Lottery odds for the jackpot are set by the pool alone, and the prize size follows from sales. A game that rolls its jackpot for weeks grows the prize and leaves the odds untouched, so a record jackpot is just as hard to hit as an ordinary one. The only change a larger jackpot brings is more players, and with them a higher chance of sharing the top prize with a second ticket.
Odds of winning lottery quick pick tickets and tickets with own numbers are exactly the same. The machine picks a random combination and a player picks a chosen one, and the draw treats every combination alike. Chosen numbers differ in one way only: birthdays and patterns are popular, so a winning ticket built from them is more likely to share its prize. Random numbers spread a ticket away from the crowd and nothing more.
Can you increase your odds of winning the lottery by choosing the game? That is the lever that works best. Odds of winning each lottery game differ widely: a draw of five numbers from thirty five is far kinder than six from fifty nine, and a small pool with a small jackpot pays more often. What lottery has the best odds is usually the one with the smallest pool and the smallest top prize, since the two travel together.