Marry into the warden service, kiss the governors backside, pay-off a legislator. . . . you get the idea. Some folks get lucky and have had several moose permits.
I have put in every year since 1980 (start of the moose hunting in Maine) and have not been picked yet. My wife put in every year and finally got one in 2002.
If you really want to shoot moose, Quebec lets you shoot two for around $600. Just buy the ticket and hire or take a guide with you.
DMOO - who knows. You might get it the first year, maybe not. Many people would like to see something put into the algorithm that would account for previous selections BUT the problem with that comes back to the money issue. When you run a moose lottery that is geared more toward a money making proposition that moose management, the fear is that the number of applicants will drop when someone knows their chances are dropping each time the get lucky and draw a permit.
You can spend money and buy chances. That's what they want you to do. More money.
dmoo, the way I read the pamphlet sent out by the state non residents can buy as many blocks of 10 chances as they wish. Each block of 10 costs $55. So the more chances you purchase the better chance you have to get drawn. Goold luck in the draw as Moose hunts are a wonderful experience.