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Ms. Otto said officials conducted an online survey at the beginning of the year asking roughly 8,000 Mega Millions players for their opinions.

“Most players understand the jackpot and secondary prize, but most can’t quote the other prizes,” Ms. Otto said. “We found that they liked the $1 price, so we had to do some others things to influence how the jackpot grows.”

Among solutions to avoid upping the $1 ticket price for Mega Millions tickets, officials adjusted the numbers available for the five white balls and one Mega Ball, Ms. Otto said. The minimum jackpot has also increased from $12 million to $15 million. Lottery officials said the jackpot should at least increase about $5 million between rollovers.

“From Friday, the jackpot has gone from $37 million to $55 million. Normally at this time it’s about $5 million more,” Ms. Otto said, adding that a faster climbing jackpot means a better chance of “reaching that tipping point of jackpot fever.”

And while the adjustment in numbers means the jackpot is more likely to rollover — or to not have a winner — Ms. Otto said the “much smaller prizes are easier to win. That’s sort of the trade off.”

Those odds were enough to comfort Mr. Johnson, who clutched his ticket in his hand as he made his way from the D.C. Lottery desk in Union Station.

“I like that there are more choices and chances to win,” Mr. Johnson said

As for the new Mega Ball number, he said, “I went with 14.”