If you join at the start of the ladder you get 4 games at once, and then 1 new game each 3 days, up to the maximum of 20.
If you join later, you get 1 new game each day until you reach the total number of games the others have, and after that 1 new game each 3 days.
e.g.check that totally-awesome little graph I made, if someone joins one week after the ladder-start his games should look like this:
So, so theoretically you could join in a month and a half and still get your 20 games, but you'll have to play many at once..
Anyway, the wiki says you says something else, so maybe someone should back me up on what I said, just to be sure.