True, but the odds are just a wee bit better. Take your California Fa$t Money game:
http://www.calottery.com/Play/Scratchers-games/$1-Scratchers/fas%24t-money-749
A buck a ticket, close to the $1.25 of a hand of quarter VP and with the same top prize; $1,000 We know its about 1 in 40,000 for the VP, for Fa$t Money it is 1 in 480,000.
Another thing to think about before investing your life savings in lottery tickets is that for every winner their has to be a greater amount of losers. So if you are playing a $10 game with a 1 million dollar prize there needs to be 100,000 losing tickets just to meet that one award, not even counting the other awards and the roughly 50% that the state takes.