Spending lesser amounts means a higher volatility of returns. The expected return on a $1000 bet might be the same, but your chances of actually equalling (or bettering) that ROI are much lower than if you bet $100k, especially if the the prize money is concentrated at the top end.
Not to mention that having even just $1000 of free cash to "invest" in a positive sum gamble already puts you in a higher income/wealth bracket than most lotteries' most loyal players.
Actually, I think this issue was brought up in the book "How Not to be Wrong" by Jordan Ellenberg, and the MIT students eliminated risk by taking advantage of a Steiner system. So I suppose it favors the intelligent, not necessarily the rich.
The Boston Globe article implies that the MIT syndicates bought so many tickets they actually affected the distribution of the prizes in their favour http://www.boston.com/news/local/massachusetts/articles/2012...
Not to mention that having even just $1000 of free cash to "invest" in a positive sum gamble already puts you in a higher income/wealth bracket than most lotteries' most loyal players.