In general, it’s best to pick tickets with lots of numbers that are greater than 31. This won’t affect your chances of winning, but it will reduce your chances of having to split the jackpot, since birthdays are a popular method of choosing lotto numbers. Some economists have found that when the jackpot swells large enough, buying “unpopularly-numbered” tickets can have positive expectation (although you’d have to buy tickets for thousands of years in order to reduce the variance). In fact, there have been some consortiums in Canadian lotteries that bought up large blocks of tickets when the potential winnings were big enough. There’s a good discussion of this in Thaler’s book The Winner’s Curse.
I’ve found it’s also better to pick numbers that are positive integers, in the range that the lottery suggests. If the lottery is numbers between 1 and 100, for instance, then I’ve found that picking numbers such as 3.1416 or 666 is usually not successful.
I don’t know whether it’s still true, but in the early days of NJ Lotto, people who bet on “000” or “0000” won big – enough to make it a favorable bet – because very few people thought to bet on them. Ye olde “Is zero a number?” trick.
All lotteries in the USA do their best to try and ensure that the numbers drawn are as random as possible. While certain numbers do seem to come up more frequently over the short-term, over the long-term, with a sufficient number of draws, all numbers should come up equally. Checkout what CA does below to try and ensure randomness:
The Norwegian state Lotto runs each week and 7 balls are drawn from 34 balls numbered 1-34 for the top prize. Despite the fact that the announcers have mentioned several times that 1-2-3-4-5-6-7 is the most used sequence it remains so, and if it’s picked the top prize will be three magnitudes lower than normal. (Ordinary top prize equivalent to .5-1 million dollars.)
A couple of weeks back the winning numbers were 16-23-24-25-26-27-29, with 28 as one of three extra numbers. The second prize, for 6 winning numbers and one of the extras, was just above $1000, a week earlier the second prize was $10,000, and the third was $1000.
But then again, if everyone made sure not to use the numbers that “everyone” use, then everyone would use the same numbers… Lesson? Humans are not good random number generators.
Ah, the joys of probability and the general ignorance of its workings! Many years ago here in the NSW state lottery (which in those days sold one hundred thousand tickets per draw, numbered from 1 to 100,000), the winning ticket was number 100,000. There were headlines in the newspapers announcing this amazing feat and stating how unlikely it was.
When it comes to extremely high odds against some event, one recalls Terry Pratchett’s rule, based on movies and TV shows: an event where the odds are a million-to-one against, happens about nine times out of ten.
Of course, the odds have to be exactly a million-to-one. A mere 999,999:1 won’t do it.