The Math of Luck: Can You Really Guarantee a Lottery Win?
- Alice Yoo
- Feb 5
- 3 min read
Difficulty Index ★☆☆☆☆
Alice Yoo '27
Without a doubt, anyone would have dreamt of winning the lottery at least once in their lives. From buying a brand new sports car to traveling around the world on a luxurious cruise to investing in stocks to building a swimming pool full of jello… It feels like you have already achieved that sweet dream just by imagination. But as if you were struck with ice water, you recall the extremely slim chances of winning. It’s nearly impossible—you reiterate to yourself. Well, what are the actual chances of winning, then?
Straight facts and numbers first; the chance for you to win the lottery is about 1 in 300 million. That’s eight zeros if you cannot fathom how tiny that probability is. That’s roughly the population of the United States too (just in case you need more comparison). There’s another famous comparison; you are four times more likely to get struck by lightning than win the lottery!
The strategy for winning the lottery is simpler than you may have thought. And of course, more costly than you may have expected. The trick is to simply buy tickets of all possible combinations (can you even call this a trick?).
Some ambitious souls may already be counting the cash in their wallets to try this out–but hold on. Theoretically, you could purchase all combinations
(69C5*25= 292,201,338 for the Power Ball and 70C5*25=302,575,350 for Mega Millions)
for less than $600,000,000–with the grand prize being $1,000,000,000, you will have a profit of $400,000,000! If anyone could win, why isn’t everyone trying this method out?
First, you might not be the sole winner of the lottery. There are often cases when you will have to split the prize, in which case you will have to split equally among the winners. Using the Poisson distribution, you can calculate the probability of being the only winner.
λ = (120,000,000/300,000,000) = 0.4
Pr(x) = e-λλx/x!
Assuming 120 million other tickets were sold, there is only a 67% chance that you will be the only winner, meaning there is a 33% chance that you will receive less than $300,000,000. Thus, you will be in the red.
If we assume that 300 million other tickets were sold (a more realistic number)
λ = (300,000,000/300,000,000) = 1
There will be only a 37% chance that you will be the only winner; now, there is a 63% chance you will be sharing the grand prize with others.
Second, you have to manually mark your desired combinations on the tickets. Marking 300 million different combinations would take an insane amount of time and effort–even if it is assumed that you take 30 seconds to mark a ticket, it would still take you over 250 years to fill them out without any breaks in between.
With that being said, perhaps you shouldn’t consider the lottery something to pour $600,000,000 on to guarantee a win.
Works Cited
Doyon, Janine, and Noreen O'Donnell. "What to Know about Playing the Lottery (from a Math Professor
Who Won)." NBC Bay Area, 31 Jan. 2024, www.nbcbayarea.com/news/national-international/
what-increases-chance-lottery-win/3408041/?amp=1. Accessed 4 Feb. 2025.
Talwalkar, Presh. "Can You Just Buy All Lottery Combinations and Win?" Mind Your Decisions, 30 July
#:~:text=Each%20lottery%20has%20odds%20of,way%20of%20this%20dream%20scheme. Accessed 4 Feb.
2025.
Tenser, Phil. "One Way to 'Guarantee' You'll Win the Powerball Jackpot, If You Can Afford It."
WCVB, 9 Oct. 2023, www.wcvb.com/article/powerball-gurantee-jackpot-win-oct-9-2023/
45487167. Accessed 4 Feb. 2025.
Kommentare