You are making an assumption you did not explain before and makes it confusing, you don’t know the number of winning tickets or the number of winning tickets affects the prize quantity, and not all lotteries work like that.
I'm essentially assuming the UK lottery (from 96-200x) rules, where players:
Pick 6 numbers from 49, so odds are independent, and roughly 1 in 14m.
The prize jackpot is determined from a set percentage from the ticket sales, and is shared between jackpot winners.
How much the jackpot prize is therefore determined by total sales and how many winners there are.
I'm also assuming your individual ticket contribution doesn't materially affect either the prize pool or the number of people playing. For a large N, small p, this holds true.
