Which numbers are least likely to be selected by people in a lottery? 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.
 A: 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.  
A: 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).
A: 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.
A: 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.
