Monday, September 22, 2008

Pick a Number, Any Number

Hello, All. I’ve done another of those enlightening calculations of mine. Those of you lucky enough have witnessed the Famous Cigarette-Butt Revelation, the River-of-Piss Report, and the Great Pocket-Lint Conspiracy of 2001; not to mention my lesser-known but none-the-less groundbreaking mathematical dissertations on life in-general. This time I’ve decided to tackle something that effects most people in popular culture today. What could it be? Is it the total mass of discarded chewing gum produced daily? The average volume of fingernail clippings produced over a human life span? The speed that hair grows in miles per hour? None of those. It’s (drum roll please) the lottery. Aw, come on! You know you spend a crap-load of money hoping to hit it big, so you can sell the house and buy a Haitian man-servant.


I’ve chosen to attempt to enlighten myself about the true mathematical probabilities and expectations that are involved with the lotto. It wasn’t easy either. Check out the state lottery’s homepage. See anything about true odds and probabilities of winning a certain prize? It’s not there. That kind of information is kept with the rest of JFK’s brain somewhere in Bethesda. Thankfully, there are people like Susan at the Illinois State Lottery offices who can’t fathom that there are evil geniuses like me out there who can put together a string of lies just long enough to get that information from her over the phone.


Ready? Here we go. I think that, perhaps, the biggest scam perpetrated on humanity of all time (besides Milli Vanilli, of course...oh, and GW being "elected" twice) are those “Scratch and Win” tickets. So, as I usually do, I started out with a couple of basic questions:
1. How much money actually gets paid back to the players?
2. What percentage of tickets will pay out more than $100?
3. How much money would you have to spend to guarantee that you will make more than you loose?


Without bogging you down with all of the numbers that I was able to get from Susan, here’s what I figured out. This is based on an average, $1, Scratch-and-Win game with a max payout of $5000. If about 15 million tickets are sold there will be about 3.8 million total winners, which means that there are 11.2 million LOSERS. Half of the winners will get $1 back. (I figure that really doesn’t count, because you just bring it back for a free ticket and lose eventually anyways, but for argument’s sake I left it in my calculations). This means that about 60% of all of the money that is paid in gets paid out. Only about .002% of all tickets will pay out more than $100. So this leads to the answer to question #3. How many tickets would I have to buy to guarantee winning more than I lose? The answer is: zero. It is not mathematically possible to do so, if you don’t count the change that you manage to dig out of your car seat to scratch off the poisonous film on the ticket.


It gets worse. Lets suppose that there are 60 Grand Prize tickets ($5000). That’s 60 out of 15 million. Odds are about 1:240,000. Now let’s suppose that 50 of those winners go out in the first three million tickets. That means that your new odds are 10 out of 12 million or 1:1.2 million. That’s about the same as getting audited by an IRS agent that has the same birthday as you. On top of it all there is something called the mathematical expectation of benefit. The average winner gets $2.40, and your odds of winning are about 1 in 4. So the expectation of benefit is about $.60. So, you’re paying a dollar to win 60 cents. Knock it off.


The big lottery is worse still. Odds of winning are 1: 135,145,920. So for a 6.5 million dollar jackpot your expectation of winning is $.05. You spend a dollar to get five cents. It’s even worse than that if you want your money in a lump sum. You’ll only get half of that 6.5 million. You spend a dollar to get two and a half cents. Seems silly right? Just as a comparison, your odds of being killed by an animal are 1: 2 million. So maybe you should start giving your money to the squirrels to hedge your bets both ways. Not enough? Well, you are 61 times more likely to be attacked by a flesh-eating virus and 25 times more likely to be executed by the state even if the worst crime you've ever committed is drinking milk straight out of the jug.


Didn’t mean to burst anyone’s bubble, but at the end of the day you’d be better off donating the couple of bucks to a charitable organization. At least then you could write it off of your taxes. Or, if you really want to gamble, just send the money to me, and I’ll bet it for you...honest.

2 comments:

julie riffell said...

YOU KNOW THERE IS ALWAYS THAT CHANCE SOME LUCKY STIFF WHILE HAVE LUCK ONE OF THIS DAYS AND BE ABLE TO WIN AND SPEAD SOME OF THAT AROUND. MAYBE I DREAM ALOT BUT I CAN ALWAYS HOLD OUT HOPE I WILL BE ABLE TO HELP FAMILY OR FRIENDS IN NEED. SO YOU WOUNT BURST MY BUBBLE BECAUSE I THINK YOU HAVE TO MUCH TIME ON YOUR HANDS TO RESEARCH THIS, AND YOU NEVER KNOW I COULD BE THAT LUCKY YOU WERE DOING RESEARCH ON......JEWELS

TJ said...

You know, I've seen the stats for the lotto time and again, but I still play once in a while, when the pot is big. I've actually gotten 4 nubers a few times and won between 50 and 100 dollars.

The fact is, however, that even though your chances are slim, people win the god damn thing all the time. So what the hell? I might get the golden ticket, but I'm not counting on it. I know the chances go down a lot if I don't have a ticket though.