According to an old joke, the lottery is a tax on people who are bad at math.

Every week, players go to their local convenience stores to buy a Megabucks ticket, hoping that the Ping-Pong balls will tumble out in the right order and make them rich.

The odds aren’t good that they will. The chance of matching all six numbers to win the jackpot is about 1 in 1.4 million, according to the Maine Lottery Commission website.

The PowerBall lottery, with huge jackpots, attracts millions more players, but its odds are even worse: close to 1 in 300 million.

But people still play, and the governments that run the games are happy to let them do it.

This week the state instituted a new lottery, one in which you don’t have to match any numbers or even buy a ticket. You just have to get a COVID vaccination before July 4.

The state will put one dollar in the pot for everyone Mainer who has been vaccinated, and everyone who has gotten at least one shot can enroll by visiting the state’s vaccination website or by calling (888) 445-4111. So far, about 900,000 people have become eligible, but only about 90,000 have signed up. That’s a one in 90,000 chance, still a long shot but the best odds by far that you are ever going to get in a game like this.

The sweepstakes idea has been tried elsewhere, and it’s been surprisingly effective.

It might not convince hard-core vaccination opponents to roll up their sleeves, but it could bring along someone who is open to the idea but just hasn’t got around to making an appointment yet. It grabs people’s attention in a way that previous sweeteners, like a $20 L.L. Bean gift card, do not.

Most rational people would understand that a guaranteed $20 is more valuable than a one-in-90,000 chance for a prize, no matter how big the prize is. But this an appeal to hope and imagination, not logic.

No disrespect to Bean’s, but people aren’t dreaming about what they would do with a discounted pair of Maine Hunting Shoes. A $1 million jackpot is another story.

And if this were just about the odds, we wouldn’t even need to encourage people to get vaccinated.

Since March 2020, 68,717 Maine people have tested positive for COVID, which is roughly 5.3 percent of the state’s population. During the pandemic, 854 Mainers have died of COVID, or 0.065 percent.

Even though our state has been one of the safest places in the country during the pandemic, you and your family members have had about a 1-in-20 chance of getting sick with COVID and a 1-in-1,500 chance of dying from it.

Those might sound like long odds, too, but they are a stone-cold lock compared to the lotteries.

For some reason, it’s much easier to see yourself winning $1 million than it is to imagine being infected by an invisible virus that could kill you or that you could transmit to someone you love. But if people were purely rational, there wouldn’t even be a lottery.

We need as many Mainers in this game as possible. Public health officials should keep looking for ways to convince everyone to get vaccinated, so we can finally put the pandemic behind us.