Always check your assertions... (Winning the Lottery)

by brilee1 min read31st Jul 201211 comments

7

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"In 2005, Dr. Zhang was having an ongoing discussion with friends about the Lottery, with Dr. Zhang taking the view that it offered poor odds and was a tax mainly on poor people. To bolster his argument, he began analyzing the Massachusetts Lottery’s various games. But when he got to Cash WinFall, he was shocked to find that during roll-down drawings the odds were in the bettor’s favor."

Full story here - it's rather engrossing.

http://www.mass.gov/ig/publications/reports-and-recommendations/2012/lottery-cash-winfall-letter-july-2012.pdf

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The article linked to is interesting, but your post isn't detailed enough to indicate what the story is actually about.

An unusual form of lottery, with capped big jackpots, and distribution of excess funds to the remaining lower winning levels, attracted large betting pools because the state lottery officials had unintentionally created a positive expectation bet.

It's unclear that this was entirely unintentional on the part of the state lottery officials. The report certainly seems to conclude that the lottery attracted a large volume of bets, just as desired. It says that the state made money on this, too... though I don't quite understand how. Clearly someone had to lose money.

Clearly someone had to lose money.

Someone did -- everyone who didn't win a prize during the weeks the jackpot was rolling up. They're the people funding this. There's no sign of anything underhand going on.

It says that the state made money on this, too... though I don't quite understand how. Clearly someone had to lose money.

If I understand the matter correctly, the "someone" who loses money is the same someone who always loses money when buying lottery tickets - the buyer. The construction of the roll down system just makes it so that some of the money lost by players from the (majority of) rounds during which the jackpot is built towards the cap, is redistributed towards the round where the roll down happens. So much so, that this roll down round actually has an expected gain for each ticket. The players clever enough to only buy tickets in the round in which the the roll down is expected to happen thus profit from those who buy tickets in all the other rounds. The state, however, takes its 40 % profit from everyone.

Right. The state still loses money when this roll-down happens, but this seems to have been intended as marketing, which makes measuring its total impact harder.

Right. The state still loses money when this roll-down happens, but this seems to have been intended as marketing, which makes measuring its total impact harder.

Well, wether the state is losing money or not when the roll-down happens depends on how you define "losing" in this context, or rather, I suppose, on bookkeeping. I would say not, for the simple reason that although the payout on rounds where the roll-down happens may exceed the income on that particular round, the excess payout, so to speak, is made with money that, as I understand it, was never counted as profit in the first place.

To elaborate: In this particular lottery, the state is taking 40 percent of every dollar betted as overhead and profit. The rest (60 percent, obviously), is paid back to the lucky winners in various proportions. However, the concept of "jackpot" basically means that each round where there is no winner with all the right numbers, a portion of the 60 percent is moved into the "jackpot" and thus made available as potential winnings in the next round. This means basically that even though the payout when the jackpot (or roll-down) falls out may exceed the total amount paid for tickets in that round, that doesn't affect the state's overall profit, which continues to be 40 percent of every dollar.

It says that the state made money on this, too... though I don't quite understand how. Clearly someone had to lose money.

It may be that the state is 'skimming' the rolled over funds from one jackpot to the next: imagine jackpot #1 is short $100 of being +EV, and $50 is kept by the state and $50 is rolled over to the second, which is now short $50; the second jackpot also goes unwon, so another $100 is split between the state and jackpot #3, and now jackpot #3 is neutral EV. Anyone who entered jackpots #1 and #2 lost money, while those entering #3 neither lose nor gain on average, and if there is a jackpot #4 (because again no one happened to win #3), then those entering #4 can expect to gain money, while the state is now up $150. If you follow me.

The people who lost money were those who bought tickets under normal circumstances; there were only certain points in time when the expected value of a bet exceeded the cost of a bet.

  • Retracted; Tristan's explanation is better
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It says that the state made money on this, too... though I don't quite understand how.

There may be an issue of time-value of the money, if the state has the money from the tickets in a large pool that they can invest well or has a slightly higher interest rate than the rate for small accounts. In that case, this essentially functions like an investment. But this seems unlikely since the time between when tickets are bought and when payout occurs is short.

It says that the state made money on this, too... though I don't quite understand how.

The state takes $0.40 of every ticket bought off the top. The betting pools bought tickets above and beyond what the "regular" customers would buy when the jackpot was getting close to $2 million dollars. These are tickets the lottery would not have sold otherwise more than likely. (The kind of people who buy massive amounts of tickets when they actually have an edge in the odds are also the kind of people who buy NO tickets when they do not have an edge.)

Clearly someone had to lose money.

Deciding which is the sensible counterfactual is always tricky, and a conclusion can be switched 180° by choosing a different counterfactual. Carpe paribus, baby!

The most reasonable counterfactual I can come up with is as follows.

First the factual, what actually happend 1) There were the usual lottery ticket buyers who bought lottery tickets when the odds were against them. During these times, the jackpot was built up over time to close to $2 million.
2) There was a second group of people who know math, know how to use it, and aren't afraid to bet they are numerate. They brought in a lot of money to buy additional tickets when they believed (correctly in virtually every case) that the jackpot would go over $2million and the average payout on tickets would exceed their cost (typically by about 15% when it happened).

The counterfactual would be that somehow the numerate were prevented from buying many tickets, but otherwise the lottery stayed the same. In this case we would see 1) Less revenue to the state as fewer overall tickets are sold 2) Less prize money paid out overall as less money was paid in to buy tickets 3) But somewhat higher average payout to the innumerate who buy a steady-ish stream of tickets in times of good odds and bad, since all the jackpot would be split between the innumerate in the absence of the numerate big bettors.

Yes, there's a market for losing scratchoff tickets because they have very broad dates during which they were sold while draw tickets are for specific dates. However it's not really practical to offset really big multi-million dollar wins with losing scratchoff tickets. If it's a few thousand then yes, rummage through the trash bins at your local store for losing tickets. Thanks Regards, http://www.eurochance100.co.uk/cgi-bin/user.pl