the jackpot winners (being a percentage of the infinite number of people taking part) would be infinite

You cannot make such predictions without more information.

One mathematical trick you can apply when dealing with infinities is to look at the limit as the number

*approaches *infinity. You can then work out what is the probability of a win. And the answer is that "it depends on the rules of the lottery".

For example, if you imagine that the number of balls in the urn is equal to the number of players, and the winner must correctly identify 6 balls drawn from the urn, you find that the probability of someone winning decreases rapidly with the number of players.

So you expect

*zero *winners in a single game following these rules, despite an infinite number of players.

I am sure you could invent other rules that provide no winners despite an infinite number of games. For example: if there are n players and m games, set the number of balls to n, and the winner must correctly identify m balls. A quick trial calculation suggests that this would produce no winners despite an infinite number of players and an infinite number of games (provided the number of players>number of games+2).

By these rules, the only winner would be the person running the lottery (this is not so different from ordinary, finite lotteries!).