A lottery is a form of gambling that is run by the province. Most
provinces have several different games, including instant-win scratch-off
games, daily games and games where you have to pick three or four numbers.
The game with the biggest jackpot is almost always Lotto 649. This
game usually involves picking the correct six numbers from a set of balls,
with each ball numbered from 1 to 49 (some games use more or less than
49).
Ever wonder why how to calculate the odds of winning the Lotto? In this
article, we'll learn the answers to this question.
Let's take a look at how to calculate the odds of picking the right number
for a typical Lotto game. In order to win our example game, you have to
pick the correct six numbers from 49 possible balls. The order in which
the numbers are picked is not important; you just have to pick the correct
six numbers.
The odds of picking a single correct number depend on how many balls have
been chosen already. For instance, let's say none of the six numbers had
been picked yet and you had to guess just one number correctly. Since
there are 49 numbers to choose from, and since six balls are going to be
picked, you have six tries at picking the number correctly. The odds of
picking one number correctly are 49/6 = 8.16:1.
Using a similar calculation, we can determine the odds of picking another
number correctly after one number has already been drawn. We know there
are 48 balls left, and that five more balls will be drawn. So the odds of
picking a number correctly after one has been drawn are 48/5 = 9.6:1.
Now let's say five numbers have been picked and you have to guess what the
last number is going to be. There are only 44 balls left to choose from,
but you only get one shot at it, so your odds are only 44:1.
In a similar manner, we can calculate the odds of picking the right number
when two, three, four and five balls have been drawn. You know the odds of
a coin toss resulting in heads are 1/2 = 2:1. The odds of two consecutive
tosses both resulting in heads are 1/2 x 1/2 = 4:1. The odds of three
consecutive tosses all resulting in heads are 1/2 x 1/2 x 1/2 = 8:1. The
odds of picking all six lottery numbers are calculated the same way -- by
multiplying together the odds of each individual event. In this case:
49/6 x 48/5 x 47/4 x 46/3 x 45/2 x 44/1 = 13,983,816:1
Some provinces have been increasing or decreasing the number of balls in
order to change the odds. If the odds are too easy, then someone will win
the jackpot almost every week and the prize will never grow.
Large jackpots tend to drive more ticket sales. If the prize is not large
enough, ticket sales can decrease. On the other hand, if the odds against
winning are too great, ticket sales can also decline. It is important for
each lottery to find the right balance between the odds and the number of
people playing.
If you add just two numbers to our hypothetical lottery, so people now
have to pick from 51 balls, the odds increase to 18,009,460:1.
How Lotteries Work?