A billboard in Des Moines promotes the Powerball jackpot, which ultimately swelled to $768.4 million. (Scott McFetridge/AP)

A $768.4 million Powerball jackpot — the third-largest in U.S. lottery history — has been won in Wisconsin.

A single ticket purchased at a gas station in New Berlin, not far from Milwaukee, matched all six numbers — 16, 20, 37, 44, 62, plus Powerball 12 — in Wednesday night’s drawing, lottery officials said. The ticket holder (or holders) may choose to take the estimated $768.4 million paid out over the next 29 years or $477 million in cash, Powerball officials said.

“This is an amazing milestone moment for Wisconsin,” Cindy Polzin, the state’s lottery director, said in a news release. “It truly is incredible to think that the winning ticket for this historic jackpot was sold in our own backyard. I am extremely excited for the winners and for our state. This event puts us in the national spotlight and turns Wisconsin into WINsconsin.”

In January 2016, winners in California, Florida and Tennessee split the largest American lottery jackpot ever won: a $1.586 billion Powerball prize.

The second-largest U.S. jackpot — $1.537 billion in the Mega Millions game — was won in South Carolina in October. Several months later, a woman in Simpsonville, S.C., who elected to remain anonymous, came forward to claim her massive prize, taking the lump sum worth $878 million — the largest jackpot ever paid out to a single winner, lottery officials said.

Wednesday’s winning ticket must be claimed within 180 days.

The odds of winning the big prize were 1 in 292,201,338, according to the Wisconsin Lottery, which is one reason the jackpot got so big.

Nearly 3½ years ago, the chance of becoming an instant millionaire by playing Powerball were 1 in about 175 million.

Tweaks to the game in October 2015 increased the number of total balls, from 59 to 69, from which players need to pick five. It may seem like a modest change, but the chance of winning decreased.

So now it's even harder to strike it rich with Powerball, leading to fewer chances of big payouts, which in turn results in ballooning jackpots: When a drawing is held and there's no winning ticket, the prize pool rolls over — and expands.

In turn, the jackpots become bigger and bigger (and bigger and bigger).

Then, you won't believe what happens next.

Media reports and social media posts fuel an ever-increasing prize, Colorado Lottery spokeswoman Kelly Tabor told The Washington Post in 2017, when the Powerball jackpot surged to $758.7 million — at the time, the second-biggest lottery prize in U.S. history.

That amount ballooned as the drawing approached because of what Tabor called “jackpot chasers,” the casual lottery players who buy in when the Powerball pot reaches astronomical heights.

“That's really driving up sales right now,” she said at the time.

That’s also how the jackpot paid out three ways in January 2016 reached its historic value of $1.6 billion.

It’s also what happened with the Mega Millions lottery, which reached $1.537 billion in October.

That lottery has existed in some form since 1996, but only recently has Mega Millions been shelling out massive jackpots. The lottery officials who run Mega Millions tweaked the rules and odds of the game in 2017 to make jackpots pay out less frequently, spurring their monster growth. Since that change, five of the eight largest Mega Millions jackpots have been paid out.

“Ultimately, these games, they’re all about the jackpots,” Gordon Medenica, Maryland’s lottery and gambling director, told The Post last fall.

Lottery officials had been worried that the relatively smaller but more frequent prizes — a “paltry” $100 million, for instance — would result in “jackpot fatigue,” which is why they tweaked Mega Millions, Medenica told The Post.

Now, the Mega Millions jackpots — such as Powerball — grow and grow, creating huge prizes with infrequent payouts.

State lottery commissions have relied on human psychology and the spirit of optimism to fuel sales.

They discovered that when the jackpot grows to an absurdly high figure, even skeptical players will buy tickets — perhaps on a whim at a convenience store or by chipping in a few bucks in an office pool, Medenica said.

The game — played in 44 states, plus the District and the U.S. Virgin Islands — becomes a “cultural phenomenon” somewhere in the $200 million to $400 million range, Medenica said.

When the jackpots flirt with the half-a-billion-dollar mark, state lotteries don’t even feel the need to advertise, he said.

Here’s how Mega Millions used to work: Players picked five numbers from one to 75 and a Mega number from one to 15. The odds of winning the top prize were 1 in 258,890,850. Since Mega Millions modified the formula, players now pick five numbers from one to 70 and a Mega number of one to 25. The odds of winning the jackpot are now 1 in 302,575,350.

Reducing the number of balls for the first five numbers increases the chances of winning a smaller prize. But raising the number of Mega Balls makes it harder to win the jackpot. (You still win the big jackpot by matching all six winning numbers in a drawing.)

The other significant change that helped fuel the jackpot growth was the increase in the Mega Millions ticket price, which doubled to $2.

Lottery officials have said that the changes were in response to demand from players that they wanted to start with a big jackpot and have a better shot at smaller prizes, such as getting their $2 back all the way up to a $1 million payout for matching all five numbers.

Read more:

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A woman claimed her $1.5 billion Mega Millions jackpot — and her identity may be a secret forever

Winner of a $560 million Powerball jackpot can keep the money and her secret, judge rules