The Mathematical Loophole that Broke the Lottery

this video was made possible by recon get top-quality comfortable and surprisingly affordable wireless earbuds for 15% off at buy rake on Comm /h a I so remember when you were a kid and you had to learn statistics in math class but you didn't want to because you were busy playing video games and asking people at prom and then getting turned down by people for prom and then going to prom by yourself and then stealing all the miniature hot dogs from prom by stuffing them in your tuxedo pockets but then getting found out when one of the chaperones dogs smelled the miniature hot dogs and then attacked you and then everyone called you a hot dog tuxedo boy for the rest of high school I mean that's just a hypothetical that probably hasn't ever happened to anyone and definitely didn't happen to me the point is you thought statistics were useless and your teacher said math is important for when you get older and then you did get older and realize that you didn't know how to do things like file taxes or buy insurance or get people to stop calling you hot dog tuxedo boy but you did know the standard deviation of a bell curve well it turns out that your teacher was right math is useful sometimes at least it was for this man Gerald Selby the retired convenience store owner who broke the Massachusetts lottery to understand how he did it first you have to understand an idea called expected value to explain let's imagine a super fun game where I flip a coin if the coin is heads I get $2 if its tail's I get nothing the odds of a coin flip are 50/50 which means each game I have a 50% chance of winning the $2 and a 50% chance of winning nothing my expected value then is $2 the prize times 1/2 the odds of winning that prize which comes out to $1 in other words on average I will win $1 per game now hopefully you follow that because if not the rest of this video is going to make about as much sense as the relationship between Elon Musk and Grimes and all the probability math it will involve probably looked as nonsensical as the name of the baby that was had by Elon Musk and Grimes so the Massachusetts cash windfall lottery worked like this you pick six numbers between 1 and 46 and then 6 winning lottery numbers were drawn from a weird spinny wheel pull of ping-pong balls and false hope and if your six numbers matched those six numbers bingo you won the jackpot and you can join the ranks of other lottery jackpot winners the majority of whom make terrible financial decisions and ultimately go bankrupt having alienated all those close to them ray but with cash windfall you didn't need to win the jackpot to win money if any five of your six numbers matched the winning numbers you would win a smaller prize insane with a four matched or three or even two but what ultimately made cash windfall beatable was something called the jackpot roll down you see unlike normal lotteries where the jackpot continues to grow until someone wins it in cash windfall once the jackpot got to 2 million dollars if nobody wanted that jackpot money would start to be distributed to people who qualify for lower prices match for five or four or three of the winning numbers and much like when the Fire Nation attacked the jackpot roll down changed everything and now it's time for a warning the following portion of this half is interesting video contains a lot of math like a truly bonkers amount of math side effects of watching me explain as much math may include crying boredom drowsiness fatigue anger itchiness redness of the face sneezing aching unsubscribing the unshakable feeling that you got tricked into learning something in Loomis to explain we're going to use the actual numbers from the actual Massachusetts cash windfall jackpot from February 8 2010 to keep the numbers pretty let's say you're buying 200,000 tickets at their real-life price of $2 each so spending $400,000 the odds of having five of your numbers match the jackpot numbers is 1 in 39,000 and 28 the price for that is normally $4,000 but with the special jackpot rollover the prize was twenty two thousand and ninety six dollars so let's calculate the expected value given one in thirty nine thousand twenty eight awed on average about five of my 200,000 tickets will match five of the six jackpot numbers multiply that by the prize twenty two thousand and ninety six dollars and we get an expected value of one hundred and ten thousand four hundred and eighty dollars so I spent four hundred thousand dollars and my expected value is 110 thousand four hundred and eighty dollars not a good deal but wait all my tickets are also eligible for a prize if four of the six numbers match the odds of that are one 800 which means about 250 of my 200,000 tickets will qualify and I'd win eight hundred and seven dollars and 52 cents for each for an expected value of two hundred and one thousand eight hundred and eighty dollars now my total expected value is three hundred and twelve thousand three hundred and sixty dollars still less than my 400 thousand dollar investment but wait I'm also eligible for a prize if only three of my numbers match which has one in forty 7.4 odds and a prize of twenty-six dollars and 85 cents expected value of one hundred and thirteen thousand two hundred and eighty dollars and alap which has happened my total expected value is now a four hundred twenty five thousand six hundred and forty dollars more than my four hundred thousand dollar investment plus if I just match two of six which happens one in 6.8 times I get a free lottery ticket worth two dollars which adds another fifty eight thousand eight hundred twenty-three point five dollars putting my total expected value for a four hundred thousand dollar investment at four hundred and eighty four thousand four hundred and sixty three point five dollars a return of about twenty one percent and that doesn't even take into account the one in nine million three hundred and sixty six thousand eight hundred and nineteen odds that I actually win the six of six jackpot when you add that in the expected value of my four hundred thousand dollar investment becomes five hundred and forty seven thousand eight hundred and eighty one dollars a thirty seven percent return on my investment that meant if you just bought enough tickets the odds would work out in your favor and you'd be basically guaranteed to make money from 2003 to 2012 Gerald and his wife Marge figured this out bought millions of tickets and 126 million dollars in the cash windfall lottery first in Michigan who later discontinued the lottery and then in Massachusetts who started using the same lottery system Michigan had because American states have a god-given right to repeat the mistakes of other American states just ask Florida Texas and Arizona but you know what isn't a mistake getting a pair of ray con earbuds ray con actually sent me a pair of their everyday a twenty fives to try out and I have to say I was really genuinely impressed not only is the sound quality fantastic but they're also super comfortable I could go through an entire workday with them in and forget they were even there but there's still plenty secure for running I spent basically all my time making the and being on calls about making videos which means I use earbuds a lot and I can tell you that ray cons are the real deal plus they started about half the price of other premium earbuds you can get 15% off they're already affordable prices by going to buy rake on Comm /h a I

Channel: Half as Interesting

Views: 1,987,516

Rating: 4.8186197 out of 5

Keywords: lottery, math, expected value, gambling, statistics, loophole, exploit

Id: TJesgv3YOf8

Length: 6min 57sec (417 seconds)

Published: Fri Jul 10 2020

Reddit Comments

[u/HobbitFoot]

Damn, that shade thrown at the end.

[u/winkytinkytoo]

Adding this to my watch list.