Lotto- The Odds Are Against You!

I buy lotto tickets- there, I said it.

Not all the time, just occasionally. I usually buy them when the jackpot gets really high- like the recent $32 million Powerball- for some reason, I have convinced myself to only buy tickets once the Powerball jackpot goes beyond $20 million. Because you know- anything below 20 million just isn’t worth my time.

But why?

Only buying tickets when the Powerball is above $20 million doesn’t make buying lotto tickets any more rational. I know the odds of winning- they are next to none. And I know I’d be better off saving that money I spend on tickets.

But I keep telling myself that someone has to win- why shouldn’t it be me.

Whenever I buy lotto tickets I find myself daydreaming about what I’d do if I won. And how I would organise my life with all that money. I seem to fall back on a sensible scheme of trying to invest everything. Only living off the interest using the 4% rule- why wouldn’t I do that?

In reality, though- I think if you suddenly found out you won such a large amount of money, you would definitely go on a decent shopping spree- even if you keep telling yourself that you wouldn’t. Your credit card’s probably going to get a workout. My garage will probably have to be extended!

I guess we’ll never know.

I like daydreaming about winning Lotto I decided- but I should just not buy tickets. Since I know the probabilities. But it isn’t always easy to comprehend and visualise the odds and then relate the probabilities to something easier to grasp.

The chances of winning Lotto

It’s easy to daydream about winning Lotto- the extended holidays, fancy cars, helping out the family. But let’s look at the odds of actually winning Lotto Powerball- because that’s the one that keeps rolling over and making the news- hitting $20 million, $30 million, and even $40 million (one time).

The problem is that it’s hard for us to understand large numbers.

It’s easy to tell the difference between 10 and 100 people and between 100 and 1000 people. But what happens when you try to imagine the difference between 100,000 and 1,000,000 people? It becomes harder- what does 100000 people look like- and what does 1 million people look like?

Harder still is trying to imagine the difference between 10,000,000 and 100,000,000.

This happens because we see smaller numbers more frequently in our daily lives. And in our daily experience can be explained by smaller numbers. You’ve never lined up in a 1 million person queue at the supermarket, or gone through 100000 stoplights on the way to work.

I’ve had some exposure to really large numbers throughout school and university- and I still find them hard to comprehend. Take one of the basic units in chemistry- the Mole. The mole is basically a way of measuring the mass of a substance that has the same number of units as atoms in 12 grams of Carbon-12. The Mole, also known as Avogadro’s Number, is roughly 6.02×1023. What does that even mean? Take a look at that number written in full.

 602,200,000,000,000,000,000,000

That’s the number of atoms in 12 grams of carbon. Now can you understand this number? Let’s try to understand how big it is.

If you had $6.02×1023 in the bank, and spend $1 billion a second- yes a second! How long would it take you to spend all your money? a year, a decade, a lifetime? It would take over 19 million years to spend Avogadro’s number of dollars if the money were spent at the rate of one billion dollars per second. And if you earned even 1% interest it would probably be impossible to spend all of the money, even at a rate of $1 billion a second. That is one stupidly large number.

Because large numbers are hard to understand, the odds of Lotto are hard to understand.

So let’s try to understand the numbers behind lotto. In every Powerball draw, there are seven divisions you can win in New Zealand’s Lotto system. I’m only going to focus on the Powerball system as the size of the power ball generally pulls players in.


Odds of winning Division 7 in Lotto Powerball

To win Division 7 in Lotto you need 3 numbers plus the Powerball. And for that, you’re rewarded with $15 and 4 bonus lines. The odds of winning this is 1 in 352

The odds of winning Division 7 are comparable to you reading this post on your birthday, 1 in 365 days.


Odds of winning Division 6 in Lotto Powerball

To win Division 6 in Lotto you need 3 numbers plus the bonus ball and the Powerball. And for that, you’re rewarded with $40. The odds of winning this is 1 in 3635

You are more likely to be born with extra fingers and toes than winning division 6. Being born with extra digits is known as polydactyly. Apparently 1 in 500 to 1,000 babies are born with extra finger or toe. Most have surgery during infancy- so who knows you may have had an extra finger or toe. The world record for the most digits is 34, with 14 fingers and 20 toes

Counted your fingers recently?

Odds of winning Division 5 in Lotto Powerball

To win Division 5 in Lotto Powerball you need 4 numbers plus the Powerball. And for that, you’re rewarded with $57. The odds of winning this is 1 in 4846

You are more likely to be struck by lightning in your lifetime than win Division 5. National Geographic estimates the odds of being struck by lightning to be 1 in 700,000 in any given year- so over the course of your lifetime- the odds increase to 1 in 3,000.

Being struck by lightning: 1 in 3000 change over your lifetime

Odds of winning Division 4 in Lotto Powerball

To win Division 4 in Lotto Powerball you need 4 numbers plus the bonus ball and the Powerball. And for that, you’re rewarded with $107. The odds of winning this is 1 in 77,543

The odds of winning Division 4 are comparable to being dealt a straight flush in 5 card poker, such as Q♥ J♥ 10♥ 9♥ 8♥ a queen-high straight flush, at 1 in 72,192. With a straight flush, you’ll nearly be guaranteed to wind the hand- only being beaten by a royal flush at 1 in 649,740

Even when the odds are in your favour- you can still lose

Odds of winning Division 3 in Lotto Powerball

From Division 3 onwards it becomes harder to understand the odds- because of our difficulties in understanding larger numbers. To win Division 3 in Lotto Powerball you need 5 numbers ball plus the Powerball. And for that, you’re rewarded with $1,155. The odds of winning this is 1 in 193,858

To help you visualise the odds of winning 3rd division take a look at the following image.

large numbers are hard to understand- that is why it's hard to understand the odds of winning lotto
1 red pixel in 195,000 yellow pixels

This image is 650 pixels by 300 pixels- a total of 195000 pixels. Winning division 3 is like picking the one correct pixel in the entire image. And there is one pixel in the above yellow image that is red. Can you spot it? you might have to clean your screen to see it.


Odds of winning Division 2 in Lotto Powerball

To win Division 2 in Lotto Powerball you need 5 numbers plus the bonus ball and the Powerball. And for that, you’re rewarded with $37,000. The odds of winning this is 1 in 6,397,300

Once you hit division 2 the numbers get even bigger. I don’t have enough screen space to even create an image with 6 million pixels and I have 3 screens! Two with a resolution of 1920×1050 and one 1680×1050- that’s a total of 5,796,000 pixels.

Now, you do have a higher chance of being killed by a shark than winding division 2. It’s estimated that you have a 1 in 3.7 million-odd of being killed by a shark.

1 in 3.7 million odds of being killed by a shark-This guy’s just asking for it!

Odds of winning First Division in Lotto Powerball

Ah yes- Division 1- this is the prize everyone is buying their tickets for. Before looking into this- I didn’t even know how much you could win with the other divisions before writing this post. And it turns out- it’s not a lot.

To win the first division in Lotto Powerball you need 6 numbers plus the Powerball. And for that, you’re rewarded with an average prize of $11,000,000 (between $4,000,000 to $50,000,000) . The odds of winning this are 1 in 38,383,800.

Your nearly 3 times more likely to have a set of identical quadruplets than winning Powerball. That’s not just having quadruplets- but identical quadruplets. The odds of quadruplets is about 1 in 800,000. Identical quadruplets are about 1 in 11 to 15 million.


Are You Still Playing Lotto for Fun?

Buying lotto tickets is supposed to be for fun- but people can fall into a gambling addiction- You can easily fall into the trap “being in to win” where you find yourself buying two lotto tickets a week (Wednesday and Saturday draws). If any of the following ring true for you, then you might have a lotto addiction:

  • You run out of money for basic grocery items
  • You miss on debt and savings targets
  • You don’t share with your family and friends that you are playing lotto
  • You regret buying the ticket later

And now, there are some people that say there is no harm in playing lotto as the money either goes to prizes or back to the community. According to the Lotto NZ Annual Report 2015-16, for every $1 of ticket sales 55 cents went to prizes, 21 cents went to the Lottery Grants Board, 12 cents went to taxes, 6 cents went to operating costs, 6 cents went to retailer commissions.

Conclusion

You are far better off investing your money or saving than playing Lotto. In reality, Lotto is a tax on people who don’t understand numbers. The rebuttal to this is to tell that to the folk who have bought a ticket and won! But you have to remember all the folk who haven’t won.

So don’t buy Lotto tickets


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