Obviously this doesn't change the fundamental probability of lotteries, but most people are happy to pay $1 for a remote chance of winning $300,000 (and you can even let people opt out if they don't want to participate). It preserves the entertainment aspect (broadcast the pulls and make a weekly event out of it), creates a shared cultural touchstone (maybe dectuple the pot for the week of Christmas or something), while also eliminating the weird perversity of our current state-run lotteries that prey on gambling addicts.
EDIT: Can I ask the downvoters to elaborate?