order doesn’t matter. We use the formula for the combination:
It is the odds or the possible amount for a 6 digit number to win the game. You can find the odds by dividing 1 by the number above to get 0.0000000344 or 0.00000344%. See what I mean about reducing the odds?
What if we talk about another lottery game that prioritizes order? Now we use the permutation formula to achieve the following:
Compare these two results and see that the odds of getting a winning combination in which order matters are 3 extra zeros! From 28 million:1 odds to 20 billion:1 odds! The probability of winning in this case is 1 divided by the odds, which is 0.0000000000479 or 0.00000000479%.
as you can see Because permutations are always greater than or equal to combinations. The probability of winning a game where order does not matter is always less than or equal to the probability of winning a game where order does matter. Because the risk is higher in consecutive games. This means that the premium must also be higher.
How to calculate the probability of less than 6 numbers matching in the lottery?
Since you can win at this site http://18.104.22.168/ if you match less than 6 numbers, this section shows you how to calculate the probability if x matches the order in which the numbers are drawn.
First, we need to find some way to pick x winning numbers from the sequence. Then multiply how many ways there are to pick the losing numbers by the remainder of the 6-x numbers. Consider how many ways to pick the x winning numbers. Since there are only 6 possible numbers, we are basically just choosing x out of six. Therefore, since the order is not important, we get C(6, x).
Next, we look at how many ways there are to select the remaining 6-x balls from the losing numbers. Since 6 is the winning number, we have 55 – 6 = 49 balls to choose the losing number from. The losing ball can get C(49, 6 – x) Again, order doesn’t matter here.
Therefore, to calculate the probability of winning with x of the six possible matching numbers, we need to divide the result from the previous two paragraphs by the total number of possible wins for the six matching numbers.
Read more : Four Reasons Why The Lottery Not Rigged