You will earn one pick for each day that you have played the Daily Free Game. These picks will then be available to be used on the special Monthly Free Game and the number of picks you get is dependent on the number of days you complete the Daily Game.
When you load up the Monthly Free Game, it will tell you how many picks you have. If you have played the Daily Game every day for 4 days, it will say "You've collected 4 picks so far this month". If you play all month, it will give you the maximum picks for the amount of days that are in the month. The more days you play the Daily Free Game, the more picks you'll get at the end of the month. More picks mean more chances to win!