Mark Kon, a professor of math and statistics at Boston University, calculated that a bettor buying even $10,000 worth of tickets would run a significant risk of losing more than they won during the July rolldown week.
A $2 Cash WinFall ticket allows you to pick a set of 6 distinct integers from the set {1..46}. The lottery commission then picks six distinct integers at random from the set {1..46}, effectively by drawing numbered balls without replacement from an urn. The payouts for May 9, 2011 were $24821 for a match-5 (a ticket that has 5 numbers in common with the set chosen by the lottery), $824 for a match-4, and $26 for a match-3 (http://goo.gl/gSTsF). It's easy to show that buying a ticket on that day had a positive expected value.
[Edit to show expected value calculation:
According to http://www.masslottery.com/games/lottery/cash-winfall.html,
the probability of a match-5 is 1/39028.41, the probability of match-4 is
1/800.58, and the probability of a match-3 is 1/47.40.
Then the expected value of a $2 ticket on May 9, 2011 was $24821/39028.41 + $824/800.58 + $26/47.40 = $2.21.]
$10,000 will buy 2,000 [Edit: oops, actually 5,000. Also fixed in what follows] Cash WinFall tickets. When you can only buy a few tickets in a lottery like this, the distribution of the numbers on your tickets greatly affects your chances of coming out ahead. For instance, if you buy 5,000 copies of the ticket {1,2,3,4,5,6}, your chances of coming out ahead are much worse than if you buy 5,000 tickets with a bunch of different numbers, although of course your expected winnings are the same in each case, provided no one hits the jackpot.
It's actually an open problem to create a set of 5,000 Cash WinFall tickets that maximize your chances of coming out ahead. Indeed, a Boston-area employer (that's still hiring!) posted a hiring problem based on this for several years.
If the total prizes won for any drawing, exceed 200% of the net sales for that drawing the prize amounts will be based upon a formula detailed in the Rules and Regulations or Administrative Bulletins issued thereunder.
Yes, although historically it's clear that the payouts make it profitable to buy tickets on rolldown days, the actual formula used to calculate the payouts was opaque. I heard that one of the lottery syndicates actually made a request under the Massachusetts Public Records Law to get the lottery commission to reveal the formula, which they eventually did.
http://en.wikipedia.org/wiki/Lottery_mathematics has a worked out example for a lottery that involves picking 6 distinct numbers from {1..49}. It would be straightforward to adapt that to Cash WinFall.
Past tense. They don't have that hiring problem posted any more, but it was for mathematicians/software developers in the R&D group. If you're asking because you have an approximate solution, let me know (email address in profile) and I can put you in touch with people there who would be very interested to see what you've come up with.
State-owned lotteries transfer wealth from one group of people to another group without any coercion. I don't see why private individuals can't participate in the transfers also.
More generally, this is an example of how simple changes (the rolldown) can have surprising consequences. TBQH I'm surprised the lottery operators aren't just keeping the surplus funds rather than doing a "roll down".
Apparently, this particular lottery was created to pay out a bigger percentage of revenue than other lotteries. That is not entirely a bad idea: if people are going to gamble, it's better that they don't lose too much money.
This particular scheme pays out most of the money to a select few, though, which defeats the point.
Wait for the political fallout when the people funding the jackpots realize all their money is going to out-of-staters and they have no chance of winning anything, ever.
(Yes, I'm pretty sure that's how this will be reported in local media.)
Good question. When I say 'local', I mean the Deming Headlight and the Havre Daily News. You know, all the papers nobody outside a hundred mile radius of the town cares about. The Boston Globe is up there with the LA Times and the Washington Post and so on and so forth, in the national, if not global, ranks.
It makes a lot more sense to just run the Lottery as a raffle (pick one serial number from all tickets sold, or have a fixed amount of sellable tickets), but you can see how states are more enticed by the idea of open-ended ticket sales.
Illinois actually has true raffles a few times a year and they have always sold out before the drawing date.
They usually have to publish a payout rate, it is a common requirement for most forms of pure chance gambling. If people dont win you need some form of rollup. However if you keep it purely on the single big win it does not lead to schemes like this.
Plus when you fund larger and larger jackpots (by keeping the rollup purely on the single big win) you get more and more people buying more and more tickets.
I think Massachusetts would be likely to earn more money by being able to advertise a much, much larger jackpot and losing these "rollup day" "gamblers" (when your mathematical theoretical return is so far above 100%, I hesitate to call it gambling) but apparently they have some incentive to keep things the way they are (do lottery officials have relatives or buddies who are among those gaming the system?) because they've let this go on so long.
By knowing the total tickets Ntt each time, Pjh can be estimated easily:
Pjh=1-(1-P6) Ntt
Lottery P6 is the probability of matching 6 numbers. In the case of the WINFall lottery, P6=1/13,983,816.
The total tickets Ntt each time can be estimated by its samples and their probabilities. The WINFall lottery has 4 samples, matching 6 numbers N6, matching 5 N5, matching 4 N4 and matching 3 N3 respectively. N3 is the largest sample of the WINFall lottery. As far as we have four samples in hand: N6 N5 N4 and N3, we use N3 to calculate the total tickets. Because the more sample are there, the small differences we have (Statistics Accuracy). The Ntt is:
Ntt=N3/P3
P3 is the probability of matching 3 numbers. In the case of lottery WINFall, P3=1/57.
To win is really practical.
However, government should make more money than buyers even following the abave rule.
Because it is a state-run monopoly in most jurisdictions, and in the remaining ones would likely require a legal staff substantially larger than the programming staff.
There are a few start-ups I know of that sell lottery technology/services to states, but afaik it's mostly dominated by big players and hard to break into.
It's been written about before. I read about it in '08 or '09, and over the years have tried to find an article on it but those always come back with articles on scratch-off flaws.
