Bite-sized knowledge for the hungrily curious

If you buy 1 million Lotto Max tickets, what are your odds of winning?

photo credit: GoodNCrazy Canadian Money Queen on the 20 Vancouver BC via photopin (license)

The Answer

3% or about 1 in 33.

Lotto Max, in Canada, doesn’t have the same mega jackpots that Powerball in the US and other lotteries around the world. The jackpot is regularly in the $50 million dollar range.

A $5 ticket allows the player to select 7 numbers between 1 and 50 and each ticket contains two additional entries containing 7 numbers each.

The odds of one set of numbers winning the Jackpot is 1 in about 99 million. The math goes like this. The number of possible combinations of numbers is 50x49x48x47x46x45x44 divided by 7x6x5x4x3x2x1 (the second part is to account for the fact that the numbers can be selected in any order).

Since there are three entries per ticket, the odds are 1 in 33,294,800.

To answer the question posed, we’re going to make two assumptions.

  • We assume that it’s possible to purchase and print one million tickets in the time available between draws.
  • We assume for these calculations that all of the number combinations are unique.

So, the simple math is you have 1,000,000 tickets which each have a 1 in 33,294,800 chance of winning.

Your overall odds are about 1 in 33 or 0.03003 to one. So after spending a whopping $5 million dollars you only have a 3% chance of winning the jackpot.

In fairness there are much better odds for winning some of the lesser prizes, so you almost certainly would get back some of your money when you don’t win the jackpot, but I wouldn’t want to be the one to have to check all those tickets.

What are some of the things are more likely than winning the lottery jackpot?

  • Being ambidextrous (33,000 times more likely 1 in 100)
  • Getting hit by lightning in your lifetime. (4,700 times more likely – 1 in 7,000)
  • Being killed in an animal attack (1700 times more likely 1 in 19,000)
  • Giving birth to quadruplets. (41 times more likely 1 in 800,000)
  • Getting killed by a shark (9 times more likely 1 in 3,700,000)
  • Dying (33 million times more likely)

For what it’s worth, these odds are averaged across the population. If you never go in the ocean, your odds of getting killed by a shark are very nearly zero. As a male human, my own odds of giving birth to quadruplets would be even closer to zero.

And… if I don’t spend $5 on a lottery ticket, I have a nearly zero chance of winning the jackpot. My spouse buying a lottery ticket makes the chance very slightly greater than zero.

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