At what point should you really go big on Powerball lottery tickets?
It’s not a simple question to answer. Besides calculating the odds of winning a decent jackpot, you’ve also got to figure out the odds that you might have to split the potential jackpot.
Add to that the fact that the odds of a split constantly change, and it all adds up to confusion.
First, Let’s Look at the Expected Value
Powerball, or any lottery for that matter, is interesting. There are several stagnant cash prizes up for grabs, as well as the ever-enticing jackpot.
So, let’s first take a look at expected value. For the Powerball, the expected value of spending $2 on a ticket is really -$1.58 – that’s not taking the jackpot into account. As you can see, the expected value of playing when you ignore the pot is negative.
And then, there’s the probability that you win the jackpot – that’s pretty small. In fact, it’s 1 in just over 175,000,000.
Confusing, right?
Expected value, though, is helpful for assessing different outcomes. So, if your expected value for buying a ticket, based on the cost of your tickets along with the odds of winning any of the different prizes, is positive, you’re likely to make money overall.
What About the Pot Size?
We find the expected value of a randomly decided process, like a lottery draw, by taking every possible outcome, multiplying each one by its probability, and then adding all those numbers. This helps you arrive at a long-run average value.
Or, you can take each prize that’s up for grabs in any given week, subtract the cost of your lottery ticket, then multiply the net return by your probability of winnings. Finally, add all those values to arrive at your expected value.
So, should you buy tickets when the pot is overflowing or when it’s a little smaller than usual?
When to Buy Your Tickets
Overall, experts suggest buying tickets when the pot is massive. Yet, that almost never makes sense financially – even if that expected value of your ticket is positive, you’d have to be massively wealthy to rationally “invest” a dollar in a ticket.
That’s because the expected value is almost always lower than the cost of your ticket. That means that buying Powerball tickets doesn’t make economic sense.
In fact, it’s even worse to buy tickets when the pot is smaller since your expected value is even lower.
But, Are There Ways to Win the Powerball Pot
Ok, that’s a lot of numbers. But, believe it or not, there is a time to play and buy as many tickets as you can comfortably afford.
In Powerball’s case, it’s recommended that you play whenever the main pot edges past $146,107,000. That’s because the chances of matching one red ball and five white balls are exactly one out of a big number, statistically speaking, and it’s a pretty good bet anytime your payout is larger than that number.
When we consider Powerball’s number of balls and their range of values, the magic number is 146,107,962. While your chances of winning don’t change, the payoff amount does increase to a level where it’s worth your while to play.
stront’s all about determining the actual magic number and the prize amount. Remember, the amount advertised isn’t the jackpot. The advertised jackpot is how much you’ll get over a period of years, paid out in smaller portions. The real jackpot, though, is the lump sum amount, and that’s usually less than half of the advertised amount.
If you realise that your Powerball lottery has grown a jackpot amount that statistically indicates it’s a good time to play, go for it.
While statistics show us that it’s not particularly a good idea to buy a ticket when the pot is smaller, if you’re new to lotteries or just want to try your luck, maybe it’s best to start with a smaller pot. After all, if Lady Luck is on your side, you may just walk away a very fortunate millionaire who took a risk when others held off!