This is a unique question and it makes a lot of sense. If you can rent a $60 game for $1 and keep renting it until you beat the game, the odds are you will save money. I always get the urge at random times to play games I have, so for me buying the game pays off in the long run because I can enjoy it whenever I want and I don't have to deal with the hassle of leaving the house every time I want to play the game.
I would also say it depends on the games you're renting. If it's an online based game where you can play literally all year long, buying the game pays off. If it's a game that you know will only take 20 or so hours to beat, renting it is the way to go.
For me, I typically rent the cheap games to see if they're worth buying. Some games get huge hype and don't live up to expectations, so it's always nice to trial play it to see if it's something I want to spend my hard earned money on or not.