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The Mega Millions is over $500 million today. I remember reading a JSTOR paper about some numbers that are most unlikely to be chosen. For example lots of people choose 7 because it's their lucky number, and I want the opposite of that. However my JSTOR membership has ran out. Which numbers are least likely to be chosen by people as their lottery selections in a lottery of numbers between 1 and 80?

Note: Each number has an equal chance of being selected; I want to choose numbers no one else does so I don't have to share the prize with anyone if I win.

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Nice question, almost more anthropology than statistics! It would be nice to know whether there are regionalities in this. For instance, 13 is considered an unlucky number in many English countries, but it is a lucky number in Italy. – nico Mar 29 '12 at 6:44
I don't know the JSTOR numbers, or whetehr they reflect counts of actual numbers chosen. – RAH Mar 29 '12 at 6:50
@nico You might be interested in this paper: Investigating the behavioural characteristics of lottery players by using a combination preference model for conscious selection (JRSS A, 17(4):1071). – chl Mar 29 '12 at 7:17
Apparently this is making the rounds in the popular press. There was also a recent column in Significance on this topic. – cardinal Mar 29 '12 at 14:27
@rolando2: I think you're maybe misunderstanding the OP's use of "selected". The OP almost surely is using it as a synonym for drawn among the winning numbers and not in the sense of chosen by other players. In fact, that's exactly the point he's trying to have addressed, the difference between maximizing your probability of winning (impossible) versus maximizing your expected gain (very possible). – cardinal Mar 30 '12 at 1:15

I have a deep lack of interest in big lotteries, so I'm going to answer this in terms of possible strategies people might use to pick a sequence of numbers that are randomly generated.

The first strategy is the familiar one of picking a distinctly systematic sequence such as birthdays, etc. on the mystical belief that since the number is personal, if it is chosen, chance has effectively chosen the chooser and validated them with a prize.

But the second more interesting strategy is that people try to choose a 'random number'. If there is regularity in what they might choose, i.e. if they aren't very good at this, then your 'strategy' would be to choose one of the ones outside these regularities.

There is, it turns out, an interesting line of work assuming that subjective randomness judgements are actually judgements about the representativeness of data from specific generation models, e.g. 'alternation' models of coin flips. Consequently people's judgements of whether a sequence is random are both incorrect and predictable. Some old work that runs with this idea is Griffiths and Tenenbaum (2001) and Griffiths and Tenenbaum (2003). No doubt there is more recent stuff, including lottery-specific things like @chl's JRSS A reference.

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To summarize, it sounds like you recommend favoring numbers >31 perhaps including perhaps some consecutive numbers, as other people won't find that "random" enough. – Michael McGowan Mar 29 '12 at 12:47
To summarise, I have no clue about lotteries and shouldn't be taken as offering any kind of advice about this kind of thing. (Unless you win, of course... :-) – conjugateprior Mar 29 '12 at 13:04
I have a deep lack of interest...: A phrase to store away for a rainy day. – cardinal Mar 29 '12 at 14:15
@cardinal Apparently one shouldn't use it too often; it's presumably what generated my latest -1. – conjugateprior Mar 30 '12 at 7:44
Re: paragraph 3, 'being random' is quite difficult, I gather. I believe there is an IQ test based on someone's ability to generate a 'random' sequence. – gung Oct 4 '13 at 18:36
up vote 7 down vote accepted

According to this paper: Thaler, R.H. & Ziemba, W.T. (1988). Parimutuel betting markets: Racetracks and lotteries. Journal of Economic Perspectives, 2, 2, pp. 161-174. (pdf)

The twelve most unpopular lottery numbers are 32, 29, 10, 30, 40, 39, 48, 12, 42, 41, 38, and 18. These numbers are chosen 15 percent to 30 percent less often than other numbers. Note that this is in a lottery between 1 and 80. Birthday numbers tend to do particularly poorly.

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Of course publication of that article might have made the results no longer true...sort of like if an article on the best passwords lists an example, that password automatically becomes terrible... – Michael McGowan Mar 30 '12 at 18:02

Herman Chernoff wrote about this back in 1981: Chernoff, H. (1981). How to beat the Massachusetts numbers game", Mathematical Intelligencer, 3, 166-172.

Other interesting papers on this subject include Kabak and Simonoff (1983) and Stern and Cover (1989).

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(+1) If I recall correctly, Cover at one point was a consultant to the California State Lottery. – cardinal Mar 30 '12 at 14:53

I'd guess people would be least likely to choose the following numbers because in this context they don't "feel" as random... 1-5 (too low in the range to seem random); 75-80 (too high); multiples of 10, 11, or 25 (seem too special to be random).

Beyond that, Dan Ariely has said in Predictably Irrational that even integers are slightly less likely to be seen as random than odd ones.

I don't know how much your chances would be improved by following these guidelines! The depth of my lack of interest only approaches @Conjugate Prior's when it comes to the NCAA tournament.

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Interestingly, the link to the popular press article in my comment to the OP gives an example where the the sequence 1,2,3,4,5,6 was the second most popular choice in data from a Jan 2010 lottery in Quebec. – cardinal Mar 30 '12 at 1:19
It is always interesting, in any largish group, to ask people to write down a "random number" between 1 and 10. The distribution is decidedly far from uniform... – whuber Mar 30 '12 at 14:12

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