Winning The Lottery Thought

The Sandbox General
61

Something called rolldown. Something about large pots that don’t get won then rolldown to lower winning tickets in future drawings?

A little more in the Wiki page on the movie and this:

Cash Winfall

Cash Winfall was drawn Mondays and Thursdays. 6 numbers 1 through 46 were chosen. The jackpot began at $500,000, it always was paid in lump sum. Lower-tier prizes were $4,000, $150, or $5 for matching 5, 4, or 3 numbers respectively, 2 numbers won a Cash Winfall bet. If the jackpot reached $2 million and was not won, the jackpot was “rolled down” with the secondary prizes increased.

After the Boston Globe published reports of individual stores selling millions of dollars in tickets, state officials suspended the game, suspecting organized crime involvement. Investigations revealed that the profiteers were a retired couple from Michigan (who had exploited the same system when that state’s lottery had the Winfall game) and a group of MIT college students who, by legally exploiting elements of the game, were practically guaranteed to win profits of approximately 20% when tickets were bought in rolldown conditions.[4] The story was adapted into the 2022 Paramount+ film Jerry & Marge Go Large.

Cash Winfall ended on January 26, 2012.[5]

62

At the end of the movie they said that they ultimately won over $26M. Not sure how much they had to spend to win that but in the movie they indicated there were times when they were winning more than double what they spent. So paid $8K for tickets and won over $16K in prizes.

63

OK, can we duplicate the math used to determine that this was an easy bet?
I mean, how much would those lower prizes have to increase in order to make it worthwhile? I mean $4000 for 5 doesn’t intuitively seem like great odds to start.
Some, please do the math!

OK, 46C6 = 9.36 million.
Not sure of the math to get 5 out of 6, cuz old and forgetful.

64

You’d be surprised at what math is involved with those puzzles.

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65

You’d be surprised at what math is involved with those puzzles .
Making them? Sure. Solving them? Eh. More logic than math.

In the trailer he also uses the Rule of 72 (simple math) to estimate how long it would take to double money at some (unheard in the trailer) interest rate (I guess I could reverse engineer it). Not sure if the financial advisor knew how to use his calculator to determine the exponent more accurately or if he needed a calculator to use the Rule of 72.

66

@dr_t_non-fan here is another resource to explain the math.

67

That article, not written by someone who knows math:

If someone flips a coin five times, then the results might be one head and four tails. But that same coin is flipped 5,000 times, the results would be closer to 2,500 heads and 2,500 tails.

Not countably closer, but percentage-wise closer. Should make that distinction here, for the idiots, and for the math whizzes who will point out the error otherwise.

Also:

“So, if you purchased 100,000 tickets then you would get $166,140 in return,” Tetali wrote in an explanation to the film’s production team. “Game on!”

Only on average. Need Variance Man to make a return here as there is a risk of ruin (might be small, again, someone will have to do that math). Just noting that it might result in a loss.

“There’s a way to win every time. There’s a loophole that they didn’t see and it’s right here in the math,” Jerry tells Steve. “On the roll-down weeks the payouts to the lower numbers increases above the amount you would pay to play. So, the math is in your favor.”

Again, ON AVERAGE. Not “every time.”

The protagonist seems to make the biggest mistake in “stealing” money: he tells everyone else about it. NO! Because some humans suck. Sure, on AVERAGE humans are decent folks, but the more people that know about your scheme, the more likely one of them is not a decent folk.

68

Also completely ignores probability waves

4 Likes
69

Ahem, probability PARTICLES!

70

Here is a 60 Minutes transcript.
Boy the movie is already taking some inspiration from sources other than the true story: they owned a convenience store; didn’t get forced retired.
Wow, the interviewer is really pandering down to his audience.

Jon Wertheim: This is not taxing the outer limits of your math skills.

Jerry Selbee: No, it is actually it’s just basic arithmetic.

Jon Wertheim: Are you thinking, “I bet there are a million people that have also caught onto this?”

Jerry Selbee: Exactly, is what I thought.

More, when they start playing the MA lottery, especially the bolded:

Jon Wertheim: You went into this looking for organized crime. As the story unfolded, were you surprised by what you found?

Greg Sullivan: I wasn’t surprised. I was dumbfoundedly amazed that these math-nerd geniuses had found a way legally to win a state lottery and make millions from it

Jon Wertheim: And the state’s getting rich in the process.

Greg Sullivan: And the state got very rich. The state made $120 million.

The investigation found no one’s odds of winning was affected by high-volume betting. When the jackpot hit the rolldown threshold, Cash Winfall became a good bet for everyone, not just the big time bettors like the Selbees. By then though, Massachusetts State Lottery had moved on to a different game without a statistical twist.

Oh, math-nerd geniuses cannot possibly use math to make money?? Maybe you need to hire some in the Lottery Department, so the state doesn’t lose out.

Also, about the second part: Not sure how this works. I mean, the state makes money offering the lottery, but these “schemes” serve to take money away from the coffers. Sure, it’s someone else’s losing lottery money, but the loophole allowed more winners and, thus, state wins less.

71

So I wonder if the state went big on advertising the game and the weeks when there wasn’t a rolldown made enough to more than offset the times when this guy was winning big on the rolldown.

In the movie they do show that his initial try didn’t turn out like he expected. But that was because he didn’t buy enough tickets to overcome the variance. I think it would be that he bought enough tickets that he expected to get X at 5, Y at 4, Z at 3. But X, Y and Z were small enough that by only getting X- (1 or 2) and Y - (10 or 20) … that the total winnings came up short. So he increased the number of tickets he bought so that the probability that being off of X by a couple was smaller and that would ensure his return was high enough.

72

That is literally how this lottery works. The roll down only exists because they made “too much” money on the previous draws.

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73

There was something in the movie about how the lottery saw the anomalies with someone winning more a lot but since it was only one person and the game was still a huge money maker, they didn’t stop it. They showed that the newspaper reporter got the information about who was winning and saw that this guy was winning huge every so many weeks.

When they say the movie is based on a true story it is very loosely based on that story. They have changed so much it is hard to even know what might be from reality.

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74

I don’t like reading about this because it makes me feel like an idiot for not finding and exploiting it myself.

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75

I’m not entirely sure about the details, but it’s my understanding that the state takes a cut of each ticket sold, then the rest goes towards prizes. The state doesn’t care how those prizes are divvied out - they already have their cut.

That’s part of why the rolldown thing existed - the extra prize money had to be paid out to prize winners. It didn’t belong to the state.

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76

I remember listening to a podcast about this story years ago. It was probably an NPR show (This American Life, Radiolab, Planet Money, or something), but I can’t find it now.

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I read that as “every time” they purchased 100,000+ tickets for a drawing. He probably should have included the word “practically” or something similar. I imagine the chances of losing money for a drawing after purchasing so many tickets would be vanishingly small.

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78

I see you have great taste in podcasts.

79

Kelly Criterion?
Someone can do the math on the Variance of such games, I’m sure.

80

$5M is mine. WTF you think you want to do with an extra $15M?

Sort of why I started the AO Lotto Investors. And why I get 5 lines for Mom-n-Dad, and Bros.
I would get my share down to the 5M by giving the rest away. Like, I never want to give another cent away for a tithe (several churches would get $ from my total winnings), to a friend because they’re down and out, no one breaking into my home because I have $100M in different places. More reasons, but…$5M seems to be a safe # that I won’t have a lot to worry about except for the next years interest rate