The lottery is a horrible, horrible system of money extraction from the hopeful, the uneducated, and (per zip code analysis of lottery sales) the poor.

Yet I still played. I joined up with 20 of my coworkers to throw some money into an office pool in hopes of increasing out lottery winning odds by a few decimal points.

Playing the lottery is a dumb idea, but I still jumped in. Why? *Math.*

## How Bad Are Lottery Odds?

We played the Mega Millions lottery which has odds of 1 out of roughly 176 million. With such big numbers like that, what does it really mean? Do you have any shot at all?

If you translate the odds from 1 in 175,711,536 to a percentage it comes out to .000000569115%. But even that number is so wildly low it is tough to understand what it really means.

To show how bad the lottery is, let’s compare it to other odds:

- Odds of dying from being struck by lightening at any point during a year: 1 in 1,000,000
- Odds of dying from being stuck by lightening at any point in your life: 1 in 84,079
- Odds of dying from a bee sting: 1 in 6,100,000
- Odds of dying from a fireworks discharge at any point in your life (most odds are listed as during one year): 1 in 386,766
- Odds of dying from a dog attack at any point in your life: 1 in 120,864

None of these are evenly remotely close to the 1 in 176 million odds of winning the lottery.

So knowing these horrible odds, why did I play?

## Expected Value Math and the Lottery

Oh no, no math!

My office played the ridiculously large Mega Millions jackpot of $640 million. The lump sum payout was $462 million before taxes. Split amongst 21 people that would be $22 million. I could live off of that just fine.

There’s a concept in math called **expected value **(or EV). EV shows the total value of an equation based on all of the individual possibilities.

In English? Let’s say I gave you a 2.5 in 10 chance to win $10 and I charge you $1 to bet. The expected value equation would look like this: EV = (25% x $10) + (75% x -$1). Essentially, you have 25% odds to win $10 and 75% odds to lose $1. Running the math you get EV = $2.5 + (-1) = $1.50.

Long term, given multiple attempts, you can expect a positive result from my bet. The more you play, the more likely you are to end up winning money. This is how gambling works against you. The common phrase is “the house always wins” because they stack the expected value equations in their favor. Where my equation has a positive $1.50 EV, gambling has, at worst, a barely negative (usually significantly negative) EV. That means the odds are stacked against you and that’s why the house always wins.

So what does this have to do with the lottery?

The expected value of the odds is positive. Now, granted, this wasn’t the type of bet where I had thousands of attempts to see the positive result so it was really an exercise in entertainment. But let’s run the EV equation for the massive Mega Millions lottery.

EV = ($462 million x odds of winning) + (-$1 x odds of losing)

The odds of winning are .000000569115% as discussed above. The odds of losing is 1 minus that amount (which for our purposes, is 99.9999999%, essentially 100%).

EV = ($462 million x .000000569115%) + (-$1 x (1 – .000000569115%))

EV = $2.62 + (-$1) = $1.61

With the odds so stacked against you it would normally be mathematically ignorant to play this specific lottery game. Your .000000569115% is so low that it is virtually 0%. But with the payout being so high it is worthwhile to use several decimals of percentage until it isn’t exactly 0%. And when you do that the expected value of the equation is actually positive. It’s one of the only times that playing the lottery makes mathematical sense.

## Why Did I Really Play?

Okay, did I really play because of math? Maybe. I guess math was more of my geeky way of justifying it to myself.

I played because I can afford to play, and $5 was well worth the entertainment. If you can’t afford to play or have the type of personality that will get addicted, don’t do it.

I played because I’d like to have my shot at showing the world how *not* to burn through your lottery winnings in 5 years or less as most lottery winners do. Instead I’ll get to keep doing things the right way with my finances: funding our Roth IRAs and spending less than we earn.

I played because $462 million or even $22 million (worth more chances to win) is an insanely large amount of money. Unless I invent something or build a mega business, I’ll never see that kind of cash. But I’ll still get to live better than 95% of the world’s population.

**Why did you play?**

{ 6 comments }

You are really paying $1 for the chance to think about how you would spend the money and how it would change your life. If you don’t play, you can’t really “entitle” yourself to think about winning. At least that’s how I justify my occasional choice to play the lottery. I get to think “what if” until I check my numbers.

It’s good fun to get caught up in the buzz of a big jackpot. Although the odds are sooooooo slim, somebody’s got to win it!

I didn’t play but I occasionally will purchase the bigger scratch offs, I always felt like I had better odds of winning with those. I’ll have to use your math formula to figure it out. Either way, the couple of times a year I do I too consider it entertainment.

You play in an office pool because you don’t want to be the only guy showing up to work the next day.

This layout is so stellar. How did you manage to make a blog that’s as smart as it is sleek? I’ve got to say, the layout alone made me come back to this blog again. But now that I’ve read what you’ve got to say, I’ve got to share it with the world!

Best entertainment you can get for a dollar. The quitting your job fantasy is worth at least that much; what you’ll do to your boss is worth double.

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