Firstly, there's definitely one strategy, in my personal opinion the only strategy, that works for american lottery as well as anything else. And that is - you need to by the ticket. That's the best strategy ever to increase your chances to winning. But other than that...
- some people choose numbers which has been chosen more frequently than others. But let's be honest, the fact that certain numbers have been chosen more than others doesn't really mean a thing. Think of a coin, when you flip it, you might flip it heads down 10 times in a row. Does it mean it will land the same side down the next time as well? No. The odds remain the same for the next flip - 50/50.
- some people use some kind of software that analyses the previous numbers and then make recommendations on what numbers to choose.
- some people choose numbers that are chosen less than others in hopes that if they do win, they win more and without having to split the winnings with too many other people.
- some people actually claim that the best way to win with a lottery is not to play lottery at all. The logic being, the money you don't spend on lottery is the money won. It's an interesting perspective, but ... well...
- some people say that selecting the numbers as randomly as possible is the best strategy. At the same time, some say that "Picking numbers at random is by far the worst and most ineffective way to play any lottery game."
- some say that wheeling lottery numbers is the only winning strategy.
- a man who won $2 million on instant lotto, purchases only odd-numbered tickets.
A paper written in 2010 actually revealed that "The commonly used strategies are no better than random guessing." (source) So by the end of the day, if you want to believe in a strategy, do it. Belief in something is good they say.