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A game with a windfall for a knowing few

boston.com

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Re: A game with a windfall for a knowing few

#21

Post by bumbledraven »

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.

Re: A game with a windfall for a knowing few

#22

Post by joezydeco »

JoachimSchipper wrote: post #7
jacques_chester wrote: post #3

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.

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.

Re: A game with a windfall for a knowing few

#26

Post by mhb »

bumbledraven wrote: post #21

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 draw…

$10,000 buys 5000 tickets, but I'd be interested in seeing how the positive expected value is easily shown.

Re: A game with a windfall for a knowing few

#27

Post by [deleted] »

bumbledraven wrote: post #21

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 draw…

[deleted]

Re: A game with a windfall for a knowing few

#28

Post by mhb »

bumbledraven wrote: post #21

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 draw…

Right. I was actually interested in seeing how the probabilities were calculated which doesn't seem as easy.

Re: A game with a windfall for a knowing few

#29

Post by mhb »

bumbledraven wrote: post #21

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 draw…

The rules also mention:

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.

which has to add a little FUD into the thinking.

Re: A game with a windfall for a knowing few

#30

Post by bumbledraven »

mhb wrote: post #28
bumbledraven wrote: post #21

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 draw…

Right. I was actually interested in seeing how the probabilities were calculated which doesn't seem as easy.

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.
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