The cost of winning the Lottery

Everybody can hit the Lotto jackpot as long as they buy enough tickets. But statistically speaking is it worth it, or would you be richer if you simply never played and made some smart financial decisions instead?


We’ve all had the dream where we were the lucky winner of the Lotto jackpot, especially when there’s a multiple rollover and the prize is in the tens of millions. Finally we would reach financial independence and all of our issues involving money would disappear overnight. We buy a ticket and secretly start to plan what we’ll do with the money; who you will tell, who will get a share of it, which house you will buy, which cars, where you will go on holiday, and in what dramatic way you’ll leave your job.


Well, first you need to actually win and currently the UK national lottery (Lotto) has a 1 in 45,057,474 chance of hitting the jackpot. You’ve probably heard of the comparisons such as being more likely to get struck by lightning, or eaten by a shark, or winning Olympic gold.


But here’s a comparison you might not have heard of:


6,769 lifetimes.


If you buy two tickets each week and play the lottery from age 16 to 80 without ever missing a single ticket, you would only statistically hit the jackpot once in 6,769 lifetimes. To really make sure this hits home, that would be 541,520 years. Here’s a diagram to show my workings:


A diagram showing how long it takes and how much it costs to statistically win the Lotto jackpot

If you're aiming to become a millionaire you might as well just save £1.85 each year, after 541,520 years you're guaranteed to make it. But in all honest, don't bother; just by not buying any lottery tickets ever you will be able to save yourself £90,108,928.


The biggest jackpot in the Lotto to date is £66,000,000. So statistically speaking you’d probably be negative when you win. Just put your lottery ticket money into a jar and enjoy it after half a million years.


I know, inflation. But hopefully you get the point.


So here’s why this comparison is better than the others besides the impact factor; it is time based. So that means you can use it to compare against other results where money and time is involved. In other words you can try to determine if compounding interest is more likely to make you richer than winning the lottery.


Obviously the answer is immediately yes based on the fact that we’ve established the cost of buying lottery tickets has a negative return but let’s ignore that for now.


Imagine you were offered a choice between two things:


  1. A magical lottery ticket that will not expire until it wins; two entries each week.

  2. A penny; nothing special about it, just a regular penny.


Assuming either item would be passed down in your family until the lottery ticket wins, should you take the ticket or the penny?


Well, let’s say you take the lottery ticket and win the Lotto jackpot in half the amount of time compared to what is statistically required; let's also say the prize money was a hundred times more than the current biggest jackpot to date. That would mean in 270,760 years time someone in your family would win £6,600,000,000.


Not bad.


On the other hand, if you had taken the penny and gained 0.01% interest each year it would have grown to £5,732,835,542.


Close, but no cigar. But if you're still waiting to hit the jackpot after 270,760 years, or if you have to split the jackpot winnings with another lucky winner, then the penny is looking like it's a better choice.


Still think the magical lottery ticket is better?


If your penny had gained just a fraction more in interest each year, let's say 0.011% (that's 0.001% more than earlier), then it would have grown to £85,929,397,450. Here's another diagram to show my workings:



Forget multiplying the lottery jackpot prize money by a hundred times, even a thousand times wouldn’t be enough to match this result. And the best thing is that the penny is a sure thing, whereas a lottery jackpot win isn't.


So here's the point of this fun little example; you have a real choice to make:


  1. Are you going to continue hoping for a lucky win to get rich.

  2. Or will you build your wealth my making smart financial decisions for the long term.


If you're in the group that makes the latter choice then this blog is for you. I have spent time thinking deeply about various scenarios and how they can be applied in my own journey towards gaining financial independence.


I feel that it is often difficult to come across this level of detail anywhere else, so I've compiled a bunch of different scenarios that I can work through using my knowledge, experience and research.


I'd like to share those scenarios and workings with you all so I'll slowly post in this blog with the hopes that some of you will find it interesting and engaging. It's just some of my scribbles and musings at the end of the day, so let's have some fun with it!

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My mission is to help people understand their money by making financial scenarios or concepts easy to understand. Support me by sharing the blog with someone that you want to help.

Thanks for reading!

Kujah

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