I don't think the straightforward Kelly Criterion quite answers the question. It would tell you how many identical tickets you should buy (in a lottery where the jackpot pays out for each winner rather than being shared). The question at hand is different, because by buying more tickets you increase the chance of winning, rather than the payoff for a win.

I'm sure there's a simple variation of the criterion you can use, but I'm too tired to work it out right now. (I still expect that for most people, the answer is "buy no tickets")