If you buy 100 lottery tickets for the same drawing, your odds of winning a prize will be better than if you just buy one ticket. However, your chances are still relatively low. Let’s break it down.

## Odds of Winning with One Ticket

First, we need to look at the odds of winning with just a single lottery ticket. This will vary depending on the specific game.

For example, the odds of winning the jackpot in Powerball are about 1 in 292 million. The odds of winning any prize (including smaller prizes) are 1 in 24.87. So if you buy just one Powerball ticket, you have a 1 in 292 million chance of hitting the jackpot and a 1 in 24 chance of winning something.

Mega Millions is similar. The odds of winning the jackpot are about 1 in 302 million. The odds of winning any prize are 1 in 24. Here again, if you buy just one Mega Millions ticket, your chance of winning the jackpot is 1 in 302 million, and your odds of winning something are 1 in 24.

State lotteries have comparable odds. For instance, the odds of winning the New York Lotto jackpot are 1 in 45 million. The odds of winning any New York Lotto prize are 1 in 8.

The specific lottery game matters, but the odds of winning a big jackpot with one random ticket are always extremely long, while the odds of winning any prize are more reasonable but still unlikely.

## Odds of Winning with Multiple Tickets

Now let’s look at how buying multiple tickets affects your chances.

If you buy 100 Powerball tickets, your odds of winning the Powerball jackpot don’t actually change. Each ticket has a 1 in 292 million chance. It’s still highly unlikely any of your 100 will have the winning numbers.

However, your odds of winning any Powerball prize improve. With 100 tickets, you now have 100 1-in-24 chances to win something. While far from guaranteed, your chances of winning a smaller prize have gone up significantly.

The same holds true for other lotteries. With 100 Mega Millions tickets, your odds are still 1 in 302 million to hit the jackpot but 1 in 24 of winning any prize. For a state lottery like New York Lotto, 100 tickets gives you 100 1-in-45 million chances at the jackpot and 100 1-in-8 chances to win something.

So when you buy 100 lottery tickets for one drawing, your odds of winning a jackpot prize are still astronomically low. But your chances of winning a smaller prize are much better than with just a single ticket.

## Expected Number of Wins

Another way to look at lottery odds is to think about the expected number of wins. This is based on probability theory.

If the odds of winning a jackpot are 1 in 300 million, and you buy 300 million tickets, probability says you would expect to win the jackpot once. If you buy 600 million tickets, you would expect to win the jackpot twice, and so on.

So when you buy 100 tickets for a 1 in 300 million jackpot, the expected number of wins is 100 divided by 300 million, or 0.000000333 wins. That’s essentially zero wins expected.

For a smaller prize with odds of 1 in 30, if you buy 100 tickets, the expected number of wins is 100 divided by 30, or around 3 wins. So you would reasonably expect to win a smaller prize about 3 times if you buy 100 tickets.

This expected value analysis shows that while 100 tickets won’t help you win the jackpot, you’re likely to win some smaller prizes.

## Probability of Winning Anything

We can also calculate the probability of winning any prize when you buy multiple lottery tickets.

With Powerball, the probability of winning something on one ticket is 1/24. If you buy 100 tickets your probability of winning on any given ticket is still 1/24. But now you have 100 opportunities.

To find the probability of winning anything, we calculate 1 minus the probability of winning nothing. The odds of winning nothing on one ticket are 23/24. With 100 tickets, the probability of winning nothing on all 100 is (23/24) to the power of 100, or about 36.6%.

So the probability of winning anything when you buy 100 Powerball tickets is 1 minus 0.366, or about 63.4%.

For a lottery with better odds, like a 1 in 8 chance, if you buy 100 tickets your probability of winning any prize is even higher, over 99%.

So while your jackpot odds don’t really change much, your probability of winning something goes up notably when you buy 100 tickets.

## Is it Worth it?

Depending on the lottery, 100 randomly selected tickets will cost you between $200 and $300. So is it worth it?

Looking at the odds, out of 100 tickets you can reasonably expect to win some smaller prizes, but your chances of hitting the jackpot are still minuscule. Even though you are likely to win a few bucks here and there, you’re probably just recouping some of your costs.

For most people, playing strategically gives you better odds. Like picking uncommon numbers to reduce split jackpots, or buying tickets when the jackpot is exceptionally high. Groups of coworkers or friends often pool together for group ticket purchases to improve their chances.

In the end, 100 random tickets improves your odds a bit, but jackpots are still a long shot. A modest amount of tickets with some strategy is likely a better approach for most players.

The lottery is meant to be fun, and buying in bulk gives you more opportunities to win small prizes. Just don’t go overboard chasing that huge jackpot. Play responsibly with a budget in mind, and never spend more than you can afford.