Seriously, Go Buy A Powerball Ticket Right Now!

powerball jackpot

Photo: ABC News Youtube

You’ve probably heard that buying a lottery ticket is a huge waste of money. People call it the “idiot tax.”Normally, that’s harsh but relatively accurate.

The jackpot has to be at least $275 million for it to be considered remotely worthwhile. 

But tonight’s Powerball lotto is the exception to that rule.

Because of the high stakes, the expected winnings of buying a $2 ticket is $1.21. In other words, if you spend $2 on tickets, then you will get back $3.21 in winnings on average, for a net gain of $1.21.

Because Powerball publishes the probabilities of winning each prize, we’re able to figure out the expected value of a ticket.

Slightly more than 96% of the time, a ticket is a loser, and a player loses $2.

But the remaining 4% of the time, the player enjoys a net financial gain. 2.7% of the time a player gains $2; 0.45% of the time a player gains $5; and so on and so forth. A tiny, tiny fraction of the time, a player gains half a billion dollars.

As a result, if you multiply through the probabilities you get the expected gains and losses of buying a ticket. The average gains of buying a ticket exceed the guaranteed loss of buying a ticket because of the huge jackpot, and the net expected value of playing a ticket turns out to be $1.21.

What’s more, there’s probably going to be a winner this time.  

Here’s the probability of at least one jackpot winner given the number of tickets sold:

oimg?key=0Aon7Ed2duFOGdEdKTVhvMXNjdG55RD

Powerball claims that they expect to sell more than 189 million tickets before the drawing tonight. That translates to a 66% probability of at least one winner, so the odds are rather good that there will be at least one new multi-millionaire tomorrow. 

The best way to determine that figure out is 1 minus the probability that there isn’t a winner at all, that every single ticket sold is wrong. Since the probability that a single ticket is wrong is 175223509/175223510, that raised to the 189 millionth power is around 34 per cent. There’s a 34% probability that every ticket is wrong, so there’s a 66% probability that at least one ticket is right. 

This brings us to the conclusion that there is a two in three chance that the Powerball lottery won’t get any better than it is now. 

Don’t miss: 17 lottery winners who blew it all >

NOW WATCH: Money & Markets videos

Want to read a more in-depth view on the trends influencing Australian business and the global economy? BI / Research is designed to help executives and industry leaders understand the major challenges and opportunities for industry, technology, strategy and the economy in the future. Sign up for free at research.businessinsider.com.au.