One of the major national lotteries in Canada is Lotto MAX.
This lottery went through a bit of an overhaul in May, 2019 where they introduced an additional ball (number 50).
This changed the odds of winning.
As seen on our LottoMAX details page, the new odds of winning per $5.00 play is 1 in 33,294,800.
There is a bit of math to figure out these odds. As described on our Odds of Winning the Lottery page, you can figure out the odds with this equation:
(50 x 49 x 48 x 47 x 46 x 45 x 44) / (7 x 6 x 5 x 4 x 3 x 2 x 1).
So, 503,417,376,000 / 5040
This results in 99,884,400
So the odds of your numbers being chosen are 1 in 99,884,400.
But wait one second. The advertised odds are 1 in 33,294,800? What gives?
Technically, the advertised odds are correct. When you play Lotto Max, you are usually buying a $5.00 ticket. This gives you 3 selections of numbers.
So you have 3 chances to win for each $5 play, one for each line selection.
Doing the math again...
99,884,400 / 3 = 33,294,800.
So the math is correct...the odds are different depending on what you are truly looking for.
Canada has 5 regional websites to inform players about their lotteries.
Oddly, none of these official sites mention the true odds of winning Lotto MAX for one selection line.
The true odds of winning with your line selection are in 1 in 99,884,400. Math doesn't lie. To choose 7 numbers from the pool of 50 balls, the odds are definitely 1 in 99,884,400.
However, the odds of your ticket winning are 1 in 33,294,800, because each $5 ticket has 3 chances of winning.
Different odds, depending on how the question is worded.
If you have any thoughts or questions, please contact us with your opinions.