Players can buy a $2 Powerball ticket in 45 states, the District of Columbia, Puerto Rico and the U.S. Virgin Islands. The five states that do not participate are Alabama, Alaska, Hawaii, Nevada and Utah.

In Franklin County and Oneida County, Idaho, which draw Powerball players from neighboring Utah, ticket sales were up 597 percent this week compared to “a more traditional week a month ago,” when the jackpot was around $354 million, David Workman, a spokesman for the Idaho Lottery, said in an email.

In Brooklyn on Friday afternoon, Powerball tickets were selling in a trickle at bodegas and liquor stores across Bedford-Stuyvesant.

Y. Patel, the owner of GB Convenience Store & Deli, said that ahead of a Mega Millions drawing a couple of months ago, people were spending $40 to $50 on tickets. This week, though, Powerball sales have been about the same as normal, he said, noting that he had sold only two tickets as of Friday afternoon.

That includes Mr. Patel, 40, a weekly player himself. He bought 14 tickets ahead of the last drawing on Wednesday, but did not even get one of the smaller cash prizes that comes with matching two or three numbers. Frustrated, he said he had bought only two tickets for the Saturday drawing.

At Lene’s Unlimited Wines & Liquors, Daquan Smith, 28, was more optimistic. He had played scratch-off tickets before,

his first Powerball ticket for the Saturday drawing after he heard that someone in Brooklyn had recently won a few million dollars in the lottery. A $1 million dollar ticket was sold at a Brooklyn deli last month, and in June, someone in Brooklyn won a $128 million Mega Millions jackpot.

Mr. Smith, who works at Lene’s, which is owned by his family, said he would not stay up on Saturday night to watch the drawing and would just wait until Sunday morning. Even if his numbers matched the winning numbers, he said, “I’m not going to believe it until the day I’m able to get some real money.”

The jackpot surged to $1 billion on Monday after several weeks of drawings without anyone purchasing a ticket that matched all six numbers. Saturday’s drawing will be the 40th since the last Powerball jackpot was won on Aug. 3, with a winner in Pennsylvania claiming the $207 million prize.

Winners can choose to have the prize paid in a lump sum or in 30 graduated payments over 29 years. The first thing winners should do, according to experts, is seek advice from a lawyer, financial adviser and an accountant.