Posted: Nov 30, 2018 11:54 am
Thanks that's perfect, it's exactly what I couldn't find.

So consideration of the jackpots alone (which doesn't reflect the expected value of the bet, for which you need to sum the expected values of every prize level) shows that \$1 in the Florida lotto gives you a 1 in 22,957,480 chance (calculated from the simple formula for number of combinations N!/(N-k)!k! ) of winning a minimum of \$2,000,000 shared among the number of winners, I can't find the statistics on that either, so I'll just assume it's about 2 on average (which would represent sales of ~23 million tickets per week). This means the jackpot gives you an expected return of \$-0.956 per dollar wagered.

The scratchcard costs \$10 to play and so has an expected return per dollar from the jackpot of of \$2,000,000/10x3,000,000 = \$-0.933 per dollar wagered, which is worse. Again note, that's only considering the jackpots.

The megamillions costs \$2 to play and so has an expected return from the jackpot of \$-0.939 per dollar wagered, again subject to the assumptions of about 23 millions tickets sold (the more sold the more likely you are to share your jackpot) and no rollover jackpot.

So the best bet depends on ticket sales, and rollovers. It's likely that the least worst option is to play only when there's a large rollover in either the lotto or megamillions draw, and the best option is not to play. The article mentioning that the megamillions jackpot had reached \$1.6bn would make the draw worth playing if few enough tickets were sold (although business insider point out in another excellent article that because of taxes, it's probably still not worth it).

I do seem to recall a few years ago there was a huge rollover in the UK national lottery draw that made it *almost* worth playing. I think this has been made less likely by more people playing "lucky dip" tickets with randomly generated numbers in recent years.

PS: All of that does assume you choose your numbers randomly, if you do something daft like pick 1,2,3,4,5,6 or your family's birthdays you drastically increase the chance of sharing the jackpot and make your chances worse.