Large jackpots don’t improve your chance of winning, and because they draw more contestants they increase your chances of having to split the pot if you do buck the astronomical odds and win.
They do increase the risk/benefit ratio.
Spending $1 for a one in 200-million chance to win a million bucks is mathematically retarded.
Spending $1 for a one in 200-million chance to win a 400-million bucks is a reasonable mathematical proposition.
Either way you probably aren't going to win, but at least it's not a mathematically retarded thing to do when the jackpot is high.