The California Lottery is running advertisements claiming that over a million Californians win the Super Lotto Plus each month. Obviously their definition of “win” is different than mine. I don’t think it can be counted a “win” for the month unless the player is cash-positive for the total of all his or her lottery plays for the month. Of those one million Californians that “win” in a given month, how many actually wind up cash positive? I don’t have an actual number, but it is far less than a million.
For Super Lotto Plus, the odds of getting any payout are approximately 1 in 23. However, almost half of those payouts are only one dollar, the cost of the play, so they only break even, which can hardly be considered a win.
Based on figures from the California Lottery web site, in March 2008 there were a total of 1,991,983 Super Lotto Plus payouts, which means that approximately 45.8 million plays were purchased. Of those, 1,194,156 paid out only the one dollar purchase price, 400,024 paid $2, 381,692 paid $8-12, and 16,111 paid $43 or more. That means only a total of 797,827 plays were cash positive, so fewer than a million Californians could be said to have won the Supper Lotto Plus in March. Perhaps the Lottery could be forgiven for exaggerating the number of winners by 25%, but in fact the real number of winners is probably much lower, because many people buy more than one play, and of course 22/23 of those plays lose one dollar.
It is likely that almost all of the persons receiving the payouts of $43 or more actually won, i.e, were cash-positive for their lottery “investments” for the month. Perhaps even the majority of people receiving $8-12 payouts are cash-positive. But it’s likely that very few of the $2 payouts went to people that were cash positive. If we assume (very conservatively) that half of the recipients of $2 payouts were cash-positive, then at most only 597,815 players were cash-positive for the month. That means that the Lottery is overstating the number of winners by at least 67%.
Maybe the million winners are the people who don’t play.
If the lottery used that criterion, they could claim that more than 35 million Californians “win” the lottery every month.
At least those people are net cash neutral, which means that they on average doing more than $0.50 better than the people that buy tickets.
“A strange game. The only winning move is not to play.” — Joshua, in _Wargames_