Do certain numbers in a lottery have a higher probability of winning than others?

by Jakub Marian

Tip: See my list of the Most Common Mistakes in English. It will teach you how to avoid mis­takes with com­mas, pre­pos­i­tions, ir­reg­u­lar verbs, and much more (PDF Version).

Does going for “nice” sequences of numbers, like 1 2 3 4 5 6, reduce the probability of winning in a lottery? Some people think so. “Have you ever seen such numbers come up in a lottery? It’s simply not going to happen,” they argue.

The mathematician in me would like to scream:

“Such an argument is a complete nonsense. The process of generating the numbers is random with a uniform distribution, so it doesn’t matter whether you bet on 1 2 3 4 5 6 or any other combination.”

The mathematician in me would be wrong, however. It turns out that people who tell you not to bet on “nice” numbers like 1 2 3 4 5 6 are, in fact, right, but mostly for completely wrong reasons.

Splitting the prize money

To understand why, we need a bit of psychology and understanding how prize money is calculated. Lotteries based on drawing numbers usually have a certain amount of money allocated to each drawing. When you get all the numbers right, you win the jackpot… but so do all the people who bet on the same numbers, and the prize money is split among all winners.

If the jackpot is $10,000,000, and there are just two winners, each one gets five million dollars. Still quite good, isn’t it? But if there are 10,000 winners… each one gets a measly $1000.

And this exactly happens. According to this article about the British Lotto:

About 10,000 people choose the combination 1 2 3 4 5 6 each week.

This makes betting on such a combination fundamentally unsoundeven if you win, your prize will be relatively small. In other words, would you bet on something with such a low probability of winning if the jackpot were just $1000? I think not.

How to choose the best numbers

There are several strategies you should follow in order to maximize winnings (or minimize losses, which is more likely):

  • Avoid numbers in arithmetic sequences. People are more likely to go for sequences like 5 10 15 20 25 30 than for completely “random” ones.
  • Avoid sequences that form a nice shape on the ticket. The numbers are usually arranged in a certain way on the ticket. People are more likely to “draw” geometric shapes (such as squares and squiggles) on the ticket than to select the numbers randomly.
  • Avoid numbers below 31. A lot of people bet on numbers representing significant dates in their lives, so especially numbers below 12 are quite common.

By the way, I have written several educational ebooks. If you get a copy, you can learn new things and support this website at the same time—why don’t you check them out?

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