DES MOINES, Iowa – Lottery players are going to have a shot at more billion-dollar jackpots and slightly better odds under new Mega Millions rules that go into effect with Tuesday’s drawing.

But the improvements come at a cost — literally: Players will have to shell out $5 per ticket, more than double the previous price. On the other hand, the jackpots are expected to grow much bigger — and at a faster rate — and officials believe sales will rise as people are stopped in their tracks by massive prizes.

“People really want big jackpots,” said Joshua Johnston, the Washington state lottery director who heads the Mega Millions game. “We expect to see a sales lift on this.”

HOW IS MEGA MILLIONS CHANGING?

The biggest change is the ticket price hike from $2 to $5. Lottery officials expect that jump to increase revenue from the twice-weekly game, enabling them to lower the odds of winning the jackpot from 1 in 303 million to 1 in 290 million.

The higher ticket price also means the jackpot can start at $50 million, rather than the previous $20 million, and the grand prize is expected to grow more quickly. Each time there isn’t a big winner, the jackpot will jump to a larger mark. Officials expect it will more frequently top the $1 billion threshold that draws extra attention — and bigger sales.

Under the new rules, prizes for tickets not matching all six numbers also will increase, with smaller winners now guaranteed at least $10. Each ticket also will include a randomly assigned multiplier that can increase the prize by up to 10 times, a previous add-on feature that cost an extra $1. The multiplier doesn’t apply to a jackpot.

WILL THIS MAKE WINNING A JACKPOT EASIER?

Yes, but it’s still incredibly unlikely: Odds of 1 in 290 million are still mind-bogglingly hard to beat. And that’s true if you buy one ticket or 100.

“When we hear 1 in 290 million, we don’t have a sense of what that means. We have a greater sense of the fact that there will be a winning number,” said Tim Chartier, a mathematics and computer science professor at Davidson College. “And it’s true that it’s possible, but the issue is the extreme improbability of it.”

How improbable? The chance of hitting a jackpot, even under the new rules, is akin to choosing one single second over a nine-year span, according to Chartier. He said he’s never been willing to risk even a couple bucks on those odds.

WHY IS THE GAME CHANGING?

The new rules have two main goals: to address what the industry calls “jackpot fatigue” and to differentiate Mega Millions from Powerball, the other lottery draw game played across the country.

Jackpot fatigue is the phenomenon under which prizes must grow to enormous amounts before most players will take note and buy a few tickets. These days, a $300 million prize that once drew lines at mini-marts barely registers.

With the new rules, officials expect those average winning jackpots to climb from about $450 million to $800 million, Johnston said. And they believe that even lottery fatigue is no match for the more frequent billion-dollar prize.

“When you get to a billion people are like, ‘Whoa, that’s a whole lot of money,’” Johnston said.

Lottery officials said there is a clear correlation between bigger jackpots and higher sales but Sandie Yeaman, of Omaha, Nebraska, expressed puzzlement at the connection.

“I’d be satisfied with $1 million, and so would others,” she said. “One person winning $50 million is ridiculous.”

HOW RARE IS A $5 TICKET PRICE?

Mega Millions will be the country’s most expensive lottery draw game, where random numbers are selected to determine a winner.

Still, that price is far less than scratch tickets offered by some states. In Texas, for example, some scratch tickets cost $100 each.

Outside the U.S., the El Gordo Christmas lottery in Spain limits the number of tickets sold and charges 20 euros for a partial ticket and 200 euros for a full ticket.

The higher Mega Millions price left Saeedith Williams of East Point, Georgia, unsure if he’ll keep buying several tickets a week. “Maybe I’ll buy one ticket a week now that it’s $5 a ticket,” he said.

WHAT ABOUT POWERBALL?

After the new rules are implemented, the two lottery games that once were remarkably similar now will have some key differences.

The biggest contrast will be the cost, as Powerball will stick with its $2 tickets — $3 in Idaho and Montana where they require a special prize bundle.

With that smaller ticket price will come smaller minimal prizes, starting at $4, or less than half the lowest Mega Millions prize. But Powerball players will still be able to pay an extra dollar for “Power Play,” a random multiplier that, as in Mega Millions, can increase all but the grand prize.

Powerball drawings will continue to be three times a week — Monday, Wednesday and Saturday nights — while Mega Millions will hold drawings on Tuesday and Friday.

The changes will bring the two games’ jackpot odds a little closer, with Powerball jackpot odds of 1 in 292.2 million just a bit worse than the new Mega Millions odds.

Remind me, what’s the point of all this?

For players, it’s a chance to spend a little money on a dream of incredible riches while acknowledging the reality that it almost certainly won’t happen.

For the 45 states plus Washington, D.C., and the U.S. Virgin Islands where Mega Millions is played, the game raises money for a variety of services, such as education scholarships. Local lottery agencies run the game in each jurisdiction and decisions about how the profits are divvied up are written into state law.

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AP writer Margery A. Beck contributed to this story from Omaha, Nebraska.