Posted in Big Numbers

The Lottery

The Lottery Posted on November 27, 2020Leave a comment

There is the old saw that says the lottery is a tax on people who don’t understand math.  And, to be honest, that is the absolute truth, albeit a bit harsh.   Sure, people win.  But considering that most of the time it’s a single person and there are millions who play, those are pretty long odds.  Besides, it’s not about how many people play.   You knew that right?  I’ll get to that in a minute.

But there has been a recent uptick in the revenues that lotteries across the country are seeing.   It’s really no surprise with the economy in the tank like it is.   People just want a little of that magic to take away the sting of the headlines or that mortgage bill or the feeling that their retirement savings are just not going to cut it in the end.

But what about that math?

Wait, time out!  I know what you’re saying.  Here he goes off on some math thing again, but bare with me here.  And all you pro-lottery, “hey, I like playing and maybe I WILL win” people, read it all.  It’s not ALL math.

First, let’s consider the odds of winning the lottery.  And let’s use the big numbers because a) I like big numbers (especially the ones with dollar signs in front…ba dum dump) and b) it makes my point seem more important than some random essay on some blog somewhere.

In the big one, Powerball, the number of ways the 5 numbers on a given ticket can match the numbers drawn is figured out using the pre-calculus study of combinations and permutations., If the order of the numbers matters, it’s permutation we care about, if the order doesn’t matter, as in the lottery, it’s a combination.   The formula for this is:



A pretty innocuous looking thing isn’t it.   Two letters and a few exclamation points, a few horizontal lines … meh, what’s so taxing about that?  Well, it’s actually pretty powerful and the answer for increasing values of n and r gets pretty big, pretty fast.   What’s it mean?  Well, let’s say n is 4, the answer to 4! is 1x2x3x4=24.  Simple right? So whenever you see that ! notation, that means take all the numbers up to n and multiply them together.   n is the number of items in the group of things from which we’re choosing, which in the case of Powerball is 59 little white balls with numbers on them and r is the number of those balls we choose from those 59 (without duplicates, since once a ball is taken out of the blowing air it is not put back in).



In a spreadsheet, you could put that in as =FACT(59)/(FACT(5)*(FACT(59-5))).   Microsoft Excel has a nice function COMBIN() which you can use to figure the above as COMBIN(59,5).  You get the same results.  If you tried it you likely got 5,006,386.   So in lottery speak, that ‘s a 1 in 5,006,386 chance of winning.  This doesn’t quite match what the lottery says, but there’s a little more to the odds and that’s more math than you want and, hell, you may be beyond your limit already as it is.   So let’s just go with a little over 5 million.

People look at that and don’t really comprehend that that’s 1 divided by 5,006,386 which is 0.000000199745.  Try putting 1/5,006,386 into a spreadsheet it gives you 1.99745E-07 which is scientific notation telling you to move the decimal seven places left.   Seven!  But say you format the cell to a number with two decimal places, it changes to 0.00.   Sure, you could click the little decimal place icon so that it added zeros to the right of the decimal but you’d have to click it 5 times to get a number other than zero and that number is just a 2.   So let’s face it, 0.000000199745 might as well be 0.00 which kinda means the chances of matching those five balls is zero.

Moreover, to get the jackpot, the really big money, Powerball throws in that red ball, which adds color to all that white but maybe also makes you think that it’s got some kind of magic (it is powerball, after all) or that it improves your odds of winning.   That red ball is selected from 39 red balls, another combination multiplied by the five million number above.   If you do that math, you’re looking at 1 in 195,249,054 (COMBIN(59,5)*COMBIN(39,1) ) which makes your odds of winning even more zero than before.

The bottom line is to win the big jackpot in Powerball, your chances are zero, to win the next big one (matching just the 5 white balls for about $200k) your chances are zero and the next one are pretty much the same.  It gets a little better after that but not much.

But that’s only statistically speaking, isn’t it?  It doesn’t address the individual.  Statistics are funny things.   When I was studying math in college my statistics professor said, “you can make statistics mean anything you want.” And in most cases, that’s true.  Numbers have weight that has been ingrained in our psyche since we first learned to count…numbers are magic and if Harry Potter taught us anything, you can make magic do some serious stuff that shouldn’t be possible.  This manipulation of statistics is one of the very reasons people play the lottery.  We tend to talk ourselves into the idea that we’re going to win.  And then some wise guy comes along and tells you that you have a better chance of dying in an airplane (1 in 354,319),  getting struck by lightning (1 in 225,107) or even dying in a legal execution (1 in 3,441,325).

And yet…

It’s all just numbers and statistics and statistics can say anything you want.   Right?  Like, maybe they can also say “What if?”  What if I am the “1”.  And everyone else is the “in 195,249,053.”

Is it just about the numbers?  Is it just about plunking down your one dollar of hard earned cash (no credit cards excepted for purchase of lottery tickets, please) and then checking to see if you won?  I don’t think so.

For just a dollar, you can buy a dream.  It might last a day or a few days, but it’s there, tooling around the landscape of your mind tapping on things like that motorcycle you’ve been eyeing and the words “debt free” and the emotional satisfaction of helping out Mom or Dad; brother or sister.   Exploring the alleys where you don’t go where there are complete strangers that suddenly have smiles on their faces because you helped them out in just a small but significant way.  All because you pulled a dollar out of your wallet on a whim.  Following that dream around the byways of your head as you think about that little slip of paper in your wallet is kind of fun.   It’s a great way to take a little Dandelion Break.  You play the lottery and you get a little of that magic that numbers have.  Magic that can make you smile.

But there’s the reality of what that dollar goes to, also.   The money the state makes from the lottery (did you know they’ve been holding lotteries since the 1700s?) goes to things like open space, parks and recreation, state parks,  school health and safety programs and probably a bunch of other stuff I was too lazy to look up.  It’s kinda like giving a buck to a favorite charity.  A really big church auction only the church is right outside your door; a few blocks down and up the trail where that deer, elk or coyote happens to cross your path.

You think about the things you would by, the places you would go, the payoffs you want to make.  There’s also that fantasy of telling the boss to kiss off and making a really stellar exit.  Since I am my boss, that won’t work for me, but plenty of people have thought it.  I’ve told myself to go pound sand plenty of times already and I’m still here.

And then sometimes the philanthropy kicks in.  For me it’s wanting to satisfy my Superman complex and swoop in to save someone’s day.   At random.  On a whim.  Just like the act that got me to this point in the first place.  Settling some stranger’s debt, just to see them smile and then walking away without telling them who I am because it’s not about me.  It’s always about them and making someone’s life just a little (or a lot, if you can) better.

And finally, because dreaming is never a bad thing.  Whether it’s about the riches of the lottery or just the general run-of-the-mill fantasy of being able to stop and clear the decks to prepare for the next adventure.  Or perhaps, it’s that thought of making the hell out of someone’s day.  It’s just a break.   And we all need a break sometimes.

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