Lottery

Identifying criminals using publicly available lottery data

Lawrence Mower’s 2014 exposé of the Florida Lottery in the Palm Beach Post argued that 8 of the 10 gamblers who had claimed the most prizes in the Florida lottery had won so much, even allowing for incredible luck, that they merit investigation by law enforcement. The math supporting this relies on the log-concavity of the regularized Beta function and a mild extension of the BKR inequality. See the math paper for full details or a more accessible overview from MAA FOCUS, or do the calculations yourself with this Jupyter notebook.

I wrote the math paper with Philip B. Stark (statistician), Lawrence Mower (investigative reporter), and Richard Arratia (probabilist). This work and the associated Palm Beach Post article led to various retailers being permanently banned from selling lottery products, arrests, improvements in lottery procedures, and follow-on investigations and news stories in Massachusetts (The Boston Globe, 7/20/14; WBUR, 4/27/18), Georgia (Atlanta Fox 5 News, 9/12/14; Atlanta Journal-Constitution, 9/18/14), Ohio (Dayton Daily News, 9/12/14; ABC 5 News Cleveland 4/20/17), Michigan (Gannett/Lansing State Journal, 11/20/14), Kentucky (WLKY, 11/20/14), New Jersey (Asbury Park Press, 12/5/14 & 2/18/15, USA Today 2/19/15), Indiana (ABC 6 Indianapolis, 2/19/15), Iowa (The Gazette, 1/23/15), California (CBS Los Angeles, 10/30/14; KPIX CBS San Francisco, 10/31/14), Pennsylvania/New Jersey (CBS Philly, 5/21/15), Washington DC (WUSA9, 10/30/15), North Carolina (Charlotte News & Observer, 9/29/16, 10/6/16, 12/6/16), New York (5/27/17), Iowa (6/3/17), Connecticut (Hartford Courant, 8/17/17), Wisconsin (3/18), a nation-wide study by PennLive (9/17, 2/18), coverage by the BBC (12/3/17) and South African news (8/14/17), and a study by the South Carolina Legislative Audit Council (6/19), Maryland (3/22), and Colorado (8/18).

Why not buy lottery tickets?

One of the first things you may learn how to calculate in an intro probability course is that casino games like roulette are “bad bets” in that you expect to lose money on every bet, on average. Is that true for the lottery? On average it surely is, because the lottery makes money, and a lot of it. But what about when the jackpot is very large? What if you only buy tickets for those drawings? It turns out that, for some lottery drawings, you might expect to make a little bit of money on average. Then why not buy lottery tickets? Aaron Abrams and I answered this question using portfolio theory in our paper Finding good bets in the lottery, and why you shouldn’t take them, which won the Lester R. Ford Award in 2011.

You can also get a shorter, more accessible versions:Brain Trust

I have talked about the lottery and our work on ABC World News, Fox & Friends, and 20/20. Aaron appeared on NPR’s All Things Considered, BBC Newshour, and CNN Newsroom.

A better way to buy scratcher tickets

There are some famous examples of people who have bought a lot of scratcher tickets and won big prizes who appear to have made money while doing so.  In a series of articles in 2014, journalist Peter Mucha pointed out that the usual mathematical analysis one uses to study scratcher tickets is the wrong model for what those people are up to.  My paper The luckiest strategy on earth?  A better way to buy lottery scratch-off tickets does the math to analyze the strategy described by Mucha.

Links to papers and posts

In summary, here are links to: