Regardless of the size of the jackpot, the odds of matching all six numbers is 1:292,000,000. By any standard of gambling, these are probably the worst odds you can take. However, once the jackpot reaches a particular size, the expected value of a single lottery ticket – the mean value of the result of many repeated trials – is positive, actually making it a “good bet.” To do the math appropriately, you need to consider the likelihood you’ll have to split the jackpot with someone else, which is explained here. On top of that, you need to consider that there are multiple prizes. My rule of thumb is when Powerball gets up to about $400M, I’ll buy a ticket. Or five.
The psychology of lotteries is a topic of increasing interest to researchers. People are notoriously unappreciative of probabilities, and make terrible bets by default. Amos Tversky and Daniel Kahneman, two of my psychology heroes, made a career of demonstrating how bad we are at making decisions, particularly with regard to determining the likelihood of events, gambling, and risk-taking. More recently, research has focused on who plays the lottery, and whether certain groups are more prone to spend money on lottery tickets than others. This information is important from a marketing perspective, but it also speaks to the notion the lottery is an “implicit tax,” and to what extent it is regressive.
A recent non-parametric analysis by Garibaldi, Frisoli, and Lim (2015) looked at lottery spending trends across demographic groups. Unlike other researchers who used modeling techniques to address this question, these authors took into consideration the shape of the distribution of the data – how much the data resemble a “bell curve” – which is critical if you want your analysis to be meaningful. It turns out that most people play the lottery very rarely, but some people spend lots and lots of money on lottery tickets every month. As a result, the distribution is very positively skewed, which limits the statistical approaches you can take. Also, people tend to under-report the extent to which they participate in risky behavior. So, the data that are determining the shape of the curve the most are the most suspect. These are all important things to consider when you’re designing research.
So who is spending the most money on the lottery? According to this research, of the top 20% of heavy lottery players, ethnic minorities are overrepresented. However, further analysis showed these differences to be accounted for by education level. Usually, buying a lottery ticket is a bad gamble, and while we all make horrible decisions, those who aren’t educated in things like probability tend to make it more often. All that said, I’ll see you at the 7-Eleven in the Powerball line!