The prize should hit a limit and be divided into another prize drawing. For example, make $300 million the limit. Still a massively life-changing sum after taxes. When the prize reaches $300 million a new drawing is established alongside the existing one and gets its own numbers for drawing. So now you have twice as many chances to win, albeit one large pool and a smaller, growing pool. Repeat when the second pool reaches $300 million. You could have had 4 simultaneous drawings for the billion+ pot that was just won by a single person.
More people get a shot at a huge sum of money. Seems like a better deal, more winners, more exciting because you get more chances per drawing if there are multiple prizes.
(I’m not encouraging anyone to play if they don’t want to, and pedants need not repeat the odds of winning. Don’t play if you don’t want to, but obviously someone wins.)
I mentally divide any lottery prize by 50% to approximate the lump sum.