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

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

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 data 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 un­sound—even 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.

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