> Wouldn't you increase your odds by buying 1 ticket per week regardless of jackpot?
> Increasing odds by actually entering vs buying tons of tickets when it's high.
The odds of winning the Powerball are roughly equivalent to being struck by lightning while being eaten by a shark during a solar eclipse. But, eventually, someone beats those odds and wins. In the Powerball, the odds of winning don't change with the number of entries, so buying more tickets does increase you chance of winning. However, when the odds are 1,000,000,000 to 1, you really haven't increased your odds of winning much by buying 100 tickets. If you only have $100 in your lottery budget, you do have very slightly better odds if you buy multiple tickets for a single drawing over buying a single ticket in multiple drawings. But, as the saying goes, "you can't win if you don't enter".
Unless it costs you something, why not enter a contest? Many years ago I won a small sweepstakes and as a result I started getting the "Contest Winners Newsletter". Half of the newsletter was which contests were available and how to enter and the other half was stories about contest winners. One of the first stories I read was about a woman who had won the largest single (non-cash?) prize ever awarded - a private island with home on it somewhere off the coast of Florida. She had one entry in that sweepstakes.
Like a lot of groups, people at the company I worked for pooled their money and bought lottery tickets. In the 30 years I was there, they never won an amount large enough to give anything back. Small amounts were just rolled into the pool to buy the next set of tickets.
About the time I lost my job, I read an article about a local woman who had won $40,000 in cash and prizes in the previous 5 years by entering online sweepstakes. The article stated that, after she sent the kids off to school, she would spend about 45 minutes online entering sweepstakes. In the 7 years I've been out of work, I've spent a few minutes each morning entering the Publisher's Clearing House Sweepstakes and playing a few of their daily prize games. In those 7 years, I haven't won anything from them. About 6 months ago, my brother's step-daughter posted on Facebook that she had won a $10 prize from PCH. Every few months, they post a video of their Prize Patrol surprising someone with a multimillion dollar check.
Despite my failures with PCH, I have won a few small prizes from different sweepstakes here and there. The total value of those prizes for the year is probably a few hundred dollars. The most valuable prize I've won is a wireless headphone set (MSRP given as about $200) from Coke in their Circle K promotion. I won it with my very first entry over a month ago. My daughter and brother have been entering the Coke Circle K sweepstake every day and haven't won anything.
You have to be careful with drawings. Several years ago there was local drawing to win a $100,000 house. An 18-year-old kid won it. He had to pay Federal and state income taxes based on the value of the house as well as the property tax. Many sweepstakes where there is a non-cash prize offered (like the time Taco Bell had the Batmobile as the top prize), have a lower value cash prize option. This drawing didn't. The kid checked into selling the property, but realtors told him it would likely sell for only about $75,000, and he would have to pay them about 7% of the selling price. When it was all over, he was going to have well less than $50,000 as well as all the hassles.