Math in… Winning the Lottery
In 2023, the Lotto Texas’ $95 million jackpot was won by a London-based gambling syndicate. That sounds almost illicit, but it was perfectly legal. If it’s all legal, though, why isn’t this sort of story more common?
In Lotto Texas, a player chooses six different numbers from 1-54. Depending on how many numbers on their ticket match the numbers on the drawn balls, the player might win a prize:
The minimum Lotto Texas Jackpot is $4 million, but increases based on the number of tickets sold since the last win.
While $4 million is a nice chunk of change, the number of ways to pick 6 distinct numbers from 1 to 54 is
To ensure you hit the jackpot, you’d need to buy all 25.8 million combinations. If you buy every possible ticket, that means you’d also win prizes from the other tiers.
This is a best-case estimate, since you might have to split the jackpot. The fine print on the prize table also suggests that you might not actually get the full amounts from the other tiers.
Since tickets are $1 a pop and you would buy over 25.8 million of them, the net earnings for this strategy are
The jackpot would need to be $19.4 million higher to break even before taxes. You’d want it to be much higher, though, since you could lose millions if you had to split the jackpot or if the lottery paid out less on other prize tiers.
The London gambling syndicate bought tickets when the jackpot was $73 million. This was high enough that, even if one other person were to hit the jackpot and no other prize tiers were honored, the syndicate would still net $10 million.
By the drawing, the jackpot had climbed to $95 million, and there were no other winners to split it with.
Jackpots rarely get high enough that the time and money needed to buy every possible ticket are worth it. Many lotteries also impose sales limits that make buying every ticket difficult. That’s why these stories are so rare.
The takeaway? Unless you have
the time and money to buy the huge number of tickets required to guarantee a win...
in a lottery that allows bulk purchases of tickets...
at a time when prizes are big enough to return a profit...
…don’t plan on winning the lottery!
