Brandi couldn't find the man of her dreams until she won the lottery
Indulge us for a few minutes before you go out and buy this week’s lottery ticket(s)?
Mega Millions and Powerball are America’s two biggest lotteries, available in 41 and 43 of the contiguous United States, respectively. And every week, tens of millions of idiots feed the beast.
Both games are for mental patients, but let’s deconstruct only Mega Millions for now.
To win the jackpot, you have to pick 5 out of 56 white balls and 1 out of a separate 46 red balls.
Regard each of the two colors separately. For white balls, you can pick any one of the 56 for your 1st ball. That leaves 55 choices for your 2nd ball, 54 for your 3rd, 53 for your 4th and 52 for your 5th.
Which would be
56 x 55 x 54 x 53 x 52
except you need to remember that every combination is counted multiple times. Say you pick balls 8, 13, 25, 33 and 50. Well, that’s the same as 25, 8, 50, 13 and 33, right? Any one of your five chosen balls can be in the 1st position, leaving four balls for the 2nd position, three for the 3rd, etc. There are 120 possible permutations, so the total number of five-ball combinations is:
56 x 55 x 54 x 53 x 52
5 x 4 x 3 x 2
Which equals…well, it doesn’t matter what it equals because we’re not done yet. We still have to multiply by the chance of you getting the red ball right, which you have a 46-to-1 shot of doing. So the chance of the numbers you pick being the numbers that come up is
56 x 55 x 54 x 53 x 52 x 46 = 175,711,536
5 x 4 x 3 x 2
That’s right, 176 million to one.
Lots of people, including most lottery players, don’t bother to distinguish among large numbers. They figure that once you get beyond 10,000 or so they’re all pretty much the same. The chance of winning Mega Millions is about the same as the chance of you choosing a U.S. resident at random, then correctly guessing her street address.
Of course, not every dollar collected goes to prizes. No lottery is or can be a zero-sum game. Each lottery corporation needs to keep some cut to cover expenses and turn a profit.
In California, that cut is about 48%.
ExxonMobil’s 2009 profit margin was 8.6%, and more than a few thousand people regard the oil and gas multinational as exactly the kind of thieving leviathan society needs to dismantle brick by brick.
This week’s estimated jackpot is “$105 million”, which is a gigantic lie. Look at this, direct from MegaMillions.com:
The ESTIMATED JACKPOT number is in 20-point font, and ALL CAPS. The Cash Option number is in 11-point font. In other words, the estimated jackpot isn’t $105 million. It’s $66 million. Wanting to believe it’s the higher number doesn’t make it so.
Do you work on commission? Even if you don’t, if your employer offered you a $40,000 bonus this week, would you be interested?
Okay, what if he then said,
“Well, the commission is really $16,900 after taxes. We could cut you a check for that much now, but if you’re willing to take $128 installments every month until 2037, and also add the taxes back in, then that totals $40,000.”
You’d cry dishonesty, and you’d be right. This is yet another example of government functionaries obfuscating the truth in a way that if you or I attempted, we’d get sued. And lose.
After taxes (which average 7¾% state and local in some jurisdictions, plus 25% federal), that jackpot shrinks to $44,452,250.
But that’s assuming that only one ticket will win. The chance of there being exactly one winner varies with the number of tickets sold, but it can never be more than 37%. In other words, there’s never a scenario in which the most likely outcome is that exactly one person wins. If you win – which as we’ve all but proven, you won’t – there’s a good chance you’re going to have to split that prize.
Say there are two winning tickets, which are thus each worth $22,226,125. For doing the near-impossible – getting all six numbers right – you’d get 6% of what you should get. The remaining 94% goes to the government. The very government that has a monopoly on these games, and also has a de facto monopoly on education – and has taken the responsibility of teaching math to the same populace it sells lottery tickets to.
As the brilliant Durango Bill points out, if you drive 1000 yards out of your way to buy a lottery ticket – 500 yards there and 500 yards back – it’s more likely that you’ll die in a car accident en route to get your ticket than you’ll win.
But hey, you can’t win if you don’t play.
**This article is featured in the Totally Money Carnival Blog Carnival #20**
